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% does not look nice, try deleting the line with the fontenc.
% Site Specific Dynamics of Structures:
%From Seismic Source to
%the Safety of Occupants and Content
\title[MS ESSI]
{Modeling and Simulation of
Earthquakes, Soils, Structures, and their Interaction}
%\subtitle
%{Include Only If Paper Has a Subtitle}
%\author[Author, Another] % (optional, use only with lots of authors)
%{F.~Author\inst{1} \and S.~Another\inst{2}}
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\author[Jeremi{\'c} et al.] % (optional, use only with lots of authors)
%{Boris~Jeremi{\'c}}
{Boris Jeremi{\'c}
}
%\institute[Computational Geomechanics Group \hspace*{0.3truecm}
\institute[\pgfuseimage{universitylogo}\hspace*{0.1truecm}\pgfuseimage{lbnllogo}] % (optional, but mostly needed)
%{ Professor, University of California, Davis\\
{ University of California, Davis, CA\\
% and\\
% Faculty Scientist, Lawrence Berkeley National Laboratory, Berkeley }
Lawrence Berkeley National Laboratory, Berkeley, CA}
%  Use the \inst command only if there are several affiliations.
%  Keep it simple, no one is interested in your street address.
\date[] % (optional, should be abbreviation of conference name)
{\small ETH Seminar, \\
Zurich, Switzerland \\
May 2018}
\subject{}
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% Structuring a talk is a difficult task and the following structure
% may not be suitable. Here are some rules that apply for this
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%  Exactly two or three sections (other than the summary).
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%  A conference audience is likely to know very little of what you
% are going to talk about. So *simplify*!
%  In a 20min talk, getting the main ideas across is hard
% enough. Leave out details, even if it means being less precise than
% you think necessary.
%  If you omit details that are vital to the proof/implementation,
% just say so once. Everybody will be happy with that.
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\section{Introduction}
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\subsection{Motivation}
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\begin{frame}
\frametitle{Motivation}
\begin{itemize}
%\vspace*{0.3cm}
\item[] Improve modeling and simulation for infrastructure objects
% \vspace*{2mm}
% \item[] Expert numerical modeling and simulation tool
\vspace*{2mm}
\item[] Use of high fidelity numerical modeling and simulation to analyze
earthquakes, and/or soils and/or structures and their interaction (ESSI)
\vspace*{2mm}
\item[] Reduce modeling uncertainty, perform desired level
of sophistication modeling and simulation
\vspace*{2mm}
% \item[] Model and simulate parametric uncertainty as it evolves in time and space
\item[] Follow evolution of parametric uncertainty
\vspace*{2mm}
\item[] Le doute n'est pas un {\'e}tat bien agr{\'e}able, mais l'assurance est
un {\'e}tat ridicule. (Fran{\c c}oisMarie Arouet, Voltaire)
% \vspace*{1mm}
% \item[] The goal is to create methodology and numerical tool that is used to
% predict and inform and not to fit
%
%\vspace*{1mm}
% \item[] Directing, in space and time, seismic energy flow in the
% soil structure system
\end{itemize}
\end{frame}
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\begin{frame}
\frametitle{Earthquake Motions, 6C vs 3$\times$1C vs 1C}
\begin{itemize}
\item Danger of picking one component of motions (1C) from 3C
% or 3$\times$1C (it is done all the time!)
\item Excellent (forced) fit, but not a prediction, information is lost
% (goal is to predict and inform and not (force) fit)
\end{itemize}
% local
%\vspace*{2mm}
\begin{center}
\hspace*{16mm}
%\movie[label=show3,width=5.6cm,poster,autostart,showcontrols]
\movie[label=show3,width=61mm,poster]
{\includegraphics[width=60mm]{movie_ff_3d_mp4_icon.jpeg}}{movie_ff_3d.mp4}
%\hspace*{2mm}
%\hfill
%\movie[label=show3,width=5.6cm,poster,autostart,showcontrols]
\movie[label=show3,width=61mm,poster]
{\includegraphics[width=60mm]{movie_ff_1d_mp4_icon.jpeg}}{movie_ff_1d.mp4}
\hspace*{16mm}
\end{center}
% local
% online
% online \begin{center}
% online \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_ff_3d.mp4}
% online {\includegraphics[width=50mm]{movie_ff_3d_mp4_icon.jpeg}}
% online %
% online \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_ff_1d.mp4}
% online {\includegraphics[width=50mm]{movie_ff_1d_mp4_icon.jpeg}}
% online \end{center}
% online
%
\end{frame}
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\begin{frame}
\frametitle{6C vs 1C NPP ESSI Response Comparison}
% local
\vspace*{2mm}
\begin{center}
\hspace*{7mm}
%\movie[label=show3,width=8.8cm,poster,autostart,showcontrols]
\movie[label=show3,width=8.8cm,poster,showcontrols]
{\includegraphics[width=92mm]{movie_2_npps_mp4_icon.jpeg}}{movie_2_npps.mp4}
\end{center}
% local
% \vspace*{2mm}
% \begin{center}
% \hspace*{7mm}
% \movie[label=show3,width=8.8cm,poster,autostart,showcontrols]
% {\includegraphics[width=90mm]{movie_2_npps_mp4_icon.jpeg}}{movie_2_npps.mp4}
% \end{center}
% online
% online \begin{center}
% online %\vspace*{15mm}
% online \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_2_npps.mp4}
% online {\includegraphics[width=80mm]{movie_2_npps_mp4_icon.jpeg}}
% online \end{center}
% online
\end{frame}
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\begin{frame}
\frametitle{Elastic and Inelastic Response: Differences}
% Elastoplastic soil with contact elements
%% Both solid and contact elements dissipate energy
% \vspace*{5mm}
\begin{center}
% \hspace*{15mm}
\movie[label=show3,width=10cm,poster,autostart,showcontrols]
{\includegraphics[width=10cm]
{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_13Aug2017/NPP_Non_Linear_Effects_Sumeet.jpg}}
{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_13Aug2017/NPP_Non_Linear_Effects_Sumeet.mp4}
\end{center}
% local
% local
% local
% local % \vspace*{5mm}
% local \begin{center}
% local % \hspace*{15mm}
% local \movie[label=show3,width=10cm,poster,autostart,showcontrols]
% local {\includegraphics[width=10cm]
% local {/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_13Aug2017/NPP_Non_Linear_Effects_Sumeet.jpg}}
% local {/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_13Aug2017/NPP_Non_Linear_Effects_Sumeet.mp4}
% local \end{center}
% local
% local
% local
% online% online
% online% online
% online% online
% online\begin{center}
% online\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/NPP_animations_August2017/NPP_Non_Linear_Effects_Sumeet.mp4}
% online {\includegraphics[width=90mm]{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/NPP_animations_August2017/NPP_Non_Linear_Effects_Sumeet.jpg}}
% online\end{center}
% online% online
% online% online
% online% online
\end{frame}
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\begin{frame}
\frametitle{Material Behavior Inherently Uncertain}
\begin{itemize}
\vspace*{0.5cm}
\item Spatial \\
variability
\vspace*{0.5cm}
\item Pointwise \\
uncertainty, \\
testing \\
error, \\
transformation \\
error
\end{itemize}
\vspace*{5cm}
\begin{figure}[!hbpt]
%\nonumber
%\begin{center}
\begin{flushright}
%\includegraphics[height=5.0cm]{/home/jeremic/tex/works/Conferences/2006/KragujevacSEECCM06/Presentation/MGMuzorak01.jpg}
\includegraphics[height=5.5cm]{/home/jeremic/tex/works/Conferences/2006/KallolsPresentationGaTech/FrictionAngleProfile.jpg}
\\
\mbox{(Mayne et al. (2000) }
\end{flushright}
%\end{center}
%\end{center}
\end{figure}
\end{frame}
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\begin{frame}
\frametitle{Parametric Uncertainty: Material and Loads}
%
% \begin{itemize}
%
%
%
% \item Significant uncertainty in material and loads
% %
% % %\vspace*{1mm}
% % \item Propagate uncertainties in space and time
% %
% %
% \end{itemize}
%
% %
%\vspace{1cm}
%\hspace{0.5cm}
%Example: Elastic Stiffness
%\vspace*{3mm}
\begin{figure}[!hbpt]
\begin{center}
%
\hspace*{7mm}
\includegraphics[width=7.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGEGoverGmax/figures/YoungModulus_RawData_and_MeanTrend_01Ed.pdf}
% \hfill
\includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGEGoverGmax/figures/YoungModulus_Histogram_Normal_01Ed.pdf}
%
\end{center}
\end{figure}
\vspace*{0.8cm}
%\hspace*{3.3cm}
\begin{flushleft}
{\tiny
Transformation of SPT $N$value:
1D Young's modulus, $E$
(cf. Phoon and Kulhawy (1999B))
~}
\end{flushleft}
\end{frame}
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\begin{frame}
\frametitle{Parametric Uncertainty: Material Properties}
\begin{figure}[!hbpt]
\begin{center}
% %
\hspace*{3mm}
\includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/FieldPhiPdf.pdf}
\hspace*{3mm}
\includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/FieldPhiCdf.pdf}
\hspace*{3mm}
\includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/FieldSuPdf.pdf}
\hspace*{3mm}
\includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/FieldSuCdf.pdf}
\\
%\vspace*{2mm}
\hspace*{2.5cm} \mbox{\tiny Field $\phi$} \hspace*{3.5cm} \mbox{\tiny Field $c_u$}
%\vspace*{45mm}
\hspace*{3mm}
\includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/LabPhiPdf.pdf}
\hspace*{3mm}
\includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/LabPhiCdf.pdf}
\hspace*{3mm}
\includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/LabSuPdf.pdf}
\hspace*{3mm}
\includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Thesis/KonstantinosKarapiperis/Soil_Uncertainty_Report_Pdf_Cdf_Figures/LabSuCdf.pdf}
\\
%\vspace*{8mm}
\hspace*{2.5cm} \mbox{\tiny Lab $\phi$} \hspace*{3.5cm} \mbox{\tiny Lab $c_u$}
\end{center}
\end{figure}
\end{frame}
%
%
%
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{It is not a new Problem}
%
% \vspace*{10mm}
%
% {\Large Le doute n'est pas un {\'e}tat bien agr{\'e}able,
% \\
% \vspace*{3mm}
% mais l'assurance est un {\'e}tat ridicule.}
%
%
%
% \vspace*{10mm}
% \begin{flushright}
% Fran{\c c}oisMarie Arouet (Voltaire)
% \end{flushright}
%
%
% \end{frame}
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\section{Seismic Motions}
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\subsection{Observations}
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\begin{frame}
\frametitle{3C (6C) Seismic Motions}
\vspace*{2mm}
\begin{itemize}
\item All (most) measured motions are full 3C (6C)
\item Example of an almost 2D motion (LSST07, LSST12)
\vspace*{5mm}
\begin{figure}[!hbpt]
\begin{center}
%
\hspace*{10mm}
\includegraphics[width=5.5truecm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/Lotung_LSST07_FA25.jpeg}
\includegraphics[width=5.5truecm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/Lotung_LSST12_FA25.jpeg}
%
\end{center}
\end{figure}
\end{itemize}
\end{frame}
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\begin{frame}
\frametitle{San Pablo Earthquake, 14Jun2017}
Courtesy of \url{http://www.strongmotioncenter.org/}
\vspace*{2mm}
%\begin{itemize}
%
% \item San Pablo, Guatemala, 14June2017 (data from \url{http://www.strongmotioncenter.org/}
%
%\vspace*{5mm}
% \end{itemize}
\begin{figure}[!hbpt]
\begin{center}
%
\hspace*{10mm}
\includegraphics[width=5.5truecm]{/home/jeremic/oofep/LJUDI/PraveenMalhotra/EQ__01_Guatemala_14Jun2017.jpg}
\\
\includegraphics[width=2.0truecm]{/home/jeremic/oofep/LJUDI/PraveenMalhotra/EQ__02_Guatemala_14Jun2017.jpg}
\includegraphics[width=1.8truecm]{/home/jeremic/oofep/LJUDI/PraveenMalhotra/EQ__03_Guatemala_14Jun2017.jpg}
\includegraphics[width=2.0truecm]{/home/jeremic/oofep/LJUDI/PraveenMalhotra/EQ__04_Guatemala_14Jun2017.jpg}
\includegraphics[width=2.0truecm]{/home/jeremic/oofep/LJUDI/PraveenMalhotra/EQ__05_Guatemala_14Jun2017.jpg}
\includegraphics[width=2.0truecm]{/home/jeremic/oofep/LJUDI/PraveenMalhotra/EQ__06_Guatemala_14Jun2017.jpg}
\includegraphics[width=2.0truecm]{/home/jeremic/oofep/LJUDI/PraveenMalhotra/EQ__07_Guatemala_14Jun2017.jpg}
%
\end{center}
\end{figure}
\end{frame}
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\subsection{Regional Geophysical Models}
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\begin{frame}
\frametitle{Regional Geophysical Models}
\begin{itemize}
\item High fidelity free field seismic motions on regional scale
\vspace*{4mm}
\item Knowledge of geology (deep and shallow) needed
\vspace*{4mm}
\item High Performance Computing using SW4 on CORI (LBNL)
\vspace*{4mm}
\item Collaboration with LLNL: Dr.~Rodgers, Dr.~Pitarka and Dr.~Petersson
\end{itemize}
\end{frame}
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\begin{frame}
\frametitle{Regional Geophysical Models}
\begin{figure}[!htb]
\begin{center}
\includegraphics[width=5truecm]{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/San_Francisco__Regional_Model_BIG.jpg}
\includegraphics[width=5.2truecm]{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/San_Francisco__Regional_Model.jpg}
\end{center}
% \caption{\label{Fig:NPP_Model_In_Real_ESSI} Nuclear Power Plant Model with Shallow Foundation }
\end{figure}
Rodgers and Pitarka
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Regional Geophysical Models}
\begin{figure}[!htb]
\begin{center}
\includegraphics[width=10truecm]{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/USGBay_Area_Model_CC_det2_sm.jpg}
\end{center}
% \caption{\label{Fig:NPP_Model_In_Real_ESSI} Nuclear Power Plant Model with Shallow Foundation }
\end{figure}
USGS
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Regional Geophysical Models}
%
% \begin{figure}[!htb]
% \begin{center}
% \includegraphics[width=8truecm]{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/San_Francisco_Model_Geology_Base_and_Stoch.jpg}
% \end{center}
% % \caption{\label{Fig:NPP_Model_In_Real_ESSI} Nuclear Power Plant Model with Shallow Foundation }
% \end{figure}
%
% Rodgers and Pitarka
%
% \end{frame}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%  \frametitle{Regional Geophysical Simulations using SW4}
% 
%  \begin{figure}[!htb]
%  \begin{center}
%  \includegraphics[width=8truecm]{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/CPU_scaling_CORI.png}
%  \end{center}
%  % \caption{\label{Fig:NPP_Model_In_Real_ESSI} Nuclear Power Plant Model with Shallow Foundation }
%  \end{figure}
%  \vspace*{2mm}
% 
%  Rodgers and Petersson
% 
% 
%  \end{frame}
% 
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%  \frametitle{HPC on CORI (LBNL/NERSC)}
% 
%  \begin{figure}[!htb]
%  \begin{center}
%  \includegraphics[width=8truecm]{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/CORI_picture.jpg}
%  \end{center}
%  % \caption{\label{Fig:NPP_Model_In_Real_ESSI} Nuclear Power Plant Model with Shallow Foundation }
%  \end{figure}
% 
%  \end{frame}
% 
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Example Regional Model}
\begin{figure}[!htb]
\begin{center}
\includegraphics[width=5.5truecm]{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/Vs_at_top.jpg}
% \includegraphics[width=5truecm]{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/Horizontal_Velocity_at_12s.jpg}
\includegraphics[width=5truecm]{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/Peak_Velocity.jpg}
\end{center}
% \caption{\label{Fig:NPP_Model_In_Real_ESSI} Nuclear Power Plant Model with Shallow Foundation }
\end{figure}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Example Regional Model (Rodgers)}
%\vspace*{2mm}
\begin{center}
\hspace*{15mm}
%
\movie[label=show3,width=8.0cm,poster,autostart,showcontrols]
{\includegraphics[width=60mm]{BJicon.png}}{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/M6.5_s500_BASIN+STOCHASTIC.mag.SLOW.mpg}
\hspace*{15mm}
%
\end{center}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Seismic Motions: SW4 to MSESSI}
\begin{figure}[!htb]
\begin{center}
\includegraphics[width=11truecm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_08June2017/pic/SW42DRM.pdf}
\end{center}
% \caption{\label{Fig:NPP_Model_In_Real_ESSI} Nuclear Power Plant Model with Shallow Foundation }
\end{figure}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Stress Test Motions}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Stress Testing SSI Systems}
\begin{itemize}
\item Excite SSI system with a suite of seismic motions
%\vspace*{2mm}
\item Simple sources, variation in strike and dip,
P and S waves, surface waves (Rayleigh, Love, etc.)
%\vspace*{2mm}
\item Stress test soilstructure system
% system
% for a variety of body and surface waves/motions
\item Try to "break" the system, shakeout strong and weak links
%\vspace*{3mm}
%\item
\end{itemize}
\vspace*{2mm}
\begin{figure}[!htb]
\begin{center}
\includegraphics[width=6.5cm]{/home/jeremic/tex/works/Conferences/2015/CNSC_July/Present/Stress_test_NPP_idea.jpg}
\hspace*{5mm}
\end{center}
\end{figure}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Stress Test Source Signals}
\begin{itemize}
% \item Gauss
% \begin{figure}[!hbpt]
% \begin{flushright}
% \vspace*{0.5cm}
% \includegraphics[width=7.0truecm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/gauss.png}
% \end{flushright}
% \end{figure}
\item Ricker
\begin{figure}[!hbpt]
\begin{flushright}
\vspace*{1cm}
\includegraphics[width=4.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Verification_and_Validation_for_Seismic_Wave_Propagation_Problems/tex_works_Thesis_NimaTafazzoli_Dissertation_Nima_Dissertation_Chapter3_Ricker2nd.pdf}
\includegraphics[width=4.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Verification_and_Validation_for_Seismic_Wave_Propagation_Problems/tex_works_Thesis_NimaTafazzoli_Dissertation_Nima_Dissertation_Chapter3_Ricker2nd_FFT.pdf}
\hspace*{0.7cm}
\end{flushright}
\end{figure}
\item Ormsby
\begin{figure}[!hbpt]
\begin{flushright}
\vspace*{1cm}
\includegraphics[width=4.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Verification_and_Validation_for_Seismic_Wave_Propagation_Problems/tex_works_Thesis_NimaTafazzoli_Dissertation_Nima_Dissertation_Chapter3_Ormsby.pdf}
\includegraphics[width=4.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Verification_and_Validation_for_Seismic_Wave_Propagation_Problems/tex_works_Thesis_NimaTafazzoli_Dissertation_Nima_Dissertation_Chapter3_Ormsby_FFT.pdf}
\hspace*{0.7cm}
\end{flushright}
\end{figure}
\end{itemize}
% \begin{figure}[!hbpt]
% \begin{center}
% %
% \includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/gauss.png}
% %
% \includegraphics[width=2.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Verification_and_Validation_for_Seismic_Wave_Propagation_Problems/tex_works_Thesis_NimaTafazzoli_Dissertation_Nima_Dissertation_Chapter3_Ricker2nd.pdf}
% \includegraphics[width=2.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Verification_and_Validation_for_Seismic_Wave_Propagation_Problems/tex_works_Thesis_NimaTafazzoli_Dissertation_Nima_Dissertation_Chapter3_Ricker2nd_FFT.pdf}
% %
% \includegraphics[width=2.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Verification_and_Validation_for_Seismic_Wave_Propagation_Problems/tex_works_Thesis_NimaTafazzoli_Dissertation_Nima_Dissertation_Chapter3_Ormsby.pdf}
% \includegraphics[width=2.5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Verification_and_Validation_for_Seismic_Wave_Propagation_Problems/tex_works_Thesis_NimaTafazzoli_Dissertation_Nima_Dissertation_Chapter3_Ormsby_FFT.pdf}
% %
% \end{center}
% \end{figure}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\subsection{Local Geology Effects}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Layered and Dyke/Sill Models}
\vspace*{5mm}
\begin{itemize}
% \item Uniform soil/rock, to show surface waves
\vspace*{1mm}
\item (a) Horizontal layers
\item (b) Dyke/Sill intrusion
\vspace*{12mm}
\begin{figure}[!hbpt]
\begin{flushright}
%
\includegraphics[width=5.0truecm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/models.png}
%
\end{flushright}
\end{figure}
%\vspace*{10mm}
\item Source locations matrix (point sources)
\item Source strike and dip variation
\item Magnitude variations
\item Range of frequencies
\end{itemize}
%\vspace*{5mm}
\begin{figure}[!hbpt]
\begin{center}
%
%\hspace*{5mm}
\includegraphics[width=8.0truecm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/geom.png}
%
\end{center}
\end{figure}
\end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% \begin{frame}
% \frametitle{Layered System, Variable Source Depth}
%
% \vspace*{2mm}
%
% \begin{itemize}
%
% \item Epicenter is $2500$m away from the location of interest
%
% \item Source depth $850$m (softer layers) and $2500$m (hard rock)
%
% \item Different wave propagation path to the point of interest
%
% \item Surface waves quite pronounced
%
% \end{itemize}
%
%
% \vspace*{5mm}
%
% \begin{figure}[!hbpt]
% \begin{center}
% %
% \hspace*{5mm}
% %\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/dyke_no/bh_x_output_z850_dip45_gaussx4750.png}
% \includegraphics[width=6.0truecm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/dyke_no/borehole_ux_gauss_x5000.png}
% \includegraphics[width=6.0truecm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/dyke_no/borehole_uz_gauss_x5000.png}
% %\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/dyke_no/bh_x_output_z850_dip45_gaussx5250.png}
% %
% \end{center}
% \end{figure}
%
% \end{frame}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Layered System, Displacement Traces}
%\vspace*{5mm}
\begin{itemize}
\item Epicenter is $2500$m away from the location of interest
\item Source depth $850$m (left) and $2500$m (right)
\item Different wave propagation path to the point of interest
\item Surface waves quite pronounced
% \item Surface waves present
\item Layered geology did not filter out surface waves
% \item Mildly incoherent motions
\end{itemize}
\vspace*{7mm}
\begin{figure}[!hbpt]
\begin{center}
%
\hspace*{5mm}
\includegraphics[width=5.8truecm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/dyke_no/cut_output_z850_dip45_gauss.png}
\includegraphics[width=5.8truecm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/dyke_no/cut_output_z2500_dip45_gauss.png}
%\hspace*{4mm}
%
\end{center}
\end{figure}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Layered System, Variable Source Depth}
%
% \begin{center}
% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_ff_3d.mp4}
% {\includegraphics[width=50mm]{movie_ff_3d_mp4_icon.jpeg}}
% %
% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_ff_1d.mp4}
% {\includegraphics[width=50mm]{movie_ff_1d_mp4_icon.jpeg}}
% \end{center}
%
%\vspace*{2mm}
\begin{center}
\hspace*{15mm}
%
\movie[label=show3,width=6.0cm,poster,autostart,showcontrols]
{\includegraphics[width=50mm]{BJicon.png}}{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/movie01.mp4}
%
\movie[label=show3,width=6.0cm,poster,autostart,showcontrols]
{\includegraphics[width=50mm]{BJicon.png}}{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/movie04.mp4}
\hspace*{15mm}
%
\end{center}
% \begin{flushleft}
% \vspace*{15mm}
% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_ff_3d.mp4}
% % \href{./homo_50mmesh_45degree_Ormsby.mp4}
% {\tiny (MP4)}
% \end{flushleft}
% %
\end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Dyke/Sill Intrusion, Variable Source Depth}
%
% \begin{itemize}
%
% \item Lower amplitudes than with layered only model!
%
% \item Difference in body and surface wave arrivals
%
% \item Surface waves present
%
% \end{itemize}
%
%
%
% \begin{figure}[!hbpt]
% \begin{center}
% %
% \hspace*{5mm}
% %\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/dyke_right/bh_x_output_z850_dip45_gaussx4750.png}
% \includegraphics[width=6.0truecm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/dyke_right/borehole_ux_gauss_x5000.png}
% \includegraphics[width=6.0truecm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/dyke_right/borehole_uz_gauss_x5000.png}
% %\includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/dyke_right/bh_x_output_z850_dip45_gaussx5250.png}
% %
% \end{center}
% \end{figure}
%
% \end{frame}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Dyke/Sill Intrusion, Variable Source Depth}
\vspace*{5mm}
\begin{itemize}
\item Lower amplitudes than with layered only model!
\item Difference in body and surface wave arrivals
\item Surface waves present, more complicated wave field
% \item Incoherent motion field
%
% \item Note incoherence is in 2D (and really in 3D, it is reduced, for this model)
\end{itemize}
\vspace*{5mm}
\begin{figure}[!hbpt]
\begin{center}
%
\includegraphics[width=5.5truecm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/dyke_right/cut_output_z850_dip45_gauss.png}
\includegraphics[width=5.5truecm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/dyke_right/cut_output_z2500_dip45_gauss.png}
%
\end{center}
\end{figure}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Dyke/Sill Intrusion, Variable Source Depth}
%
% \begin{center}
% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_ff_3d.mp4}
% {\includegraphics[width=50mm]{movie_ff_3d_mp4_icon.jpeg}}
% %
% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_ff_1d.mp4}
% {\includegraphics[width=50mm]{movie_ff_1d_mp4_icon.jpeg}}
% \end{center}
%
%\vspace*{2mm}
\begin{center}
\hspace*{15mm}
%
\movie[label=show3,width=6.0cm,poster,autostart,showcontrols]
{\includegraphics[width=50mm]{BJicon.png}}{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/movie02.mp4}
%
\movie[label=show3,width=6.0cm,poster,autostart,showcontrols]
{\includegraphics[width=50mm]{BJicon.png}}{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/movie03.mp4}
\hspace*{15mm}
%
\end{center}
% \begin{flushleft}
% \vspace*{15mm}
% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_General_Aspects/ESSI_VisIt_movies_Jose_19May2015/movie_ff_3d.mp4}
% % \href{./homo_50mmesh_45degree_Ormsby.mp4}
% {\tiny (MP4)}
% \end{flushleft}
% %
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Dyke/Sill as Seismic Energy Sink}
\vspace*{2mm}
\begin{itemize}
\item Dyke/Sill (right Fig), made of stiff rock, is an energy sink, as well as energy
reflector
\item Variable wave lengths behave differently, depending on dyke/sill geometry
and location
\end{itemize}
\vspace*{5mm}
\begin{figure}[!hbpt]
\begin{center}
%
\includegraphics[width=5.5truecm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/dyke_no/cut_output_z2500_dip45_gauss.png}
\includegraphics[width=5.5truecm]{/home/jeremic/tex/works/Thesis/JoseAntonioAbellMena/Dyke_results/dyke_right/cut_output_z2500_dip45_gauss.png}
%
\end{center}
\end{figure}
\end{frame}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Plane Wave Stress Test Motions}
\begin{itemize}
%\vspace*{2mm}
\item Plane wave stress test motions: 3D6C (Haskel's solution for plane harmonic waves)
and/or 3D3$\times$1C and/or 3D1C and or 1D1C motions
\vspace*{4mm}
\item Knowledge of geology and the site is important
\end{itemize}
\end{frame}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Example Structure, a Small Modular Reactor (SMR)}
%
%
%
% %\vspace*{4mm}
% \begin{figure}[!htb]
% \begin{center}
% %\hspace*{5mm}
% \includegraphics[width=5.2cm]{/home/jeremic/tex/works/Reports/2012/DOELLNLSSI/SMR_generic_LLNL_01.jpg}
% \end{center}
% \end{figure}
%
%
%
% \end{frame}
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Stress Test Motions}
%\vspace*{10mm}
\begin{itemize}
\item Variation in inclination, frequency, energy and duration
\item Try to "break" the system, shakeout strong and weak links
\end{itemize}
%\vspace*{4mm}
\begin{figure}[!htb]
\begin{flushleft}
\hspace*{5mm}
\includegraphics[width=8.5cm]{/home/jeremic/tex/works/Conferences/2018/BestPSHANI/Presentation/stress_test_Best_SHANI_May2018.jpg}
\end{flushleft}
\end{figure}
\vspace*{45mm}
\begin{figure}[!htb]
\begin{flushright}
\includegraphics[width=3cm]{/home/jeremic/tex/works/Conferences/2015/CNSC_July/Present/Stress_test_NPP_idea.jpg}
\hspace*{5mm}
\end{flushright}
\end{figure}
\vspace*{5mm}
\begin{figure}[!htb]
\begin{flushright}
\includegraphics[width=3cm]{/home/jeremic/tex/works/consulting/2017/IAEA/TECDOC/Version_14Mar2017/1Dvs3x1Dvs3D_waves_02.pdf}
\hspace*{5mm}
\end{flushright}
\end{figure}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Free Field, Variation in Input Wave Angle, $f = 5$Hz}
% Elastoplastic soil with contact elements
%% Both solid and contact elements dissipate energy
% \vspace*{5mm}
\begin{center}
% \hspace*{15mm}
%\movie[label=show3,width=10cm,poster,autostart,showcontrols]
\movie[label=show3,width=10cm,poster,showcontrols]
{\includegraphics[width=10cm]
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_animations_angle_or_frequency_variation/Free_Field_variation_in_wave_angle.jpg}}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_animations_angle_or_frequency_variation/free_field_inclination.mp4}
\end{center}
% online
\vspace*{12mm}
\begin{flushleft}
\hspace*{4mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_animations_angle_or_frequency_variation/free_field_inclination.mp4}
{\tiny (MP4)}
\end{flushleft}
% online
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{SMR ESSI, Variation in Input Wave Angle, $f = 5$Hz}
% Elastoplastic soil with contact elements
%% Both solid and contact elements dissipate energy
% \vspace*{5mm}
\begin{center}
% \hspace*{15mm}
%\movie[label=show3,width=10cm,poster,autostart,showcontrols]
\movie[label=show3,width=10cm,poster,showcontrols]
{\includegraphics[width=10cm]
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/SMR_animations_May2018/SMR_ESSI_4_inclinations.jpg}}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/SMR_animations_May2018/SMR_ESSI_4_inclindations.mp4}
\end{center}
% online
\vspace*{12mm}
\begin{flushleft}
\hspace*{4mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/SMR_animations_May2018/SMR_ESSI_4_inclindations.mp4}
{\tiny (MP4)}
\end{flushleft}
% online
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Free Field, Variation in Input Frequency, $\theta = 60^{o}$}
% Elastoplastic soil with contact elements
%% Both solid and contact elements dissipate energy
% \vspace*{5mm}
\begin{center}
% \hspace*{15mm}
%\movie[label=show3,width=10cm,poster,autostart,showcontrols]
\movie[label=show3,width=10cm,poster,showcontrols]
{\includegraphics[width=10cm]
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_animations_angle_or_frequency_variation/Free_Field_variation_in_wave_frequency.jpg}}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_animations_angle_or_frequency_variation/free_field_frequency.mp4}
\end{center}
% online
\vspace*{12mm}
\begin{flushleft}
\hspace*{4mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_animations_angle_or_frequency_variation/free_field_frequency.mp4}
{\tiny (MP4)}
\end{flushleft}
% online
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{SMR ESSI, Variation in Input Frequency, $\theta = 60^{o}$}
% Elastoplastic soil with contact elements
%% Both solid and contact elements dissipate energy
% \vspace*{5mm}
\begin{center}
% \hspace*{15mm}
%\movie[label=show3,width=10cm,poster,autostart,showcontrols]
\movie[label=show3,width=10cm,poster,showcontrols]
{\includegraphics[width=10cm]
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_animations_angle_or_frequency_variation/ESSI_SMR_variation_in_wave_frequency.jpg}}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_animations_angle_or_frequency_variation/SMR_frequency.mp4}
\end{center}
% online
\vspace*{12mm}
\begin{flushleft}
\hspace*{4mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_animations_angle_or_frequency_variation/SMR_frequency.mp4}
{\tiny (MP4)}
\end{flushleft}
% online
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
%\frametitle{SMR ESSI, Variation in Input Frequency, $\theta = 60^{o}$}
\frametitle{SMR ESSI, Variation in Input Frequency, REAL TIME}
% Elastoplastic soil with contact elements
%% Both solid and contact elements dissipate energy
% \vspace*{5mm}
\begin{center}
% \hspace*{15mm}
%\movie[label=show3,width=10cm,poster,autostart,showcontrols]
\movie[label=show3,width=10cm,poster,showcontrols]
{\includegraphics[width=10cm]
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Free_Field_animations_angle_or_frequency_variation/ESSI_SMR_variation_in_wave_frequency.jpg}}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/SMR_animations_May2018/SMRESSI_real_time_four_freq.mp4}
\end{center}
% online
\vspace*{12mm}
\begin{flushleft}
\hspace*{4mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/SMR_animations_May2018/SMRESSI_real_time_four_freq.mp4}
{\tiny (MP4)}
\end{flushleft}
% online
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% OVDE
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{3D wave effects  different frequencies}
\begin{textblock*}{8cm}(1.0cm,2.5cm) % {block width} (coords)
\scriptsize Acceleration response  Surface center point A
\end{textblock*}
\begin{textblock*}{2cm}(0.2cm,4cm) % {block width} (coords)
\tiny X direction
\end{textblock*}
\begin{textblock*}{2cm}(0.2cm,6.3cm) % {block width} (coords)
\tiny Z direction
\end{textblock*}
\begin{textblock*}{3cm}(2.4cm,7.6cm) % {block width} (coords)
\tiny (a) $f=1Hz \ \ \theta=60^{o}$
\end{textblock*}
\begin{textblock*}{3cm}(5.6cm,7.6cm) % {block width} (coords)
\tiny (b) $f=5Hz \ \ \theta=60^{o}$
\end{textblock*}
\begin{textblock*}{3cm}(8.8cm,7.6cm) % {block width} (coords)
\tiny (c) $f=10Hz \ \ \theta=60^{o}$
\end{textblock*}
\vspace*{30mm}
\begin{figure}[!H]
\centering
% \begin{flushleft}
\includegraphics[width=3.3cm]{/home/jeremic/tex/works/Thesis/HexiangWang/plots_slides_14May2018/Updated_SMR_slides/pic/1Hz_center_ax.pdf}
\includegraphics[width=3.3cm]{/home/jeremic/tex/works/Thesis/HexiangWang/plots_slides_14May2018/Updated_SMR_slides/pic/5Hz_center_ax.pdf}
\includegraphics[width=3.3cm]{/home/jeremic/tex/works/Thesis/HexiangWang/plots_slides_14May2018/Updated_SMR_slides/pic/10Hz_center_ax.pdf}
\\
\includegraphics[width=3.3cm]{/home/jeremic/tex/works/Thesis/HexiangWang/plots_slides_14May2018/Updated_SMR_slides/pic/1Hz_center_az.pdf}
\includegraphics[width=3.3cm]{/home/jeremic/tex/works/Thesis/HexiangWang/plots_slides_14May2018/Updated_SMR_slides/pic/5Hz_center_az.pdf}
\includegraphics[width=3.3cm]{/home/jeremic/tex/works/Thesis/HexiangWang/plots_slides_14May2018/Updated_SMR_slides/pic/10Hz_center_az.pdf}
% \end{flushleft}
\end{figure}
\vspace*{75mm}
\begin{figure}[!H]
\begin{flushright}
\hspace*{30mm}
\includegraphics[width=2.5cm]{/home/jeremic/tex/works/Thesis/HexiangWang/plots_slides_14May2018/Updated_SMR_slides/pic/Points_configuration.pdf}
\hspace*{10mm}
\end{flushright}
\end{figure}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%
% \frametitle{SMR, Free Field vs ESSI, $f=2.5$Hz, $\theta = 60^{o}$}
%
% % Elastoplastic soil with contact elements
% %% Both solid and contact elements dissipate energy
%
%
% % \vspace*{5mm}
% \begin{flushleft}
% \hspace*{7mm}
% %\movie[label=show3,width=54mm,poster,autostart,showcontrols]
% \movie[label=show3,width=54mm,poster,showcontrols]
% {\includegraphics[width=54mm]
% {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/SMR_animations_May2018/SMR_FreeField_f2_5_theta_60.jpg}
% }
% {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/SMR_animations_May2018/SMR_free_field_2frequency.mp4}
% \end{flushleft}
% % online
% %\vspace*{12mm}
% \begin{flushleft}
% \hspace*{4mm}
% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/SMR_animations_May2018/SMR_free_field_2frequency.mp4}
% {\tiny (MP4)}
% \end{flushleft}
% % online
%
%
%
%
% % \vspace*{5mm}
% \vspace*{49mm}
% \begin{flushright}
% % \hspace*{15mm}
% %\movie[label=show3,width=58mm,poster,autostart,showcontrols]
% \movie[label=show3,width=58mm,poster,showcontrols]
% {\includegraphics[width=58mm]
% {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/SMR_animations_May2018/SMR_ESSI_f2_5_theta_60.jpg}
% }
% {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/SMR_animations_May2018/SMR_2frequency.mp4}
% \end{flushright}
% \hspace*{7mm}
% % online
% %\vspace*{12mm}
% \begin{flushright}
% %\hspace*{4mm}
% \vspace*{9mm}
% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/SMR_animations_May2018/SMR_2frequency.mp4}
% {\tiny (MP4)}
% \hspace*{4mm}
% \end{flushright}
% % online
%
%
%
% \end{frame}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%
% \frametitle{SMR, Free Field vs ESSI, $f=10$Hz, $\theta = 60^{o}$}
%
% % Elastoplastic soil with contact elements
% %% Both solid and contact elements dissipate energy
%
%
% % \vspace*{5mm}
% \begin{flushleft}
% \hspace*{7mm}
% %\movie[label=show3,width=54mm,poster,autostart,showcontrols]
% \movie[label=show3,width=54mm,poster,showcontrols]
% {\includegraphics[width=54mm]
% {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/SMR_animations_May2018/SMR_FreeField_f10_theta60.jpg}
% }
% {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/SMR_animations_May2018/SMR_free_field_10frequency.mp4}
% \end{flushleft}
% % online
% %\vspace*{12mm}
% \begin{flushleft}
% \hspace*{4mm}
% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/SMR_animations_May2018/SMR_free_field_10frequency.mp4}
% {\tiny (MP4)}
% \end{flushleft}
% % online
%
%
%
%
% % \vspace*{5mm}
% \vspace*{48mm}
% \begin{flushright}
% % \hspace*{15mm}
% %\movie[label=show3,width=58mm,poster,autostart,showcontrols]
% \movie[label=show3,width=58mm,poster,showcontrols]
% {\includegraphics[width=58mm]
% {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/SMR_animations_May2018/SMR_ESSI_f10_theta60.jpg}
% }
% {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/SMR_animations_May2018/SMR_10frequency.mp4}
% \end{flushright}
% \hspace*{7mm}
% % online
% %\vspace*{12mm}
% \begin{flushright}
% %\hspace*{4mm}
% \vspace*{9mm}
% \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/SMR_animations_May2018/SMR_10frequency.mp4}
% {\tiny (MP4)}
% \hspace*{4mm}
% \end{flushright}
% % online
%
%
%
% \end{frame}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Free Field Motion Verification}
%
%
% \vspace*{3mm}
%
% \begin{figure}[!H]
% \begin{center}
% \hspace*{8mm}
% \includegraphics[width=4cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/free_field_ux_time_series.pdf}
% \hspace*{1mm}
% \includegraphics[width=4cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/free_field_uy_time_series.pdf}
% \hspace*{1mm}
% \includegraphics[width=4cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/free_field_uz_time_series.pdf} \\
% \hspace*{3mm}
% %
% \\
% \hspace*{8mm}
% \includegraphics[width=4cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/free_field_ax_time_series.pdf}
% \hspace*{1mm}
% \includegraphics[width=4cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/free_field_ay_time_series.pdf}
% \hspace*{1mm}
% \includegraphics[width=4cm]{/home/jeremic/tex/works/Thesis/HexiangWang/Files_SMiRT_11Aug2017/pic/free_field_az_time_series.pdf}
% \hspace*{3mm}
% \end{center}
% \end{figure}
% \end{frame}
%
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Regional Geophysical Models}
%
% \begin{figure}[!htb]
% \begin{center}
% \includegraphics[width=5truecm]{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/San_Francisco__Regional_Model_BIG.jpg}
% \includegraphics[width=5.2truecm]{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/San_Francisco__Regional_Model.jpg}
% \end{center}
% % \caption{\label{Fig:NPP_Model_In_Real_ESSI} Nuclear Power Plant Model with Shallow Foundation }
% \end{figure}
%
% Rodgers and Pitarka
%
% \end{frame}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Regional Geophysical Models}
%
% \begin{figure}[!htb]
% \begin{center}
% \includegraphics[width=10truecm]{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/USGBay_Area_Model_CC_det2_sm.jpg}
% \end{center}
% % \caption{\label{Fig:NPP_Model_In_Real_ESSI} Nuclear Power Plant Model with Shallow Foundation }
% \end{figure}
%
% USGS
%
% \end{frame}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Regional Scale Model (Rodgers et al, LLNL)}
%
% \begin{figure}[!htb]
% \begin{center}
% \includegraphics[width=5.5truecm]{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/Vs_at_top.jpg}
% % \includegraphics[width=5truecm]{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/Horizontal_Velocity_at_12s.jpg}
% \includegraphics[width=5truecm]{/home/jeremic/tex/works/Conferences/2017/CompDyn2017/Present_PLENARY/Peak_Velocity.jpg}
% \end{center}
% % \caption{\label{Fig:NPP_Model_In_Real_ESSI} Nuclear Power Plant Model with Shallow Foundation }
% \end{figure}
%
% \end{frame}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\section{Inelasticity and Energy Dissipation}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Energy Dissipation}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Seismic Energy Input and Dissipation}
\begin{itemize}
\vspace*{1mm}
\item[] Seismic energy input, through a closed boundary
\vspace*{4mm}
\item[] Mechanical dissipation outside SSI domain:
\begin{itemize}
\item[] Reflected wave radiation
\item[] SSI system oscillation radiation
\end{itemize}
%\vspace*{1mm}
\item[] Mechanical dissipation/conversion inside SSI domain:
\begin{itemize}
\item[] Inelasticity of soil and contact zone
\item[] Inelasticity/damage of structure and foundation
\item[] Viscous coupling of fluids and soils and structure
% % \item[] potential and kinetic energy
% \item[] potential $\leftarrow \! \! \! \! \! \! \rightarrow$ kinetic energy
\end{itemize}
%\vspace*{1mm}
% \item[] Numerical energy dissipation (numerical damping/production and period errors)
% \item[] Numerical energy dissipation (damping/production)
\item[] Numerical energy dissipation/production
\end{itemize}
%
\end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Incremental Plastic Work: $d W_p = \sigma_{ij} \, d\epsilon_{ij}^{pl}$}
\begin{itemize}
\item Negative incremental energy dissipation
\item Plastic work is NOT plastic dissipation
\end{itemize}
\begin{figure}[!H]
\begin{center}
\includegraphics[height=5.2cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/Negative_Dissipation_Problem.png}
\end{center}
\end{figure}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%
% \frametitle{Negative incremental energy dissipation!}
%
% \begin{itemize}
% \item Direct violation of the second law of thermodynamics
% \item Where is the problem?
% \item[]
% \item[]
% \end{itemize}
%
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%
% \frametitle{Negative incremental energy dissipation!}
%
% \begin{itemize}
% \item Direct violation of the second law of thermodynamics
% \item Where is the problem?
% \item One important form of energy is missing!
% \item \textbf{Plastic Free Energy}
% \end{itemize}
%
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% % \subsection{ThermodynamicsBased Theory and Formulation}
% %
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%
% \frametitle{Plastic Free Energy}
%
% \begin{itemize}
% \item Direct violation of the second law of thermodynamics
% % \item Where is the problem?
% \item Missing is the plastic free energy
%
%
% \item Multiscale effect of particle interlocking/rearrangement
% \item Strain energy on particle level
% \end{itemize}
%
% \begin{figure}[!h]
% \begin{center}
% \includegraphics[width=7truecm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/Plastic_Free_Energy.png}
% \end{center}
% \end{figure}
%
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%f%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%
% \frametitle{Energy Transformation in ElasticPlastic Material}
%
% \begin{figure}[!H]
% \begin{center}
% \includegraphics[height=6cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/Energy_Transformation.png}
% \end{center}
% \end{figure}
%
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%
% \frametitle{Traditional Energy Components}
%
% \begin{itemize}
% \item Kinetic Energy Density:
% \begin{equation*}
% d E_K({x},t) = \rho({x}) \, v_i({x}, t) \, d v_i({x}, t)
% \end{equation*}
%
% \item Strain Energy Density:
% \begin{equation*}
% d E_S({x},t) = \sigma_{ij}({x},t) \, d \epsilon_{ij}^{el}({x}, t)
% \end{equation*}
%
% \vspace*{1mm}
%
% \item Plastic Work Density:
% \begin{equation*}
% d W_P(x,t) = \sigma_{ij}(x,t) \, d \epsilon_{ij}^{pl}(x, t)
% \end{equation*}
% \end{itemize}
%
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%
% \frametitle{Plastic Free Energy and Dissipation}
%
% \begin{itemize}
% \item Free Energy
% \begin{itemize}
% \item Based on the second law of thermodynamics
% \item Decomposed into elastic and plastic components
% \end{itemize}
%
% \item Plastic Free Energy
% \begin{itemize}
% \item Decomposed into isotropic and kinematic components
% \item Related to hardening laws in classic plasticity theory
% \item Related to material state variables (back stress etc.)
% \end{itemize}
% \begin{equation*}
% d\Psi_{pl}^{iso} = \frac{1}{\kappa_1} k \, dk; \quad d\Psi_{pl}^{kin} = \frac{1}{a_1} \alpha_{ij} \, d \alpha_{ij}
% \end{equation*}
%
% \item Energy Dissipation due to Plasticity
% \begin{itemize}
% \item Incremental dissipation should always be nonnegative
% \end{itemize}
% \begin{equation*}
% d D_P = d W_P  d\Psi_{pl} = \sigma_{ij} \, d \epsilon^{pl}_{ij}  d\Psi_{pl} \ge 0
% \end{equation*}
% \end{itemize}
%
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%
% \frametitle{Use Incremental Equation: $d\Phi = \sigma_{ij} \, d\epsilon_{ij}^{pl}$}
%
% \begin{itemize}
% \item \textbf{Plastic Work} vs. \textbf{Energy Dissipation due to Plasticity}
% \end{itemize}
%
% \begin{figure}[!H]
% \begin{center}
% \includegraphics[height=5.5cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/Negative_Dissipation_Problem2.png}
% \end{center}
% \end{figure}
%
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
%
%
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % %\begin{frame}
% % %
% % %\frametitle{Area of Hysteresis Loop}
% % %
% % %\begin{figure}[!H]
% % %\begin{center}
% % %\includegraphics[height=6cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/StressStrain.png}
% % %\end{center}
% % %\end{figure}
% % %
% % %\end{frame}
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % %
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % %\begin{frame}
% % %
% % %\frametitle{Area of Hysteresis Loop}
% % %
% % %\begin{figure}[!H]
% % %\begin{center}
% % %\includegraphics[height=6cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/StressStrainDissipation.png}
% % %\end{center}
% % %\end{figure}
% % %
% % %\end{frame}
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % %
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % %\begin{frame}
% % %
% % %\frametitle{Area of the StressStrain Loop}
% % %
% % %\begin{itemize}
% % %\item[] Evolving loop? Monotonic loading?
% % %\end{itemize}
% % %
% % %\begin{figure}[!H]
% % %\begin{center}
% % %\includegraphics[height=5.5cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/StressStrainMonotonic.png}
% % %\end{center}
% % %\end{figure}
% % %
% % %\end{frame}
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %\begin{frame}
% %
% %\frametitle{Use Incremental Equation: $\sigma_{ij} \, d\epsilon_{ij}^{pl}$}
% %
% %\end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \begin{frame}
% %
% % \frametitle{Use Incremental Equation: $d\Phi = \sigma_{ij} \, d\epsilon_{ij}^{pl}$}
% %
% %
% % \end{frame}
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \begin{frame}
% %
% % \frametitle{Use Incremental Equation: $d\Phi = \sigma_{ij} \, d\epsilon_{ij}^{pl}$}
% %
% % \begin{itemize}
% % \item[] Notice any problem?
% % \end{itemize}
% %
% % \begin{figure}[!H]
% % \begin{center}
% % \includegraphics[height=5.5cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/Negative_Dissipation.png}
% % \end{center}
% % \end{figure}
% %
% % \end{frame}
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%
% \frametitle{Incremental Equation: $d W = \sigma_{ij} \, d\epsilon_{ij}^{pl}$}
%
% \begin{itemize}
% \item[] PROBLEM: negative incremental energy dissipation!
% \item[] 600 papers since 1990 (!?!): \\
%
% \end{itemize}
%
% \begin{figure}[!H]
% \begin{center}
% \includegraphics[height=5cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/Negative_Dissipation_Problem2.png}
% \end{center}
% \end{figure}
%
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \begin{frame}
% %
% % \frametitle{Negative incremental energy dissipation!}
% %
% % \begin{itemize}
% % \item[] Direct violation of the second law of thermodynamics
% % \item[] Where is the problem?
% % \item[]
% % \item[]
% % \end{itemize}
% %
% % \end{frame}
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Negative Incremental Energy Dissipation!}
\begin{itemize}
\item[] Direct violation of the second law of thermodynamics
\vspace*{2mm}
\item[] 600 papers use Uang and Bertero (1990) and repeat their error
\vspace*{2mm}
\item[] Important form of energy missing: {Plastic Free Energy}
\vspace*{2mm}
\item[] Observed by Farren and Taylor (1925) and explained by Taylor and
Quinney (1934)
\vspace*{2 mm}
\item[] Plastic Work vs. {Plastic Energy Dissipation}
%\vspace*{4mm}
%\item[] However it seems to be forgotten
\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Energy Dissipation on Material Level}
\vspace*{2mm}
Single elasticplastic element under cyclic shear loading
\begin{itemize}
\item[] Difference between plastic work and dissipation
\item[] Plastic work can decrease, dissipation always increases
\end{itemize}
\vspace*{7mm}
\begin{figure}[!hbpt]
\begin{center}
\hspace*{5mm}
\includegraphics[width=12.0truecm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/Dissipation_Material.png}
\end{center}
\end{figure}
\end{frame}
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\begin{frame}
\frametitle{Plastic Free Energy}
\begin{itemize}
% \item Direct violation of the second law of thermodynamics
% % \item Where is the problem?
% \item Missing is the plastic free energy
\item Multiscale effect of particle interlocking/rearrangement
\item Strain energy on particle level
\end{itemize}
\begin{figure}[!h]
\begin{center}
\includegraphics[width=7truecm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/Plastic_Free_Energy.png}
\end{center}
\end{figure}
\end{frame}
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\begin{frame}
\frametitle{Energy Transformation in ElasticPlastic Material}
\begin{figure}[!H]
\begin{center}
\includegraphics[height=6cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/Energy_Transformation.png}
\end{center}
\end{figure}
\end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Energy Dissipation in LargeScale Model (NPP)}
% Elastoplastic soil with contact elements
%% Both solid and contact elements dissipate energy
% \vspace*{5mm}
\begin{center}
% \hspace*{15mm}
\movie[label=show3,width=10cm,poster,autostart,showcontrols]
{\includegraphics[width=10cm]
{/home/jeremic/tex/works/Conferences/2017/SMiRT_24/present/3D_Nonlinear_Modeling_and_it_Effects/NPP_Plastic_Dissipation_grab.jpg}}
{/home/jeremic/tex/works/Thesis/HanYang/Files_10Aug2017/NPP_Plastic_Dissipation.mp4}
\end{center}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Energy Dissipation in LargeScale Model (SMR)}
% Elastoplastic soil with contact elements
%% Both solid and contact elements dissipate energy
% \vspace*{5mm}
\begin{center}
% \hspace*{15mm}
\movie[label=show3,width=10cm,poster,autostart,showcontrols]
{\includegraphics[width=10cm]
{/home/jeremic/tex/works/Conferences/2017/SMiRT_24/present/Nonlinear_Analysis_of_ESSI_for_SMR/SMR_Energy_Dissipation_screen_grab.jpg}}
{/home/jeremic/tex/works/Thesis/HanYang/Files_16Aug2017/SMR_Energy_Dissipation.mp4}
\end{center}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%
% \frametitle{Energy Dissipation in SmallScale Model}
%
% Short cantilever under shear/bending loading
%
% \vspace*{5mm}
% \begin{figure}[!hbpt]
% \begin{center}
% \hspace*{10mm}
% \includegraphics[width=4.2truecm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/Rectangular_Block1.png}
% \hspace*{2mm}
% \includegraphics[width=4.2truecm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/Rectangular_Block2.png}
% \hspace*{2mm}
% \includegraphics[width=4.2truecm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/Rectangular_Block3.png}
% \end{center}
% \end{figure}
%
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%
% \frametitle{Energy Dissipation in SmallScale Model}
%
% Irregularshaped block under surface shear loading
%
% \vspace*{5mm}
% \begin{figure}[!hbpt]
% \begin{center}
% \hspace*{10mm}
% \includegraphics[width=4.3truecm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/Cornered_Block1.png}
% \hspace*{3mm}
% \includegraphics[width=4.3truecm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/Cornered_Block2.png}
% \hspace*{3mm}
% \includegraphics[width=4.3truecm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/Cornered_Block3.png}
% \end{center}
% \end{figure}
%
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%
% \frametitle{Energy Dissipation in Contact Zone}
%
% Elastoplastic brick elements coupled with contact elements.
%
% \vspace*{6mm}
% \begin{figure}[!hbpt]
% \begin{center}
% \hspace*{7mm}
% \includegraphics[width=4truecm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/DEMO_Dissipation1.png}
% \includegraphics[width=4truecm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/DEMO_Dissipation2.png}
% \includegraphics[width=4truecm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/DEMO_Dissipation3.png}
% \\
% \hspace*{7mm}
% \includegraphics[width=4truecm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/DEMO_Dissipation4.png}
% \includegraphics[width=4truecm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/DEMO_Dissipation5.png}
% \includegraphics[width=4truecm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/DEMO_Dissipation6.png}
% \end{center}
% \end{figure}
%
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%
% \frametitle{Energy Dissipation in a LargeScale Model (NPP)}
%
% %
% % Some notes:
% % Energy density curves at the corner of the structure (as indicated in the picture of NPP model).
% % Can see large amount of energy dissipated in both soil and contact elements.
% % An arcshaped area of "elastic zone" formed beneath the structure, where soil strength can be better utilized.
% %
%
% %\vspace*{2mm}
% \begin{figure}[!hbpt]
% \begin{center}
% % \hspace*{7mm}
% \includegraphics[width=9truecm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/NPP_Energy_Dissipation_Curve.pdf}
% \end{center}
% \end{figure}
%
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \begin{frame}
% %
% % \frametitle{Energy Dissipation in a LargeScale Model (NPP)}
% %
% % Elastic soil with contact elements
% % % Only contact elements dissipate energy
% %
% % % \vspace*{5mm}
% % \begin{center}
% % % \hspace*{15mm}
% % \movie[label=show3,width=7cm,poster,autostart,showcontrols]
% % {\includegraphics[width=7cm]
% % {/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/NPP_Plastic_Dissipation_Density.png}}
% % {/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/NPP_with_Contact_Elastic.mp4}
% % \end{center}
% %
% %
% % \end{frame}
% %
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%
% \frametitle{Energy Dissipation in LargeScale Model (NPP)}
%
% Elastoplastic soil without contact elements
% % Only solid elements dissipate energy
%
% % \vspace*{5mm}
% \begin{center}
% % \hspace*{15mm}
% \movie[label=show3,width=7cm,poster,autostart,showcontrols]
% {\includegraphics[width=7cm]
% {/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/NPP_Plastic_Dissipation_Density.png}}
% {/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/NPP_without_Contact_vonMises.mp4}
% \end{center}
%
%
% \end{frame}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%
% \frametitle{Energy Dissipation in LargeScale Model (NPP)}
%
% Elastoplastic soil with contact elements
% % Both solid and contact elements dissipate energy
%
% % \vspace*{5mm}
% \begin{center}
% % \hspace*{15mm}
% \movie[label=show3,width=7cm,poster,autostart,showcontrols]
% {\includegraphics[width=7cm]
% {/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/NPP_Plastic_Dissipation_Density.png}}
% {/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/NPP_with_Contact_vonMises.mp4}
% \end{center}
%
%
% \end{frame}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%
% \frametitle{Energy Dissipation in LargeScale Model (SMR)}
%
% %
% % Some notes:
% % Energy density curves at the corner of the structure (as indicated in the picture of NPP model).
% % Can see large amount of energy dissipated in both soil and contact elements.
% % An arcshaped area of "elastic zone" formed beneath the structure, where soil strength can be better utilized.
% %
%
% \vspace*{2mm}
% \begin{figure}[!hbpt]
% \begin{center}
% % \hspace*{7mm}
% \includegraphics[width=8truecm]{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/SMR_Energy_Dissipation_Curve.pdf}
% \end{center}
% \end{figure}
%
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%
% \frametitle{Energy Dissipation in LargeScale Model (SMR)}
%
% Elastoplastic soil without contact elements
% % Only solid elements dissipate energy
%
% % \vspace*{5mm}
% \begin{center}
% % \hspace*{15mm}
% \movie[label=show3,width=9cm,poster,autostart,showcontrols]
% {\includegraphics[width=9cm]
% {/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/SMR_Plastic_Dissipation_Density.png}}
% {/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/SMR_without_Contact_vonMises.mp4}
% \end{center}
%
%
% \end{frame}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Quality Assurance}
% 
% \begin{itemize}
% 
% \item[] Full verification suit for each element, model, algorithm
% 
% \vspace*{4mm}
% \item[] Certification process in progress for NQA1 and ISO900032014
% 
% %\vspace*{3mm}
% %\item[] Verification examples given below
% 
% \end{itemize}
% 
% 
% 
% 
% \end{frame}
% 
% 
% 
% %
% \begin{frame}{High Fidelity (Parametric, Geometric and Algorithmic)}
% 
% \begin{figure}
% \includegraphics[width=0.95\textwidth]{/home/jeremic/tex/works/Thesis/YuanFeng/Files_06June2017/latex_slides/Figurefiles/verification/asymptotic_converge.png}
% \end{figure}
% \end{frame}
% 
% % \begin{frame}{One of Verification Techniques}
% % Richardson Extrapolation
% % \begin{itemize}
% % \item[] Stress solution with the strain increment size as:
% % \begin{equation}
% % \sigma(d\epsilon) = \sigma^* + C d\epsilon^{\beta} + O(d\epsilon^{\beta+1})
% % \end{equation}
% % where $\sigma^*$ is the accurate result.
% %
% % \item[] Richardson extrapolation is defined as
% % \begin{equation}
% % \begin{aligned}
% % R(d\epsilon, k) & = \frac{k^{\beta}\sigma(d\epsilon)  \sigma(k d\epsilon) } { k^{\beta}  1} \\
% % & = \frac{k^{\beta}
% % \left(\sigma^* + C d\epsilon^{\beta} + O(d\epsilon^{\beta+1}) \right) }
% % { k^{\beta}  1}
% % 
% % \frac{\sigma^* + C k^{\beta} d\epsilon^{\beta} + O(d\epsilon^{\beta+1}) }
% % { k^{\beta}  1} \\
% % & = \sigma^* + O (d\epsilon^{\beta + 1})
% % \end{aligned}
% % \end{equation}
% % % The higher order error is cancelled out.
% % \end{itemize}
% % \end{frame}
% %
% %
% %
% %
% %
% 
% 
% 
% 
% %
% \begin{frame}{Verification of Elastoplastic Algorithms}
% Comparison between forward and backward Euler algorithms.
% \begin{figure}
% \includegraphics[width=0.5\textwidth]{/home/jeremic/tex/works/Thesis/YuanFeng/Files_06June2017/latex_slides/Figurefiles/verification/NonAssociate.pdf}
% \includegraphics[width=0.5\textwidth]{/home/jeremic/tex/works/Thesis/YuanFeng/Files_06June2017/latex_slides/Figurefiles/verification/verification_example.png}
% \end{figure}
% \end{frame}
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% \subsection{Inelastic Response}
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Soil Inelastic Response}
% 
% 
% A number of new models have been implemented and verified:
% 
% 
% \begin{itemize}
% 
% 
% \item[] Nested Surface Models (von Mises, DruckerPrager, rounded MohrCoulomb)
% 
% \vspace*{2mm}
% \item[] PM4 model (2D/3D)
% 
% \vspace*{2mm}
% \item[] Bounding Surface Liquefaction (Tsinghua) Model
% 
% \vspace*{2mm}
% \item[] Concrete01 and Concrete02 fiber models (for nonlinear fiber beam and wall element)
% 
% \vspace*{2mm}
% \item[] Steel01 and Steel02 fiber models (for nonlinear fiber beam and wall element)
% 
% 
% \end{itemize}
% 
% \end{frame}
% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Partially Saturated Soil Modeling: Verification}
% 
% %\vspace*{5mm}
% \begin{figure}[!hbpt]
% \begin{center}
% %\hspace*{10mm}
% \includegraphics[width=11truecm]{/home/jeremic/tex/works/Conferences/2017/DOE_Project_Review_Meeting_LBNL_09June2017/Present/upU_unsatruated_verification.jpg}
% \end{center}
% \end{figure}
% 
% 
% \end{frame}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Partially Saturated Soil Modeling: Validation}
% 
% %\vspace*{5mm}
% \begin{figure}[!hbpt]
% \begin{center}
% %\hspace*{10mm}
% \includegraphics[width=11truecm]{/home/jeremic/tex/works/Conferences/2017/DOE_Project_Review_Meeting_LBNL_09June2017/Present/upU_unsatruated_validation.jpg}
% \end{center}
% \end{figure}
% 
% 
% \end{frame}
% 
% 
% 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \begin{frame}
% % \frametitle{Structural Inelastic Response}
% %
% %
% %
% % \end{frame}
% 
% 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % %\begin{frame}
% % %\frametitle{Dry Contact (SoilStructure) Inelastic Response}
% % %
% % %
% % %
% % %\end{frame}
% % %
% 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \begin{frame}
% % \frametitle{Contact Modeling}
% %
% %
% % \begin{itemize}
% %
% % \item[] Soft contact, concrete to soil
% %
% % \hspace*{3mm}
% % \item[] Hard contact, concrete to rock/concrete
% %
% % \hspace*{3mm}
% % \item[] Dry contact,
% %
% %
% % \hspace*{3mm}
% % \item[] Saturated contacts, effective contact force/stress
% %
% %
% % \hspace*{3mm}
% % \item[] Buoyant force (dynamic) modeling
% %
% %
% % \end{itemize}
% %
% %
% % \end{frame}
% % %
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Saturated Contact}
% 
% 
% %\vspace*{5mm}
% \begin{figure}[!hbpt]
% \begin{center}
% %\hspace*{10mm}
% \includegraphics[width=9truecm]{/home/jeremic/tex/works/Conferences/2017/DOE_Project_Review_Meeting_LBNL_09June2017/Present/coupled_contact_schematics.jpg}
% \end{center}
% \end{figure}
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\subsection{Probabilistic Inelastic Modeling}
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%
%
% \subsection{FPK Formulations}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}
\frametitle{Uncertainty Propagation through
Inelastic System}
%
\begin{itemize}
\item Incremental elpl constitutive equation
%
\begin{eqnarray}
\nonumber
\Delta \sigma_{ij}
=
% E^{EP}_{ijkl}
E^{EP}_{ijkl} \; \Delta \epsilon_{kl}
=
\left[
E^{el}_{ijkl}

\frac{\displaystyle E^{el}_{ijmn} m_{mn} n_{pq} E^{el}_{pqkl}}
{\displaystyle n_{rs} E^{el}_{rstu} m_{tu}  \xi_* h_*}
\right]
\Delta \epsilon_{kl}
\end{eqnarray}
\vspace*{2mm}
\item Dynamic Finite Elements
%
\begin{equation}
{ M} \ddot{ u_i} +
{ C} \dot{ u_i} +
{ K}^{ep} { u_i} =
{ F(t)}
\nonumber
\end{equation}
\vspace*{2mm}
\item What if all (any) material and load parameters are uncertain
\end{itemize}
\end{frame}
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\begin{frame}
\frametitle{Probabilistic ElasticPlastic Response}
\begin{figure}[!hbpt]
\begin{center}
%\includegraphics[width=8cm]{/home/jeremic/tex/works/Papers/2007/ProbabilisticYielding/figures/vonMises_G_and_cu_very_uncertain/Contour_PDFedited.pdf}
\includegraphics[width=8cm]{/home/jeremic/tex/works/Conferences/2012/DOELLNLworkshop2728Feb2012/ProbabilisticYielding_vonMises_G_and_cu_very_uncertain_Contour_PDFedited.pdf}
\end{center}
\end{figure}
\end{frame}
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% \begin{frame}
%
% \frametitle{Previous Work}
%
%
%
% \begin{itemize}
%
% \item
% Linear algebraic or differential equations:
%
% \begin{itemize}
% \item Variable Transf. Method (Montgomery and Runger 2003)
% \item Cumulant Expansion Method (Gardiner 2004)
% \end{itemize}
%
% \item
% Nonlinear differential equations:
%
% \begin{itemize}
%
% \item Monte Carlo Simulation (Schueller 1997, De Lima et al 2001, Mellah
% et al. 2000, Griffiths et al. 2005...) \\ $\rightarrow$ can be accurate, very costly
%
% \item Perturbation Method (Anders and Hori 2000, Kleiber and Hien 1992,
% Matthies et al. 1997) \\ $\rightarrow$ first and second order Taylor series
% expansion about mean  limited to problems with small C.O.V. and inherits
% "closure problem"
%
% \item SFEM (Matthies et al, 2004, 2005, 2014...)
%
%
% \end{itemize}
%
% %
% % \item
% % Monte Carlo method: accurate, very costly
% %
% % \item
% % Perturbation method:
%
% \end{itemize}
%
%
%
%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% \end{frame}
%
%
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\begin{frame} \frametitle{{3D FPK Equation}}
\begin{footnotesize}
\begin{eqnarray}
\nonumber
\lefteqn{\displaystyle \frac{\partial P(\sigma_{ij}(x_t,t), t)}{\partial t} = \displaystyle \frac{\partial}{\partial \sigma_{mn}}
\left[ \left\{\left< \vphantom{\int_{0}^{t}} \eta_{mn}(\sigma_{mn}(x_t,t), D_{mnrs}(x_t), \epsilon_{rs}(x_t,t))\right> \right. \right.} \\
\nonumber
&+& \left. \left. \int_{0}^{t} d\tau Cov_0 \left[\displaystyle \frac{\partial \eta_{mn}(\sigma_{mn}(x_t,t), D_{mnrs}(x_t),
\epsilon_{rs}(x_t,t))} {\partial \sigma_{ab}}; \right. \right. \right. \\
\nonumber
& & \left. \left. \left. \eta_{ab} (\sigma_{ab}(x_{t\tau}, t\tau), D_{abcd}(x_{t\tau}), \epsilon_{cd}(x_{t\tau}, t\tau)
\vphantom{\int_{0}^{t}} \right] \right \} P(\sigma_{ij}(x_t,t),t) \right] \\
\nonumber
&+& \displaystyle \frac{\partial^2}{\partial \sigma_{mn} \partial \sigma_{ab}} \left[ \left\{ \int_{0}^{t} d\tau Cov_0 \left[
\vphantom{\int_{0}^{t}} \eta_{mn}(\sigma_{mn}(x_t,t), D_{mnrs}(x_t), \epsilon_{rs}(x_t,t)); \right. \right. \right. \\
\nonumber
& & \left. \left. \left. \eta_{ab} (\sigma_{ab}(x_{t\tau}, t\tau), D_{abcd}(x_{t\tau}), \epsilon_{cd}(x_{t\tau}, t\tau))
\vphantom{\int_{0}^{t}} \right] \vphantom{\int_{0}^{t}} \right\} P(\sigma_{ij}(x_t,t),t) \right]
\end{eqnarray}
\end{footnotesize}
% \begin{itemize}
%
%
%
% \item 6 equations
%
% \item Complete description of 3D probabilistic stressstrain response
%
% \end{itemize}
%
%
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\end{frame}
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\begin{frame}
\frametitle{FPK Equation}
\begin{itemize}
\item Advectiondiffusion equation
%
\begin{equation}
\nonumber
\frac{\partial P(\sigma,t)}{\partial t} = \frac{\partial}{\partial \sigma}\left[N_{(1)}P(\sigma,t)\frac{\partial}{\partial \sigma}
\left\{N_{(2)} P(\sigma,t)\right\} \right]
\end{equation}
%
\item Complete probabilistic description of response
\item Solution PDF is secondorder exact to covariance of time (exact mean and variance)
\item It is deterministic equation in probability density space
\item It is linear PDE in probability density space
$\rightarrow$ simplifies the numerical solution process
%\vspace*{0.2truecm}
\end{itemize}
%
% \vspace*{0.5cm}
% {%
% \begin{beamercolorbox}{section in head/foot}
% \usebeamerfont{framesubtitle}\tiny{B. Jeremi\'{c}, K. Sett, and M. L. Kavvas, "Probabilistic
% ElastoPlasticity: Formulation in 1D", \textit{Acta Geotechnica}, Vol. 2, No. 3, 2007, In press (published
% online in the \textit{Online First} section)}
% %\vskip2pt\insertnavigation{\paperwidth}\vskip2pt
% \end{beamercolorbox}%
% }
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%
%
%
% \frametitle{Template Solution of FPK Equation}
%
%
%
% \begin{itemize}
%
%
%
%
% \item FPK diffusionadvection equation is applicable to any material model $\rightarrow$
% only the coefficients $N_{(1)}$ and $N_{(2)}$ are different for different material models
% % %
% % %
% % %
% % %\begin{normalsize}
% % \begin{equation}
% % \nonumber
% % \frac{\partial P(\sigma,t)}{\partial t} = \frac{\partial}{\partial \sigma}\left[N_{(1)}P(\sigma,t)\frac{\partial}{\partial \sigma}
% % \left\{N_{(2)} P(\sigma,t)\right\} \right]
% % %\nonumber
% % = \frac{\partial \zeta}{\partial \sigma}
% % \end{equation}
% % %\end{normalsize}
%
% %
%
% \item Initial condition
%
% \begin{itemize}
%
% \item Deterministic $\rightarrow$ Dirac delta function $\rightarrow$ $ P(\sigma,0)=\delta(\sigma) $
%
% \item Random $\rightarrow$ Any given distribution
%
% \end{itemize}
%
% \item Boundary condition: Reflecting BC $\rightarrow$ conserves probability mass
% $\zeta(\sigma,t)_{At \ Boundaries}=0$
%
% \item Solve using finite differences and/or finite elements
%
%
% \item However (!!) it is a stress solution and probabilistic stiffness is an
% approximation!
%
% \end{itemize}
%
%
% \end{frame}
%
%
%
%
%
%
%
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\subsection{Direct Solution for Probabilistic Stiffness and Stress in 1D}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%% BEGGINING PEP %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}{Direct Probabilistic Constitutive Modeling in 1D}
% \begin{itemize}
%
% \vspace{0.5cm}
%
% \item<1> Probabilistic constitutive modeling : \vspace{0.5cm}
\begin{itemize}
\item Zero elastic region elastoplasticity with stochastic ArmstrongFrederick
kinematic hardening
$ \Delta\sigma =\ H_a \Delta \epsilon  c_r \sigma \Delta \epsilon ;
\hspace{0.5cm}
E_t = {d\sigma}/{d\epsilon} = H_a \pm c_r \sigma $
\vspace*{2mm}
\item Uncertain:
init. stiff. $H_a$,
shear strength $H_a/c_r$,
strain $\Delta \epsilon$:
$ H_a = \Sigma h_i \Phi_i; \;\;\;
C_r = \Sigma c_i \Phi_i; \;\;\;
\Delta\epsilon = \Sigma \Delta\epsilon_i \Phi_i $
\vspace*{2mm}
\item Resulting stress and stiffness are also uncertain
% 
%  $ \sum_{l=1}^{P_{\sigma}} \Delta\sigma_i \Phi_i = \sum_{i=1}^{P_h} \sum_{k=1}^{P_e}\ h_i \Delta \epsilon_k \Phi_i \Phi_k  \sum_{j=1}^{P_g} \sum_{k=1}^{P_e}\sum_{l=1}^{P_{\sigma}} \ c_i \Delta \epsilon_k \sigma_l \Phi_j \Phi_k \Phi_l$
% 
%  $ \sum_{l=1}^{P_{E_t}} \Delta E_{t_i} \Phi_i = \sum_{i=1}^{P_h} h_i \Phi_i \pm \sum_{i=1}^{P_c} \sum_{l=1}^{P_{\sigma}} \ c_i \sigma_l \Phi_i \Phi_l$
% 
\end{itemize}
% \vspace{0.5cm}
% \vspace{1cm}
%\item<1> Time integration is done via Newmark algorithm
%
% \end{itemize}
%
\end{frame}
% % % % % % % % % % % % % % % %
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}{Probabilistic Stiffness Solution}
%
% \begin{itemize}
%
%
% \item Analytic product for all the components,
%
% $ E^{EP}_{ijkl}
% =
% \left[
% E^{el}_{ijkl}
% 
% \frac{\displaystyle E^{el}_{ijmn} m_{mn} n_{pq} E^{el}_{pqkl}}
% {\displaystyle n_{rs} E^{el}_{rstu} m_{tu}  \xi_* h_*}
% \right]
% $
%
%
%
%
% \item Stiffness: each Polynomial Chaos component is updated incrementally
% % at each Gauss Point via stochastic Galerkin projection
%
%
%
% \small{$E_{t_1}^{n+1} = \frac{1}{<\Phi_1\Phi_1> }\{\sum_{i=1}^{P_h} \ h_i <\Phi_i \Phi_1> \pm \sum_{j=1}^{P_c} \sum_{l=1}^{P_{\sigma}} \ c_j \sigma_l^{n+1} <\Phi_j \Phi_l \Phi_1>\}$}
%
% $\large{\vdots}$
%
% \small{$E_{t_P}^{n+1} = \frac{1}{<\Phi_1\Phi_P> }\{\sum_{i=1}^{P_h} \ h_i <\Phi_i \Phi_P> \pm \sum_{j=1}^{P_c} \sum_{l=1}^{P_{\sigma}} \ c_j \sigma_l^{n+1} <\Phi_j \Phi_l \Phi_P>\}$}
%
%
% \item Total stiffness is :
%
% $ E_{t}^{n+1} = \sum_{l=1}^{P_{E}} E_{t_i}^{n+1} \Phi_i $
%
%
%
%
% \end{itemize}
%
%
% \end{frame}
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}{Probabilistic Stress Solution}
%
% \begin{itemize}
%
%
%
% \item Analytic product, for each stress component,
%
% $ \Delta \sigma_{ij} = E^{EP}_{ijkl} \; \Delta \epsilon_{kl} $
% % =
% % \left[
% % E^{el}_{ijkl}
% % 
% % \frac{\displaystyle E^{el}_{ijmn} m_{mn} n_{pq} E^{el}_{pqkl}}
% % {\displaystyle n_{rs} E^{el}_{rstu} m_{tu}  \xi_* h_*}
% % \right]
% % \Delta \epsilon_{kl}
% %
%
%
% \vspace*{1mm}
% \item Incremental stress: each Polynomial Chaos component is updated
% incrementally
% % via stochastic Galerkin projection
%
%
%
%
% {$\Delta\sigma_1^{n+1} = \frac{1}{<\Phi_1\Phi_1> }\{\sum_{i=1}^{P_h} \sum_{k=1}^{P_e}\ h_i \Delta \epsilon_k^n <\Phi_i \Phi_k \Phi_1> \sum_{j=1}^{P_g} \sum_{k=1}^{P_e}\sum_{l=1}^{P_{\sigma}} \ c_j \Delta \epsilon_k^n \sigma_l^n <\Phi_j \Phi_k \Phi_l \Phi_1>\}$}
%
% ${\vdots}$
%
% {$\Delta\sigma_P^{n+1} = \frac{1}{<\Phi_P\Phi_P> }\{\sum_{i=1}^{P_h} \sum_{k=1}^{P_e}\ h_i \Delta \epsilon_k^n <\Phi_i \Phi_k \Phi_P> \sum_{j=1}^{P_g} \sum_{k=1}^{P_e}\sum_{l=1}^{P_{\sigma}} \ c_j \Delta \epsilon_k^n \sigma_l^n <\Phi_j \Phi_k \Phi_l \Phi_P>\}$}
%
%
% \vspace*{1mm}
% \item Stress update:
%
% $ \sum_{l=1}^{P_{\sigma}} \sigma_i^{n+1} \Phi_i = \sum_{l=1}^{P_{\sigma}} \sigma_i^{n} \Phi_i + \sum_{l=1}^{P_{\sigma}} \Delta\sigma_i^{n+1} \Phi_i$
%
%
%
% \end{itemize}
%
% \end{frame}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Probabilistic ElasticPlastic Modeling}
% % \vspace*{5mm}
% \begin{center}
% % \hspace*{15mm}
% \movie[label=show3,width=7cm,poster,autostart,showcontrols]
% {\includegraphics[width=7cm]
% {/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/NPP_Plastic_Dissipation_Density.png}}
% %{/home/jeremic/tex/works/Thesis/HanYang/Files_06June2017/DOE_Annual_2017/Figures/NPP_without_Contact_vonMises.mp4}
% {NPP_without_Contact_vonMises.mp4}
% \end{center}
%\vspace*{5mm}
\begin{center}
% \hspace*{15mm}
\movie[label=show3,width=9cm,poster,autostart,showcontrols]
{\includegraphics[width=9cm]
{/home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Latex/img/figure_PEP_25.png}}
% /home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Latex/img/figure_PEP_25.pdf
%{/home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Animations/PEP_Animation.mp4}
{PEP_Animation.mp4}
\end{center}
%
% \includegraphics[width = 12cm]{./img/figure_PEP_25.pdf}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Stochastic ElasticPlastic Finite Element Method}
\begin{itemize}
\item Material uncertainty expanded into stochastic shape fion
%$E(x,t,\theta) = \sum_{i=0}^{P_d} r_i(x,t) * \Phi_i[\{\xi_1, ..., \xi_m\}]$
\vspace*{1mm}
\item Loading uncertainty expanded into stochastic shape fion
%$f(x,t,\theta) = \sum_{i=0}^{P_f} f_i(x,t) * \zeta_i[\{\xi_{m+1}, ..., \xi_f]$
\vspace*{1mm}
\item Displacement expanded into stochastic shape fion
%$u(x,t,\theta) = \sum_{i=0}^{P_u} u_i(x,t) * \Psi_i[\{\xi_1, ..., \xi_m, \xi_{m+1}, ..., \xi_f\}]$
%\item
%Stochastic system of equation resulting from Galerkin approach (static example):
\item Time domain integration using Newmark and/or HHT, in probabilistic spaces
\end{itemize}
\begin{tiny}
\[
%$
\begin{bmatrix}
\sum_{k=0}^{P_d} <\Phi_k \Psi_0 \Psi_0> K^{(k)} & \dots & \sum_{k=0}^{P_d} <\Phi_k \Psi_P \Psi_0> K^{(k)}\\
\sum_{k=0}^{P_d} <\Phi_k \Psi_0 \Psi_1> K^{(k)} & \dots & \sum_{k=0}^{P_d} <\Phi_k \Psi_P \Psi_1> K^{(k)}\\ \\
\vdots & \vdots & \vdots & \vdots\\
\sum_{k=0}^{P_d} <\Phi_k \Psi_0 \Psi_P> K^{(k)} & \dots & \sum_{k=0}^{M} <\Phi_k \Psi_P \Psi_P> K^{(k)}
\end{bmatrix}
\begin{bmatrix}
\Delta u_{10} \\
\vdots \\
\Delta u_{N0}\\
\vdots \\
\Delta u_{1P_u}\\
\vdots \\
\Delta u_{NP_u}
\end{bmatrix}
=
%\]
%\[
\begin{bmatrix}
\sum_{i=0}^{P_f} f_i <\Psi_0\zeta_i> \\
\sum_{i=0}^{P_f} f_i <\Psi_1\zeta_i> \\
\sum_{i=0}^{P_f} f_i <\Psi_2\zeta_i> \\
\vdots \\
\sum_{i=0}^{P_f} f_i <\Psi_{P_u}\zeta_i>\\
\end{bmatrix}
%$
\]
\end{tiny}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{SEPFEM: System Size}
\begin{itemize}
\item SEPFEM offers a complete solution (single step)
\item It is NOT based on Monte Carlo approach
\item System of equations does grow (!)
\end{itemize}
% \normalsize{Typical number of terms required for a SEPFEM problem} \vspace{1cm}\\
\scalebox{0.7}{
\begin{tabular}{ c c c c}
\# KL terms material & \# KL terms load & PC order displacement& Total \# terms per DoF\\ \hline
4 & 4 & 10 & 43758 \\
4 & 4 & 20 & 3 108 105 \\
4 & 4 & 30 & 48 903 492 \\
6 & 6 & 10 & 646 646 \\
6 & 6 & 20 & 225 792 840 \\
6 & 6 & 30 & 1.1058 $10^{10}$ \\
8 & 8 & 10 & 5 311 735 \\
8 & 8 & 20 & 7.3079 $10^{9}$ \\
8 & 8 & 30 & 9.9149 $10^{11}$\\
... & ... & ... & ...\\
% \hline
\end{tabular}}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{SEPFEM: Example in 1D}
\vspace*{2mm}
\begin{center}
% \hspace*{15mm}
\movie[label=show3,width=9cm,poster,autostart,showcontrols]
{\includegraphics[width=9cm]{/home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Latex/img/figure_elastic_900.png}}
% /home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Latex/img/figure_PEP_25.pdf
%{/home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Animations/SEPFEM_Animation_Elastic.mp4}
{SEPFEM_Animation_Elastic.mp4}
\end{center}
% \includegraphics[width = 12cm]{./img/figure_elastic_900.pdf}
\end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
% \begin{frame}
% \frametitle{SEPFEM: Example in 3D}
%
%
%
% %\vspace*{5mm}
% \begin{center}
% % \hspace*{15mm}
% \movie[label=show3,width=11cm,poster,autostart,showcontrols]
% {\includegraphics[width=11cm]
% {/home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Latex/img/SFEM_3D.png}}
% % /home/jeremic/tex/works/Thesis/MaximeLacour/Files_06Jun2017/Panel_Review_Slides_ML/Latex/img/figure_PEP_25.pdf
% {SFEM_Animation_3D.mp4}
% \end{center}
%
% % \includegraphics[width = 12cm]{./img/SFEM_3D.pdf}
%
%
% \end{frame}
%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%
%
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}{Application of SEPFEM to Practical Problems}
%
%
% Obtain accurate fragility curves (CDFs) for each soil structure system location
% for stress, strain, displacements, etc.
%
%
%
%
%
% \begin{figure}[!htbp]
% \begin{center}
% \includegraphics[width=3.5cm]{/home/jeremic/tex/works/Conferences/2017/SEECMM_2017_Kragujevac/present/Brana_3D_01.jpg}
% %
% \includegraphics[width=4.0cm]{/home/jeremic/tex/works/Reports/2006/NEESDemoProject/PrototypeMesh.jpg}
% %
% \includegraphics[width=4.0cm]{/home/jeremic/tex/works/Conferences/2017/SEECMM_2017_Kragujevac/present/NPP01.jpg}
%
% %\includegraphics[width=5.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Slope_Stability_in_2D_and_3D/3D_final04.jpg}
% %//
% %\includegraphics[width=5.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Slope_Stability_in_2D_and_3D/3D_final05.jpg}
% %\includegraphics[width=5.0cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Slope_Stability_in_2D_and_3D/3D_final_Top.jpg}
%
% %\hspace*{0.9cm}
% %bridge.}
% \end{center}
% \end{figure}
%
% %
% %
% %
% % \begin{figure}[!htbp]
% % \begin{center}
% % %
% % \includegraphics[width=5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figurefiles/_Chapter_Applications_Earthquake_Soil_Structure_Interaction_NEES_Bridge/tex_works_Thesis_GuanzhouJie_thesis_Verzija_Februar_Images_3BentModel.pdf}
% % %
% % \hfill
% % %
% % \includegraphics[width=4.0cm]{/home/jeremic/tex/works/Reports/2006/NEESDemoProject/PrototypeMesh.jpg}
% % %
% % %\hspace*{0.9cm}
% % %bridge.}
% % \end{center}
% % \end{figure}
% %
%
%
% \end{frame}
%
%
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\section{Energy Dissipation}
%
\section{Summary}
\subsection{\ }
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{USDOE Project for ESSI of Nuclear Facilities}
%
% \begin{itemize}
%
% \item[] The MSESSI Simulator (inelastic, deterministic and probabilistic,
% time domain, 3D FEM) \url{http://msessi.info}
%
% % \vspace*{2mm}
% \item[] Modeling from seismic source to NPP (SW4 $\rightarrow$ MSESSI)
%
% % \vspace*{2mm}
% \item[] Extensive Verification (NQA1, ISO), and Validation
%
%
%
% \vspace*{2mm}
% \begin{figure}[!hbpt]
% \begin{center}
% %
% \hspace*{7mm}
% \includegraphics[width=8.2truecm]{/home/jeremic/tex/works/Conferences/2017/CNWG_INL_1618_May_2017/Presentation/DOE_project_UNR_test_01.jpg}
% \end{center}
% \end{figure}
%
%
%
% \end{itemize}
%
%
% \end{frame}
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Summary}
\begin{itemize}
\item[] Importance of using proper models correctly (verification,
validation)
\vspace*{1mm}
\item[] Availability of different levels of sophistication of modeling is
important for reduction of modeling uncertainty
\vspace*{1mm}
\item[] Development of the MSESSI Simulator system
\url{http://msessi.info}
\vspace*{1mm}
\item[] Collaborators: Feng, Abell, Han, Sinha, Wang, Lacour,
Pisan{\'o}, Kova{\v c}evi{\' c}, McCallen, McKenna, Petrone, Rodgers
% ,
% Petersson, Pitarka
\vspace*{2mm}
\item[] Funding from and collaboration with the USDOE, USNRC, USNSF,
CNSCCCSN, UNIAEA, and Shimizu Corp. is greatly appreciated,
\end{itemize}
\end{frame}
%
\end{document}
%
%