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%  \usetheme{Hannover} % ima naslov i sadrzaj sa leve strane
%  \usetheme{Singapore} % ima sadrzaj i tackice gore
%  \usetheme{Antibes}  % ima sadrzaj gore i kao graf ...
%  \usetheme{Berkeley} % ima sadrzaj desno
%  \usetheme{Berlin} % ima sadrzaj gore i tackice
%  \usetheme{Goettingen} % ima sadrzxaj za desne strane
%  \usetheme{Montpellier} % ima graf sadrzaj gore
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%  \setbeamercovered{transparent}
% or whatever (possibly just delete it)
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%  \usecolortheme{beetle} % siva pozadina (vrh plav)
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%%%%%%%
%  \usecolortheme{BorisJeremic}
%%%%%%%
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\usepackage{hyperref}
\hypersetup{
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% Commenting this out fixes Windows acrobat problem (?!)
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             urlcolor=webblue,
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%             colorlinks=true,
%             linkcolor=webblue,
%             citecolor=webblue,
%             urlcolor=webblue,
%             linktocpage,
%             pdftex]{hyperref}


\usepackage{pause}
% or whatever
%\usepackage{html}
%\usepackage{url}

\usepackage[latin1]{inputenc}
% or whatever
\usepackage{times}
\usepackage[T1]{fontenc}
% Or whatever. Note that the encoding and the font should match. If T1
% 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[Real-ESSI]
{Computational Modeling and Simulation of \\
Earthquake Soil Structure Interaction \\
Behavior of Nuclear Installations}
%       {A Modern Computational Framework for \\
%       the Nonlinear Seismic Analysis of \\
%       Nuclear Facilities and Systems}
% 
%      {Interface Between Earthquake Ground Motions and Structural
%Response: Numerical Modeling and Simulation of ESSI Behavior}


%\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}}
% % - Give the names in the same order as the appear in the paper.
% % - Use the \inst{?} command only if the authors have different
% %   affiliation.
 \pgfdeclareimage[height=0.2cm]{university-logo}{/home/jeremic/BG/amblemi/ucdavis_logo_blue_sm}
\pgfdeclareimage[height=0.7cm]{lbnl-logo}{/home/jeremic/BG/amblemi/lbnl-logo}



%\pgfdeclareimage[height=0.15cm]{UCD-logo}{/home/jeremic/BG/amblemi/ucdavis_logo_blue_sm}
%\pgfdeclareimage[height=0.18cm]{LBNL-logo}{/home/jeremic/BG/amblemi/LBNL/BerkeleyLab_Masterbrand_logo}
% % \pgfdeclareimage[height=0.15cm]{ESSI-C-logo}{/home/jeremic/BG/amblemi/ESSI/ESSI_Consultants_gray_02}
%  \pgfdeclareimage[height=0.17cm]{ESSI-C-logo}{/home/jeremic/BG/amblemi/ESSI/ESSI_Consultants_white_01}

% \pgfdeclareimage[height=0.20cm]{UCD-logo}{/home/jeremic/BG/amblemi/UCD/UCD_white_01}
% \pgfdeclareimage[height=0.20cm]{LBNL-logo}{/home/jeremic/BG/amblemi/LBNL/LBNL_white_01}
% % \pgfdeclareimage[height=0.15cm]{ESSI-C-logo}{/home/jeremic/BG/amblemi/ESSI/ESSI_Consultants_gray_02}
%  \pgfdeclareimage[height=0.20cm]{ESSI-C-logo}{/home/jeremic/BG/amblemi/ESSI/ESSI-C_white_01}


 
% \pgfdeclareimage[height=0.40cm]{Best_PSHANI_2018_logo}{/home/jeremic/tex/works/Conferences/2018/BestPSHANI/Presentation/Best_PSHANI_2018_logo}

%\author[Jeremi{\'c} et al. Best PSHANI] % (optional, use only with lots of authors)
\author[Jeremi{\'c} et al.] % (optional, use only with lots of authors)
%{Boris~Jeremi{\'c}}
{Boris Jeremi{\'c}}
%Feng, Yang, Wang, Wang, Behbehani, Sinha,  Abell, Pisan{\'o}}
%Fangbo Wang, David McCallen}
%Floriana Petrone, Francis McKenna, David McCallen}
\institute[\pgfuseimage{university-logo}\hspace*{0.1truecm}\pgfuseimage{lbnl-logo}] % (optional, but mostly needed)
%\institute[Computational Geomechanics Group \hspace*{0.3truecm}
%\institute[] % (optional, but mostly needed)
%\institute[\pgfuseimage{UCD-logo}\hspace*{0.15truecm}\pgfuseimage{LBNL-logo}] % (optional, but mostly needed)
%\institute[\pgfuseimage{UCD-logo}\hspace*{0.15truecm}\pgfuseimage{LBNL-logo}\hspace*{0.15truecm}\pgfuseimage{ESSI-C-logo}] % (optional, but mostly needed)
%\institute[\pgfuseimage{UCD-logo}\mbox{;}\pgfuseimage{LBNL-logo}\mbox{;}\pgfuseimage{ESSI-C-logo}] % (optional, but mostly needed)
%{ Professor, University of California, Davis\\
%     { University of California, Davis, CA, USA}
%{ UCD and LBNL}
{ University of California, Davis, CA\\
  and\\
  Lawrence Berkeley National Laboratory, Berkeley, CA}
%  ESSI Consultants, Davis, 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 CNERDWG, ANL, Apr2019}

\subject{}
% This is only inserted into the PDF information catalog. Can be left
% out.



% If you have a file called "university-logo-filename.xxx", where xxx
% is a graphic format that can be processed by latex or pdflatex,
% resp., then you can add a logo as follows:

%\pgfdeclareimage[height=0.2cm]{university-logo}{/home/jeremic/BG/amblemi/ucdavis_logo_gold_lrg}
%\logo{\pgfuseimage{university-logo}}

% \pgfdeclareimage[height=0.5cm]{university-logo}{university-logo-filename}
% \logo{\pgfuseimage{university-logo}}




% Delete this, if you do not want the table of contents to pop up at
% the beginning of each subsection:
% \AtBeginSubsection[]
\setcounter{tocdepth}{3}
\AtBeginSubsection[]
% \AtBeginSection[]
 {
   \begin{scriptsize}
   \begin{frame}<beamer>
     \frametitle{Outline}
     \tableofcontents[currentsection,currentsubsection]
%    \tableofcontents[currentsection]
   \end{frame}
   \end{scriptsize}
 }


% If you wish to uncover everything in a step-wise fashion, uncomment
% the following command:





\begin{document}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}
  \titlepage
\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}
  \frametitle{Outline}

   \begin{scriptsize}
  \tableofcontents
% You might wish to add the option [pausesections]
   \end{scriptsize}
\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% Structuring a talk is a difficult task and the following structure
% may not be suitable. Here are some rules that apply for this
% solution:

% - Exactly two or three sections (other than the summary).
% - At *most* three subsections per section.
% - Talk about 30s to 2min per frame. So there should be between about
%   15 and 30 frames, all told.

% - 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.



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Introduction}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\subsection{Motivation}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Motivation}

\begin{itemize}



%\vspace*{0.3cm}
  \item Improve  modeling  and  simulation  for seismic behavior of Nuclear
  Installations
 

% \vspace*{2mm}
%  \item[]  Expert numerical modeling and simulation tool
% 
% \vspace*{1mm}
%   \item[]      Use of numerical models to
%   analyze statics and dynamics of soil/rock-structure systems
% 

\vspace*{3mm}
  \item  Reduce  modeling uncertainty

%\vspace*{1mm}
%  \item[]  Desired level
%  of sophistication (high  $\leftrightarrow$ low) analysis


\vspace*{3mm}
  \item  Follow  the  flow, input and dissipation,  of seismic  energy, 


\vspace*{3mm}
  \item  Practical  system  for modeling and simulation of
  Earthquakes,    Soils,    Structures    and    their    Interaction (ESSI):
%   Real-ESSI:
 \\
 \vspace*{3mm}
  \hspace*{20mm} 
    \href{http://real-essi.info/}{http://real-essi.info/}





\end{itemize}
\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Predictive Capabilities}
% \frametitle{High Fidelity Modeling of SFS System:
% Verification, Validation and Prediction}

\begin{itemize}

   \item {  Prediction under Uncertainty}
%		   use  of  computational  model
%   to  predict  the  state  of SSI system under
%   conditions for which the computational model has not been validated.


\vspace*{3mm}
     \item  {{  Verification:} 
%      provides  
      evidence  that  the  model is solved
     correctly.} 
%     Mathematics issue.

\vspace*{3mm}
     \item  {{  Validation:}  
%     provides  
     evidence  that  the  correct  model is
     solved.} 
%     Physics issue.

\vspace*{3mm}
   \item  Modeling  and  parametric uncertainties are always present
%    need to be
%   addressed 

% \vspace*{1mm}
%    \item Predictive capabilities with {low Kolmogorov Complexity}
% 

\vspace*{3mm}
     \item Goal: Predict and Inform rather than (force) Fit


\vspace*{3mm}
     \item Risk informed is not enough $\rightarrow$ full risk calculations for ESSI,
     analytical/numerical, accurate



\end{itemize}


\end{frame}



% 





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Verification and Validation Details}

     
     
\begin{figure}[!ht]
%\vspace*{-0.5cm}
%\hspace*{-0.5cm}
\begin{center}
{\includegraphics[width=11cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Verification_and_Validation_Introduction/tex_works_Conferences_2005_OpenSeesWorkshopAugust_DeveloperSymposium_VerifValidFund01.pdf}}
\end{center}
\end{figure}

\end{frame}










  
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Verification}

  
  The  process  of  determining  that    a  model
   implementation  accurately  represents the developer's conceptual description
   and specification. 
%   Mathematics issue. {\it Verification provides evidence that the
%   model is solved correctly.}

   \begin{itemize}
     \item Identify and remove errors in computer coding 
       \begin{itemize}
         \item Numerical algorithm verification
         \item Software quality assurance practice
       \end{itemize}

     \item Quantification of the numerical errors in computed solution
   \end{itemize}

%
%\begin{figure}[!ht]
%\vspace*{-3mm}
%%\hspace*{4.5cm}
%\begin{center}
%{\includegraphics[width=6cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Verification_and_Validation_Introduction/tex_works_Conferences_2005_OpenSeesWorkshopAugust_DeveloperSymposium_VerifValidFund02.pdf}}
%\end{center}
%\end{figure}
%



\end{frame}



% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Real-ESSI Verification}
% 
% \begin{itemize}
% 
% 
%   \item Implementation  verification
% 
% \vspace*{2mm}
%   \item Solution verification for each component
%     \begin{itemize}
%        \item Finite elements
%        \item Constitutive algorithms
%        \item Solution advancement, static and dynamic 
% 
%     \end{itemize}
% 
% 
% \vspace*{2mm}
%   \item Error quantification for ranges of modeling parameters
% 
% \vspace*{2mm}
%   \item Automatic verification, a 13 hour process on multiple CPUs
% 
% \vspace*{2mm}
%   \item Still finding and resolving  issues, using large scale modeling
% 
% 
% 
% \end{itemize}
%  
% \end{frame}
% 
%          

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Validation}


    The process of determining the degree to which a
   model  is  accurate  representation of the real world from the perspective of
   the  intended  uses  of  the  model.  
%   Physics issue. {\it Validation provides
%   evidence that the correct model is solved.}

   \begin{itemize}
     \item    Tactical  goal: Identification  and  minimization of uncertainties
     and errors in the computational model
     \item    Strategic    goal:  Increase    confidence    in  the quantitative
     predictive capability of the computational model
   \end{itemize}

%\begin{figure}[!ht]
%\vspace*{-4mm}
%%\hspace*{5.5cm}
%\begin{center}
%%\begin{flushright}
%{\includegraphics[width=5cm]{/home/jeremic/tex/works/lecture_notes_SOKOCALO/Figure-files/_Chapter_Verification_and_Validation_Introduction/tex_works_Conferences_2005_OpenSeesWorkshopAugust_DeveloperSymposium_VerifValidFund03.pdf}}
%%\end{flushright}
%\end{center}
%\end{figure}
%



\end{frame}




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Types of Physical Experiments}

  
   
\begin{itemize}

   
\vspace*{1mm}
   \item {Traditional Experiments}
     \begin{itemize}
\vspace*{1mm}
       \item Improve the fundamental understanding of physics involved
\vspace*{1mm}
       \item Improve the mathematical models for physical phenomena
\vspace*{1mm}
       \item Assess component performance
     \end{itemize}

   
\vspace*{3mm}
   \item {Validation Experiments}
     \begin{itemize}
\vspace*{1mm}
       \item Model validation experiments
\vspace*{1mm}
       \item  Designed  and  executed  to  quantitatively estimate mathematical
       model's ability to simulate well defined physical behavior
\vspace*{1mm}
       \item   The  simulation  tool, Real-ESSI, computational model,
       computational solution, is the customer

     \end{itemize}


\end{itemize}
  


\end{frame}













%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Uncertainties}


  


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Uncertainties}


\begin{itemize}




%\vspace*{1mm}
\vspace*{2mm}
  \item    \underline{Modeling Uncertainty}, from simplifying assumptions
    \begin{itemize}

\vspace{2mm}
      \item Low, medium, high  sophistication modeling and simulation

\vspace{2mm}
      \item Sophistication level for confidence in analysis results

    \end{itemize}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\vspace*{4mm}
  \item   \underline{Parametric    Uncertainty},  
	 ${M}  \ddot{u_i}  +  {C}  \dot{u_i} + {K}^{ep} {u_i} = {F(t)}$

  \begin{itemize}

\vspace{2mm}
    \item Propagation  of uncertainty  in $M$, $C$ and  $K^{ep}$

\vspace{2mm}

    \item Propagation  of uncertainty in  loads, $F(t)$

\vspace{2mm}

    \item Results are PDFs   and   CDFs  for  $\sigma_{ij}$,  $\epsilon_{ij}$,  $u_i$,  $\dot{u}_i$,  $\ddot{u}_i$

  \end{itemize}




\end{itemize}

% 
% 
% %Le doute n'est pas un {\'e}tat bien agr{\'e}able,\\ 
%        mais l'assurance est un {\'e}tat ridicule.  (Fran{\c c}ois-Marie Arouet, Voltaire)



\end{frame}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Modeling Uncertainty}

\begin{itemize}



  \item      Simplified  modeling:    Features (important ?)   are neglected (3C, 6C
  ground motions, inelasticity)

\vspace*{4mm}
     \item   Modeling   Uncertainty:   unrealistic   and   unnecessary  modeling
     simplifications

\vspace*{4mm}
     \item  Modeling  simplifications   are  justifiable  if  one  or  two  level  higher
     sophistication  model  shows  that  features  being  simplified out are not
     important



\end{itemize}
\end{frame}




      

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Modeling Uncertainty, 6C vs 1C Motions}

     
% 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]
  {/home/jeremic/tex/works/Conferences/2016/IAEA_TecDoc_February2016/My_Current_Work/movie_2_npps_mp4_icon.jpeg}}
  {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Model01_ESSI_Response_May2015/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
\vspace*{-12mm}
\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_2_npps.mp4}
  {\tiny (MP4)}
\end{flushleft}
% online





\end{frame}






%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Parametric Uncertainty: Soil Stiffness}


\vspace*{10mm}
\begin{figure}[!hbpt]
\begin{center}
%
\hspace*{-7mm}
\includegraphics[width=6.2truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/YoungModulus_RawData_and_MeanTrend_01-Ed.pdf}
% \hfill
\includegraphics[width=4.8truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/YoungModulus_Histogram_Normal_01-Ed.pdf}
%
\end{center}
\end{figure}

%\vspace*{-1.8cm}
%\hspace*{-3.3cm}
\begin{flushright}
{\small
%Transformation  of SPT $N$-value: 
%1-D Young's modulus, $E$ 
cf. Phoon and Kulhawy (1999B)
~}
\end{flushright}

\end{frame}


% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Parametric Uncertainty: Material Strength}
% 
% 
% \begin{figure}[!hbpt]
% \begin{center}
% %
% \hspace*{-7mm}
% \includegraphics[width=6.50truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/ShearStrength_RawData_and_MeanTrend-Mod.pdf}
% \hspace*{-7mm}
% % \hfill
% \includegraphics[width=6.0truecm]{/home/jeremic/tex/works/Papers/2008/JGGE-GoverGmax/figures/ShearStrength_Histogram_PearsonIV-FineTuned-Mod.pdf}
% %
% \end{center}
% \end{figure}
% 
% % \vspace*{-1.8cm}
% % %\hspace*{-3.3cm}
% % \begin{flushright}
% % {\tiny
% % Transformation  of SPT $N$-value: \\
% % 1-D Young's modulus, $E$ \\
% % (cf. Phoon and Kulhawy (1999B))\\
% % ~}
% % \end{flushright}
% % %
% 
% 
% \end{frame}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \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}
% 



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\section{Modeling and Simulation }

      
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% \subsection{Real-ESSI Simulator System}
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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Real-ESSI}
% 
% \begin{itemize}
% 
% 
% 
% %\vspace*{2mm}
%   \item    A  system  for  time domain, nonlinear/inelastic,  deterministic  or 
%   probabilistic, modeling and simulation of
% 
%     \begin{itemize}
%       \item  statics and dynamics of soil,
%       \item  statics and dynamics of rock,
%       \item  statics and dynamics of structures,
%       \item  statics of soil-structure systems, and
%       \item  dynamics of earthquake-soil-structure system interaction.
%       \end{itemize}
% 
% 
% \vspace*{2mm}
%   \item \underline{Design:} linear elastic, load combinations, dimensioning
% 
% 
% \vspace*{2mm}
%   \item \underline{Assessment:} nonlinear/inelastic, DBE/BDBE, safety margins
% 
% 
% 
% %\vspace*{1mm}
% %  \item  Develops methods and models that inform and predict rather than (force) fit.
% 
% % \vspace*{1mm}
% %         \item  Collaboration  and  financial  support  from  the US-DOE, US-NRC,
% %        US-NSF,  Caltrans,  CNSC-CCSN,  UN-IAEA, Shimizu, Basler\&Hofmann, ILEE,
% %        etc.
% %
% 
% 
% \end{itemize}
%  
% \end{frame}
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Real-ESSI Modeling Features}
% 
% \begin{itemize}
% 
% 
% 
% %\vspace*{2mm}
%   \item Solid elements, dry, saturated, elastic, inelastic
% 
% \vspace*{1mm}
%   \item Structural elements, beams, shells, elastic, inelastic 
% 
% \vspace*{1mm}
%   \item Contact elements, dry, coupled/saturated, hard, soft
% 
% \vspace*{1mm}
%   \item Super element, stiffness and mass matrices
% 
% \vspace*{1mm}
%   \item Material models, soil, concrete, steel... 
%   
% \vspace*{1mm}
%   \item Seismic input, 1C and 3C, deterministic or probabilistic
% 
% \vspace*{1mm}
%   \item Energy dissipation calculations, material, viscous, algorithmic
% 
% \vspace*{1mm}
%   \item Solid/Structure -- Fluid interaction, full coupling
% 
% % \vspace*{1mm}
% %   \item Features listed at
% %   \hspace*{5mm}
% % %  \hspace*{5mm} 
% % %  \href{http://real-essi.info/}{http://real-essi.info/}
% % 
% 
% \end{itemize}
%  
% \end{frame}
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Real-ESSI Simulation Features}
% 
% \begin{itemize}
% 
% 
% 
% 
%   \item Static loading stages
% 
% 
% 
% \vspace*{2mm}
%   \item Dynamic loading stages
% 
% \vspace*{2mm}
%   \item Restart, simulation tree
% 
% \vspace*{2mm}
%   \item Solution advancement methods/algorithms, on global and
%   constitutive levels, with and without enforcing equilibrium
% 
% 
% %\vspace*{1mm}
% %  \item Load combinations, elastic, for design
% 
% \vspace*{2mm}
%   \item High Performance Computing
% %  clusters, cloud, supercomputers 
%     \begin{itemize}
% %\vspace*{1mm}
%       \item Fine grained, template mataprograms, small matrix library
% %\vspace*{1mm}
%       \item Coarse grained, distributed memory parallel 
%     \end{itemize}
% 
% 
% % \vspace*{1mm}
% %   \item Features listed at  
% %   \hspace*{5mm}
% % %  \hspace*{5mm} 
% % %  \href{http://real-essi.info/}{http://real-essi.info/}
% 
% 
% 
% \end{itemize}
%  
% \end{frame}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Real-ESSI Model Development}
% 
% \begin{itemize}
% 
%     \item Pre-Processing, gmsh/gmESSI, translation (SASSI...)
% 
% 
% \vspace*{2mm}
%     \item Choose level of sophistication, reduce modeling uncertainty
% 
% 
% %\vspace*{1mm}
% %    \item Verify code, solutions, methods, elements, material models 
% 
% 
% 
% \vspace*{2mm}
%     \item Model developed in phases
% 
% \vspace*{2mm}
%     \item Verify model components
% 
% 
% \vspace*{2mm}
%     \item  Build confidence in inelastic modeling
% 
% 
% %%\vspace*{2mm}
% %%    \item  Use such developed models to predict and inform, rather than force fit
% 
% 
% 
% \end{itemize}
%  
% \end{frame}
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%   \frametitle{Real-ESSI  Modeling Phases}
% 
% 
% 
% \begin{figure}[htbp]
% \begin{center}
%   \includegraphics[width = 2.3cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/soil-structure/overview.png}
% \vspace*{-1mm}
% \\
%   \includegraphics[width = 0.35cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/free_field_1D/DRM_1D_motion_3D_just_column.jpg}
% \hspace*{5mm}
% %  \includegraphics[width = 0.1cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/free_field_1D/DRM1D_Motion3D.png}
%   \includegraphics[width = 2.5cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/free_field_3D/motion3D_DRM3D_free_field.png}
% \hspace*{5mm}
% %  \includegraphics[width = 1cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/soil-foundation/soil_foundation.png}
% %  \includegraphics[width = 3cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/soil-foundation/slice.png}
%   \includegraphics[width = 2.5cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/soil-foundation/foundation_results.png}
% %  \includegraphics[width = 3cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/soil-structure/overview.png}
% \\
% \vspace*{-3mm}
%   \includegraphics[width = 1.0cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/structure/eigen/structure-only.png}
% \hfill
%   \includegraphics[width = 1.2cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/structure/eigen/eigen1.png}
% \hfill
%   \includegraphics[width = 1.2cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/structure/eigen/eigen2.png}
% \hfill
%   \includegraphics[width = 1.2cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/structure/eigen/eigen3.png}
% \hfill
%   \includegraphics[width = 1.2cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/structure/eigen/eigen4.png}
% \hfill
%   \includegraphics[width = 1.2cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/structure/eigen/eigen5.png}
% \hfill
%   \includegraphics[width = 1.2cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/structure/eigen/eigen6.png}
% \hfill
% %  \includegraphics[width = 1.0cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/structure/imposed_motion/structure-only.png}
% %\hfill
%   \includegraphics[width = 1.2cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/structure/imposed_motion/imposed_motion_results.png}
% %   \includegraphics[width = 0.1cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/soil-structure/overview.png}
% \\
% \vspace*{-1mm}
%   \includegraphics[width = 6cm]{/home/jeremic/tex/works/Thesis/YuanFeng/Real_ESSI_short_course_examples_day_123/short_course_document/Figure-files/nonlinear_analysis_steps/soil-structure/DRM3D_motion3D_structure.png}
% \end{center}
% \end{figure}
% 
% 
% 
% \end{frame}
% 
% 
% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Real-ESSI Results Post Processing}
% 
% \begin{itemize}
% 
% 
%       \item All output is saved (stress, strain, displacements, energy...)
% 
% \vspace*{5mm}
%       \item Time histories, scripts to plot or extract in preferred format
% 
% \vspace*{5mm}
%       \item 3D visualization, Paraview with pvESSI plugin
% 
% % OVDE dodaj primere vizualizacije
% 
% 
% \end{itemize}
%  
% \end{frame}
% 
% 
% 
%   
% 
% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% \frametitle{Real-ESSI Training and Education}
% 
% \begin{itemize}
% 
% 
%   \item Short Courses: 
%     \begin{itemize}
% %\vspace*{1mm}
%       \item In person short course last year
% %\vspace*{1mm}
%       \item Online short course this winter
% %\vspace*{1mm}
%       \item Professional practice 
% % %\vspace*{1mm}
% %       \item Developers 
% %\vspace*{1mm}
%       \item Examples available in lecture notes, and documentation
% %\vspace*{1mm}
%       \item Real-ESSI system, with examples on Amazon Web Services
% 
%     \end{itemize}
% 
% %\vspace{1mm}
% %  \item Documentation, extensive
% 
% \vspace{2mm}
%   \item Full documentation / lecture notes (2600+ pages) available online at
%   \\
%   \vspace*{2mm} 
%   \hspace*{5mm} 
%   \href{http://real-essi.info/}{http://real-essi.info/}
% 
% 
% \end{itemize}
%  
% \end{frame}
% 
% % OVDE  OVDE  OVDE   
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  \frametitle{Real-ESSI Core Functionality}
% 
% \begin{itemize}
% 
% 
% 
% % %\vspace*{2mm}
% %   \item  Introduction to inelastic/nonlinear analysis for practicing engineers
% 
% 
% % \vspace*{3mm}
%   \item Models for professional practice
% 
% %\vspace*{2mm}
%  \item  Core  functionality  needed  for  nonlinear  modeling  in professional
%  practice
% % 
% 
% 
% 
% %\vspace*{0.3cm}
% %\vspace*{2mm}
%   \item Hierarchy of modeling capabilities, 
%   
%      \begin{itemize}
% 
% %\vspace*{1mm}
%         \item Linear elastic models, elastic constants, viscous damping
% 
% %\vspace*{1mm}
%         \item    Nonlinear  models,  core  functionality,  does not require much
%         material data however, sensitivity study is advised
%   
% %\vspace*{1mm}
%         \item High sophistication  nonlinear models, require material data
%      
%      
%      \end{itemize}
% 
% 
% 
% % \vspace*{2mm}
%   \item    Use  of prescribed/required (low, medium, high) fidelity numerical
%   models to analyze ESSI behavior
% 
% 
% % \vspace*{2mm}
%   \item  Set of suggested modeling and simulation parameters
% 
% % \vspace*{2mm}
%   \item  Investigate  sensitivity  of  response  to model sophistication
% 
% % \vspace*{2mm}
%   \item  Investigate  sensitivity  of response  to model parameters
% 
% % 
% % \vspace*{1mm}
% %   \item[]  Accurately   follow  the  flow   of  seismic  energy  in  a
% %   soil structure system
% % 
% % \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}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% 
% 
% 
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  \frametitle{Real-ESSI Core Functionality Components}
% 
% \begin{itemize}
% 
% 
%    \item Structural elements: Truss, Beam, Shell, Super-Element
% 
% \vspace*{2mm}
%    \item Soil, solids:  elastic, $G/G_{max}$
% 
% \vspace*{2mm}
%    \item Contacts: Bonded, Frictional, Gap open/close
% 
% 
% \vspace*{2mm}
%    \item Loads: Static, Dynamic (earthquake, 1C or 3$\times$1C)
%      
% \vspace*{2mm}
%    \item Restart: Logic tree of load cases   
% 
% \vspace*{2mm}
%    \item Simulation: Explicit (no-equilibrium), Implicit (equilibrium),
% 
% \vspace*{2mm}
%    \item Core Functionality Application programs: APPs
% % 
% 
% 
% \end{itemize}
% 
% 
% \end{frame}
% 
% 
% 
% 
% 
% 
% 
% 
% 
% 
% 
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\subsection{Modeling and Simulation Examples}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Energy Input and Dissipation}

\begin{itemize}

\vspace*{1mm}
     \item[] Energy input, static and dynamic forcing


\vspace*{4mm}
     \item[] Energy dissipation outside SSI domain:
       \begin{itemize}
         \item SSI system oscillation radiation
         \item Reflected wave radiation
       \end{itemize}
\vspace*{1mm}
     \item[] Energy dissipation/conversion inside SSI domain:
       \begin{itemize}
         \item Inelasticity of soil, contact zone, structure, foundation, dissipators
         \item Viscous coupling with internal/pore fluids, and external fluids
% %         \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)
%\vspace*{4mm}
   \item[] Numerical energy dissipation/production


\end{itemize}

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\end{frame}
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% %  
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% % \begin{frame}
% %  
% % \frametitle{Incremental Plastic Work: 
% % \makebox[0pt][l]{\hspace*{2mm}\raisebox{-0.60ex}{\includegraphics[width=3.0truecm]{/home/jeremic/tex/works/Conferences/2018/GeoMEast2018/Short_Course/present/GeoMEast_presentation_EQ03.png}}}%
% % %$d W_p = \sigma_{ij} \, d\epsilon_{ij}^{pl}$
% % }
% %  
% % \begin{itemize}
% % \item Negative incremental energy dissipation
% % %\item Plastic work is NOT plastic dissipation
% % \end{itemize}
% %  
% % \begin{figure}[!H]
% % \begin{center}
% % \includegraphics[height=5.5cm]{/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{Energy Dissipation on Material Level}
% % 
% % 
% % \vspace*{2mm}
% %  
% %  Single elastic-plastic 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}
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % 
% % 
% % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% % \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 Multi-scale 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 Elastic-Plastic 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 Control Mechanisms}
% 
% \begin{figure}[!H]
% %\hspace*{-10mm}
%      \includegraphics[width=3.4cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_plasticity.pdf}
%      \includegraphics[width=3.4cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_Rayleigh.pdf}
%      \includegraphics[width=3.4cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_Newmark.pdf}
% \end{figure}
% 
% 
% % \hspace*{10mm} Numerical  \hspace*{20mm}  Viscous  \hspace*{20mm} Plasticity 
%  \hspace*{10mm} Plasticity \hspace*{20mm}  Viscous  \hspace*{20mm} Numerical
% 
% 
% 
% \end{frame}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% 
% \frametitle{Energy Dissipation Control}
% 
% \begin{figure}[!H]
% %\hspace*{-10mm}
% %     \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_a.pdf}
% %     \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_b.pdf}
%      \includegraphics[width=9cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_g.pdf}
% %     \includegraphics[width=3cm]{/home/jeremic/tex/works/Thesis/HanYang/Files_Energy_dissipation_01Dec2017/case_e.pdf}
% \end{figure}
% 
% 
% 
% 
% \end{frame}
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% 


%  
%  
%  

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  \frametitle{Inelastic Modeling for NPP Soil Structure System}
% 
% \begin{itemize}
% 
% %\vspace*{1mm}
%      \item Soil elastic-plastic
%        \begin{itemize}
%          \item Dry, single phase
%          \item Unsaturated (partially saturated)
%          \item Fully saturated
%        \end{itemize}
% 
% 
% %\vspace*{1mm}
%      \item Contact, inelastic, soil/rock -- foundation
%        \begin{itemize}
%          \item  Dry,  single  phase,  Normal  (hard  and  soft, gap open/close),
%                 Friction (nonlinear)
%          \item Fully saturated, suction and excess pressure (buoyant force)
%        \end{itemize}
% 
% 
% %\vspace*{1mm}
%      \item Structural inelasticity/damage
%        \begin{itemize}
%          \item Nonlinear/inelastic fiber beams
%          \item Nonlinear/inelastic reinforced concrete walls. plates, shells
%          \item Alcali Silica Reaction concrete modeling
%        \end{itemize}
% 
% 
% %%\vspace*{1mm}
% %     \item Fluid-Solid interaction (open surface)
% 
% 
% 
% \end{itemize}
% 
% %
% \end{frame}


% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% 
%  \frametitle{NPP Model }
% 
%   \begin{figure}[!h]
%   \begin{center}
%    \includegraphics[width=8.5cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/NPP_With_Shallow_Foundation.pdf}
%   \end{center}
% %  \caption{\label{Fig:NPP_Model_In_Real_ESSI} Nuclear Power Plant Model with Shallow Foundation }
%   \end{figure}
% 
% 
% % \begin{tikzpicture}[remember picture,overlay]
% %     \node[xshift=3.5cm,yshift=-0.6cm] at (current page.center) {\includegraphics[width=0.5\textwidth]{images/Contact_In_Industry}};
% % \end{tikzpicture}
% 
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% 
%  \frametitle{Structure Model}
% 
%  The nuclear power plant structure comprise of
%  \begin{itemize}
%   \item Auxiliary building, $f^{aux}_{1}= 8Hz$
%   \item Containment/Shield building, $f^{cont}_{1}= 4Hz$
%   \item Concrete raft foundation: $3.5m$ thick
%  \end{itemize}
%   \begin{figure}[!h]
%   \begin{center}
%    \includegraphics[width=0.8\textwidth]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/NPP_Model_Auxiliary_And_Containment_Building.pdf}
%   \end{center}
%   \caption{\label{Fig:NPP_Structure_Model_In_Real_ESSI} Auxiliary and Containment Building }
%   \end{figure}
% 
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% \begin{frame}
% 
%  \frametitle{Inelastic Soil and Inelastic Contact}
% 
%  \begin{itemize}
%   \item Shear velocity of soil $V_s=500m/s$
%   \item Undrained shear strength (Dickenson 1994) $V_s [m/s] = 23 (S_u [kPa])^{0.475}$
%   \item For $V_s=500m/s$ Undrained Strength $S_u=650kPa$ and Young's Modulus of $E=1.3GPa$
%   \item von Mises, Armstrong Frederick kinematic hardening
%   ($S_u=650kPa$ at $\gamma=0.01\%$; $h_a = 30MPa$, $c_r = 25$)
%   \item Soft contact (concrete-soil), gaping and nonlinear shear
%   \end{itemize}
% 
%  \begin{figure}[!h]
%  \begin{center}
%   \includegraphics[width=4cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/Von_Mies_non_Linear_Hardening.pdf}
%   \includegraphics[width=3.5cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/SoftContact.pdf}
%  \end{center}
%   \end{figure}
% 
% 
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%
%  \frametitle{Simulation Result}
%
%  \begin{figure}[!h]
%  \begin{center}
% \subfigure[Selected Locations
%   \label{Specific_Locations}]{\includegraphics[width=0.45\textwidth]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/NPP_Selected_Location_For_Study.pdf}}
% \subfigure[Total Displacement
%   \label{Total_Displacement}]{\includegraphics[width=0.40\textwidth]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/Total_Displacement_Z.pdf}}
%  \end{center}
%  \caption{\label{Fig:NPP_Selected_Location_For_Study} Locations selected to study non-linear effects and plot of total displacement at center of model}
%  \end{figure}
%
%
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% 
%  \frametitle{Acc. Response, Top of Containment Building}
% 
%  \begin{figure}[!h]
%  \begin{center}
% \hspace*{-8mm}
%   \includegraphics[width=4cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/D_Acceleration_X.pdf}
%   \includegraphics[width=4cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/D_Acceleration_Y.pdf}
%   \includegraphics[width=4cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/D_Acceleration_Z.pdf}
% \\
% \hspace*{-8mm}
%   \includegraphics[width=4cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/FFT_D_Acceleration_X.pdf}
%   \includegraphics[width=4cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/FFT_D_Acceleration_Y.pdf}
%   \includegraphics[width=4cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/FFT_D_Acceleration_Z.pdf}
% % \caption{\label{Fig:Response_of_Top_of_Containment_Building} Seismic Response at Top of Containment Building}
%  \end{center}
% \end{figure}
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% 
%  \frametitle{Acceleration Traces, Elastic vs Inelastic }
%   \begin{figure}[!h]
%   \vspace*{-2mm}
%   \begin{center}
%   \hspace*{-15mm}
%    \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/Acceleration_Elastic_Without_Contact_SMIRT_2017.pdf}
%   \hspace*{-20mm}
%    \includegraphics[width=8cm]{/home/jeremic/tex/works/Thesis/SumeetKumarSinha/Files_10Aug2017/Npp_Non_Linear_Effects/images/Acceleration_Inelastic_With_Contact_SMIRT_2017.pdf}
%   \hspace*{-7mm}
%   \end{center}
%  \end{figure}
% \end{frame}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% 


% 
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}

\frametitle{Energy Dissipation in NPP Model}

% 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}




\begin{flushleft}
\vspace*{-15mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/NPP_Plastic_Dissipation.mp4}
%  \href{./homo_50m-mesh_45degree_Ormsby.mp4}
  {\tiny (MP4)}
\end{flushleft}
%



\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\begin{frame}

\frametitle{Energy Dissipation for an SMR Model}

% 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/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/SMR_Energy_Dissipation_screen_grab.jpg}}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/SMR_Energy_Dissipation.mp4}
\end{center}


\begin{flushleft}
\vspace*{-15mm}
\href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/SMR_Energy_Dissipation.mp4}
%  \href{./homo_50m-mesh_45degree_Ormsby.mp4}
  {\tiny (MP4)}
\end{flushleft}
%





% \vspace*{-5mm}



\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  
%  \frametitle{Wall, Regular and ASR Concrete}
% 
% \vspace{-5mm}
% 
%    \begin{figure}[!h]
%     \begin{center}
%      \includegraphics[width=2truecm]{/home/jeremic/tex/works/Conferences/2018/DOE_LBNL_Advisory_Board_meet_08Jun2018/present/OECD_presentation/Figures/Rebar_Plan.pdf}
%      \includegraphics[width=4truecm]{/home/jeremic/tex/works/Conferences/2018/DOE_LBNL_Advisory_Board_meet_08Jun2018/present/OECD_presentation/Figures/3D_mesh.pdf}
% \includegraphics[width=3truecm]{/home/jeremic/tex/works/Conferences/2018/DOE_LBNL_Advisory_Board_meet_08Jun2018/present/OECD_presentation/Figures/Reg_A_Force_Displacement.pdf}
% \includegraphics[width=3truecm]{/home/jeremic/tex/works/Conferences/2018/DOE_LBNL_Advisory_Board_meet_08Jun2018/present/OECD_presentation/Figures/ASR_A1_Force_Displacement.pdf}
%     \end{center}
% \end{figure}
% 
% 
% \vspace{-2mm}
% \begin{figure}[!htbp]
% \begin{center}
% \includegraphics[width=10.0truecm]{/home/jeremic/tex/works/Conferences/2018/DOE_Natural_Hazartd_Oct2018/Present/OECD_wall_damage_3_stages.jpg}
% \end{center}
% \end{figure}
% 
% 
% 
% % \vspace{-20mm}
% % \begin{figure}[!htbp]
% % \hspace*{-10mm}
% % \begin{center}
% % \includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Conferences/2018/DOE_LBNL_Advisory_Board_meet_08Jun2018/present/OECD_presentation/Figures/Damage_3000.pdf}
% % \hspace*{-5mm}
% % \includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Conferences/2018/DOE_LBNL_Advisory_Board_meet_08Jun2018/present/OECD_presentation/Figures/Damage_5000.pdf}
% % \hspace*{-5mm}
% % \includegraphics[width=4.0truecm]{/home/jeremic/tex/works/Conferences/2018/DOE_LBNL_Advisory_Board_meet_08Jun2018/present/OECD_presentation/Figures/Damage_10000.pdf}
% % \end{center}
% % \end{figure}
% % 
% % 
% % \vspace*{-5mm}
% % \hspace*{12mm}
% % \begin{footnotesize}
% % $u_y$ = 1.4 mm
% % \hspace{12mm}
% % $u_y$ = 1.8 mm
% % \hspace{12mm}
% % $u_y$ = 3.0 mm
% % \end{footnotesize}
%   
% \end{frame}
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 


% %  
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
%  \frametitle{Solid/Structure -- Fluid Interaction}
% 
% 
% %OVDE dodaj link na online...
% 
% %\vspace*{-5mm}
% \begin{center}
% % \hspace*{-15mm}
% \movie[label=show3,width=8cm,poster,autostart,showcontrols]
% {\includegraphics[width=8.5cm]
% {/home/jeremic/tex/works/Conferences/2017/DOE_Project_Review_Meeting_LBNL_09June2017/Present/Solid-Fluid-Interaction.jpg}}
% {/home/jeremic/tex/works/Thesis/HexiangWang/Files_06June2017/pic/Solid_Fluid_Interaction.mp4}
% \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/Fluid_Solid_interaction/Solid_Fluid_Interaction.mp4}
% %  \href{./homo_50m-mesh_45degree_Ormsby.mp4}
%   {\tiny (MP4)}
% \end{flushleft}
% %
% 
% 
% 
% 
% \end{frame}
% 
% 
% 


% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%    
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%  \begin{frame}
%  
%  \frametitle{Energy Dissipation for an SMR}
%  
%  % Elastoplastic soil with contact elements
%  %% Both solid and contact elements dissipate energy
%  
%       
%  % \vspace*{-5mm}
%  \begin{center}
%  % \hspace*{-15mm}
%  %\movie[label=show3,width=9cm,poster,autostart,showcontrols]
%  \movie[label=show3,width=10cm,poster,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/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/SMR_Energy_Dissipation.mpg}
%  %{/home/jeremic/tex/works/Thesis/HanYang/Files_16Aug2017/SMR_Energy_Dissipation.mp4}
%  \end{center}
%  
%   
%  \begin{flushleft}
%  \vspace*{-15mm}
%  \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/SMR_Energy_Dissipation.mp4}
%  %  \href{./homo_50m-mesh_45degree_Ormsby.mp4}
%    {\tiny (MP4)}
%  \end{flushleft}
%  %
%  
%  
%  
%  
%  \end{frame}
%  
%  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%











%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
\frametitle{Seismic Motions}


%\vspace*{-10mm}  

\begin{itemize}

\item Variation in  inclination, frequency, energy, duration...

\item Deterministic and Probabilistic

\item Stress test the soil-structure system

\end{itemize}



%\vspace*{-4mm}  
\begin{figure}[!htb]
\begin{flushleft}
\hspace*{-5mm}
\includegraphics[width=6.5cm]{/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=4cm]{/home/jeremic/tex/works/Conferences/2015/CNSC_July/Present/Stress_test_NPP_idea.jpg}
% \hspace*{-5mm}
% \end{flushright}
% \end{figure}


\vspace*{-35mm}  
\begin{figure}[!htb]
\begin{flushright}
\includegraphics[width=5cm]{/home/jeremic/tex/works/consulting/2017/IAEA/TECDOC/Version_14Mar2017/1Dvs3x1Dvs3D_waves.pdf}
\hspace*{-5mm}
\end{flushright}
\end{figure}




\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}

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% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \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/SMR-ESSI_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/SMR-ESSI_real_time_four_freq.mp4}
%   {\tiny (MP4)}
% \end{flushleft}
% % online  
%    
% 
% \end{frame}
% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}

%\frametitle{SMR ESSI, Variation in Input Frequency, $\theta = 60^{o}$}
\frametitle{SMR ESSI, 3C vs 3$\times$1C}

% 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=11cm,poster,showcontrols]
{\includegraphics[width=11cm]
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/SMR_animations_May2018/3Dvs1D_deconvolution.jpg}}
{/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/SMR_animations_May2018/3Dvs1D_deconvolution.ogv}
\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_May2018/3Dvs1D_deconvolution.ogv}
  {\tiny (OGV)}
\end{flushleft}
% online  
   

\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%




% 
% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame}
% 
% \frametitle{Free Field vs ESSI - 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}
%       \\
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% \movie[label=show3,width=54mm,poster,showcontrols]
% {\includegraphics[width=54mm]
% {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/NPP_animations_June2018/Displacement_Inclined_Wave_3_times_1C.jpg}
% }
% {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/NPP_animations_June2018/Displacement_Inclined_Wave_3_times_1C.mp4}
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%  \frametitle{NPP, Inelastic Response, Energy Dissipation}
%  
%  % 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/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/NPP_Plastic_Dissipation_grab.jpg}}
%  {/home/jeremic/public_html/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animations/NPP_Plastic_Dissipation.mp4}
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%  \href{http://sokocalo.engr.ucdavis.edu/~jeremic/lecture_notes_online_material/_Chapter_Applications_ESSI_for_NPPs/Energy_Dissipation_Animation/NPP_Plastic_Dissipation.mp4}
%  %  \href{./homo_50m-mesh_45degree_Ormsby.mp4}
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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 el--pl 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 Material and load parameters are uncertain



\end{itemize}



\end{frame}






 
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\begin{frame} 

\frametitle{Probabilistic Elastic-Plastic Response}


\begin{figure}[!hbpt]
\begin{center}
%\includegraphics[width=8cm]{/home/jeremic/tex/works/Papers/2007/ProbabilisticYielding/figures/vonMises_G_and_cu_very_uncertain/Contour_PDF-edited.pdf}
\includegraphics[width=8cm]{/home/jeremic/tex/works/Conferences/2012/DOE-LLNL-workshop-27-28-Feb-2012/ProbabilisticYielding_vonMises_G_and_cu_very_uncertain_Contour_PDF-edited.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}
% 
% 
%  
% 
% 
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% 
% \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 3-D probabilistic stress-strain response
% %-- 
% %-- \end{itemize}
% %-- 
% %--  
% 
% 
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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 
% \end{frame}
% 
% 
% 



% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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% \begin{frame} 
% 
% \frametitle{FPK Equation}
% 
%  
% 
% \begin{itemize}
% 
% \item Advection-diffusion 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 second-order 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
% % Elasto--Plasticity: Formulation in 1--D", \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}
% 
% 
% 
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% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% \begin{frame} 
% 
% 
% 
% \frametitle{Template Solution of FPK Equation}
% 
%  
% 
% \begin{itemize}
% 
% 
% 
% 
% \item FPK diffusion--advection 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 elasto-plasticity with stochastic Armstrong-Frederick
% 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}
% 



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\begin{frame}
\frametitle{Probabilistic Elastic-Plastic 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}
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%
% \includegraphics[width = 12cm]{./img/figure_PEP_25.pdf}


\end{frame}















 



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\begin{frame}
\frametitle{Stochastic Elastic-Plastic Finite Element Method}



\begin{itemize}

\item Material uncertainty expanded into stochastic shape funcs.
%$E(x,t,\theta) = \sum_{i=0}^{P_d} r_i(x,t) * \Phi_i[\{\xi_1, ..., \xi_m\}]$

\vspace*{1mm}
\item Loading uncertainty expanded into stochastic shape funcs.
%$f(x,t,\theta) = \sum_{i=0}^{P_f} f_i(x,t) * \zeta_i[\{\xi_{m+1}, ..., \xi_f]$

\vspace*{1mm} 
\item Displacement expanded into stochastic shape funcs.
%$u(x,t,\theta) = \sum_{i=0}^{P_u} u_i(x,t) * \Psi_i[\{\xi_1, ..., \xi_m, \xi_{m+1}, ..., \xi_f\}]$

%\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}








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\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}












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\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}






















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\section{Summary}

%\subsection*{Summary}
%\subsection{Summary}
\subsection{\ }

% 
  

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
  \frametitle{Summary}

  \begin{itemize}

\vspace*{1mm}
%    \item Numerical modeling to predict and inform, rather than fit
    \item Numerical modeling to predict, rather than fit


%\vspace*{1mm}
%    \item Inelastic/nonlinear analysis done in phases


\vspace*{4mm}
    \item Education and Training is the key!





\vspace*{4mm}
  \item Real-ESSI Simulator System: \\
%\vspace*{1mm}
  \url{http://real-essi.info/} \\
%\vspace*{1mm}
%    \url{http://real-essi.info/} 

      

%\vspace*{1mm}
%        \item  Challenges in project funding management

% \vspace*{2mm}
%         \item  Collaboration  and  financial  support  from  the US-DOE, US-NRC,
%         US-NSF,  Caltrans,  CNSC-CCSN,  UN-IAEA, Shimizu, Basler\&Hofmann, ILEE,
%         etc.



\end{itemize}



\end{frame}
%


\end{document}

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