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\title[UCD CompGeoMech \\ Contributions to OpenSees:\\ Deliverables]
% (optional, use only with long paper titles)
{UCD CompGeoMech \\ Contributions to OpenSees:\\ Deliverables}

%\subtitle
%{{\tiny full set of slides available at:}\\
%%\verb{http://sokocalo.engr.ucdavis.edu/~jeremic/}
%}

\author[Boris Jeremi{\'c}, University of California, Davis] % (optional, use only with lots of authors)
{Prof. Yang, Dr. Cheng, \\
GSRs Jie, Sett, Taiebat, Preisig, Wu, Liu
\\
~
\\
Boris Jeremi{\'c}}   


% - Give the names in the same order as the appear in the paper.
% - Use the \inst{?} command only if the authors have different
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\institute[UC Davis] % (optional, but mostly needed)
{
%  Department of Civil and Environmental Engineering\\
  University of California, Davis}
% - 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 OpenSees Annual Meeting, San Francisco, January 2007, \\
%\texttt{http://sokocalo.engr.ucdavis.edu/$\tilde{~}$jeremic/}
}
% - Either use conference name or its abbreviation.
% - Not really informative to the audience, more for people (including
%   yourself) who are reading the slides online

\subject{}
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\begin{document}

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\begin{frame}
  \frametitle{Outline}
  \tableofcontents
  % You might wish to add the option [pausesections]
\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.

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\section{Material Models, Elements and Procedures}




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\subsection{Elastic Material Models}

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\begin{frame}
 \frametitle{Elastic Material Models}

\begin{itemize}
  \item Small deformation elasticity 
    \begin{itemize}
     \item linear isotropic
     \item nonlinear isotropic
     \item cross anisotropic
    \end{itemize}


\vspace*{0.5cm}
  \item  Large  deformation  hyperelasticity 
    \begin{itemize} 
      \item Neo--Hookean
      \item Ogden
      \item Logarithmic
      \item  Mooney--Rivlin
      \item Simo--Pister
    \end{itemize} 

\end{itemize}
%\vspace*{-2.0cm}
\end{frame}


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\subsection{Elastic--Plastic (Templated3DEP) Continuum Models}

\begin{frame}
 \frametitle{Elastic--Plastic Continuum Models: Small Deformations}

    \begin{itemize} 
      \item Yield surfaces:   
        \begin{itemize}
          \item von Mises
          \item Drucker--Prager
          \item Cam--Clay
          \item Rounded Mohr--Coulomb
          \item Parabolic Leon
        \end{itemize}
        
       \item  Plastic  flow  directions (plastic potential functions): 
        \begin{itemize}
          \item von Mises
          \item Drucker--Prager
          \item Cam--Clay
          \item Rounded Mohr--Coulomb
          \item Parabolic Leon
          \item Dafalias Manzari
        \end{itemize}

%      \item  Evolution  Laws (hardening and/or softening laws):  
%        \begin{itemize}
%          \item linear  scalar,  
%          \item nonlinear  scalar  (Cam--Clay type), 
%          \item linear tensorial (kinematic hardening/softening: translational  
%          and/or   rotational)
%          \item nonlinear tensorial (kinematic hardening/softening: translational  
%          and/or   rotational)
%            \begin{itemize}
%              \item Armstrong Frederick hardening 
%              \item bounding surface hardening/softening
%            \end{itemize}
%        \end{itemize}
    \end{itemize}

%\vspace*{-2.0cm}
\end{frame}


%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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%\subsection{Elastic--Plastic Continuum Models}

\begin{frame}
 \frametitle{Elastic--Plastic Continuum Models: Small Deformations (continued)}

    \begin{itemize} 
%      \item Yield surfaces:   
%        \begin{itemize}
%          \item von Mises
%          \item Drucker--Prager
%          \item Cam--Clay
%          \item Rounded Mohr--Coulomb
%          \item Parabolic Leon
%        \end{itemize}
%        
%       \item  Plastic  flow  directions (plastic potential functions): 
%        \begin{itemize}
%          \item von Mises
%          \item Drucker--Prager
%          \item Cam--Clay
%          \item Rounded Mohr--Coulomb
%          \item Parabolic Leon
%          \item Dafalias Manzari
%        \end{itemize}
%
      \item  Evolution  Laws (hardening and/or softening laws):  
        \begin{itemize}
          \item linear  scalar,  
          \item nonlinear  scalar  (Cam--Clay type), 
          \item linear tensorial (kinematic hardening/softening: translational  
          and/or   rotational)
          \item nonlinear tensorial (kinematic hardening/softening: translational  
          and/or   rotational)
            \begin{itemize}
              \item Armstrong--Frederick hardening 
              \item bounding surface hardening/softening
            \end{itemize}
        \end{itemize}
    \end{itemize}

%\vspace*{-2.0cm}
\end{frame}


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%\subsection{Small Deformation Elastic--Plastic Continuum}

\begin{frame}
 \frametitle{Hyperelastic--Plastic Continuum Models: Large Deformations}

    \begin{itemize} 
      \item Yield surfaces
        \begin{itemize}
          \item von Mises, 
          \item Drucker--Prager...
        \end{itemize}
      \item  Plastic  flow  directions (plastic potential functions):  
        \begin{itemize}
          \item Drucker--Prager, 
          \item von Mises, 
        \end{itemize}
      \item  Evolution  Laws:  
        \begin{itemize}
          \item linear and nonlinear scalar,  
          \item nonlinear  scalar 
          \item linear and nonlinear (AF) tensorial (kinematic hardening/softening: translational  
          and/or   rotational)
        \end{itemize}
    \end{itemize}
%\vspace*{-2.0cm}
\end{frame}


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%%\subsection{Small Deformation Elastic--Plastic Continuum}
%
%\begin{frame}
% \frametitle{Probabilistic Elasto--Plasticity }
%
%\begin{itemize}
%  \item    Small  deformation {\it template} elasto--plasticity
%    \begin{itemize} 
%      \item Yield surfaces:   
%      von Mises, Drucker--Prager, Cam--Clay, Rounded Mohr--Coulomb, Parabolic Leon...
%      \item  Plastic  flow  directions:  Drucker--Prager, von
%      Mises, Cam--Clay, Rounded Mohr--Coulomb, Manzari Dafalias
%      \item  Evolution  Laws:  Linear  scalar,  nonlinear  scalar  (CamClay), Linear
%      (translational   and   rotational)   tensorial,   nonlinear  (translational  and
%      rotational) tensorial (Armstrong Frederick and bounding surface),
%    \end{itemize}
%  \item  Large deformation {\it template} hyperelasto--plasticity
%    \begin{itemize} 
%      \item Yield surfaces:   
%      von Mises, Drucker--Prager...
%      \item  Plastic  flow  directions:  Drucker--Prager, von
%      Mises, Cam--Clay, Rounded Mohr--Coulomb, Manzari Dafalias
%      \item  Evolution  Laws:  Linear/nonlinear  scalar,  Linear
%      (translational   and   rotational)   tensorial
%    \end{itemize}
%  \item Stochastic elasto--plasticity
%
%\end{itemize}
%%\vspace*{-2.0cm}
%\end{frame}
%
%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%
%\begin{frame}
% \frametitle{Elastic--Plastic Continuum Models (Contd.)}
%
%\begin{itemize}
%  \item  Pressure dependent soil model (for sand and silt)
%  \item  Pressure independent soil model (for clays and silts)
%  \item  Large deformation {\it template} hyperelasto--plasticity
%  \item Stochastic elasto--plasticity
%
%\end{itemize}
%%\vspace*{-2.0cm}
%\end{frame}
%
%
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\subsection{Single Phase Solid Finite Elements}

\begin{frame}
 \frametitle{Single Phase Formulations}

\begin{itemize}
  \item Small deformation solid elements, bricks (8, 20, 21, 27, 8-20 variable node bricks)

\vspace*{0.5cm}

   \item Stochastic Elastic--Plastic Finite Element Method


  \item Large deformation (total Lagrangian) solid elements, bricks (20 node brick)
\end{itemize}
%\vspace*{-2.0cm}
\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{Multi Phase Solid Finite Elements, Coupled}

\begin{frame}
 \frametitle{Multi Phase Formulations}

\begin{itemize}
  \item Fully coupled, u--p--U elements (3D) for small deformations

\vspace*{0.5cm}

  \item Fully coupled, u--p  (3D) elements for small deformations

\vspace*{0.5cm}

  \item Fully coupled u--p (3D) elements for large deformations
\end{itemize}

% Degrees of freedom (DOFs)  are: 
% 
% \begin{itemize}
%   \item   $u  \rightarrow$  solid displacements, 
%   \item $p \rightarrow$ pore fluid pressures, 
%   \item $U \rightarrow$ pore fluid displacements
% \end{itemize}

%\vspace*{-2.0cm}
\end{frame}

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\subsection{Solution Control Computational Procedure}

\begin{frame}
 \frametitle{Hyperspherical Arc--length Solution Control}


 
\begin{equation}
\left[
\begin{array}{cc}
{\bf  K}_{t}           & - {\bf f}_{ext}^{} \\
2 \frac{\psi_{u}^{2}}{u_{ref}^{2}} \Delta {\bf u}^{T} {\bf S} &   2 \Delta \lambda \;
\psi_{f}^{2}\\
\end{array}
\right]
\left[
\begin{array}{c}
\delta {\bf u} \\
\delta \lambda
\end{array}
\right]
=
- \left[
\begin{array}{c}
{\bf r}^{old} \\
a^{old}
\end{array}
\right]
\nonumber
\end{equation}



 
 \vspace*{-1cm}
\begin{figure}[htb]
\begin{center}
\includegraphics[width=5.0cm]{/home/jeremic/tex/works/psfigures/ArcLengthMethod02.pdf}
\hfill
\includegraphics[width=5.0cm]{/home/jeremic/tex/works/psfigures/ArcLengthMethod03.pdf}
\end{center}
\label{ArcLengthMethodFig023}
\end{figure}
 \vspace*{-1cm}


%\vspace*{-2.0cm}
\end{frame}


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\subsection{Domain Reduction Method: Seismic Loading Application}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}
 \frametitle{Domain Reduction Method (Bielak et al.)}
\vspace*{-1.0cm}

 \begin{figure}[!htb]
      {\includegraphics[width=4cm]{/home/jeremic/tex/works/Conferences/2003/7USNCCM/PlasticBowl/DRM05.pdf}}
\end{figure}


\vspace*{-1.5cm}

%\unitlength 1cm
%\begin{large}
    \begin{eqnarray*}
      \left\{\begin{array}{c} P^{eff}_i \\ P^{eff}_b \\ P^{eff}_e \end{array}\right\}
      = \left\{\begin{array}{c} 0 \\ -M^{\Omega+}_{be} \ddot{u}^0_e-K^{\Omega+}_{be}u^0_e
         \\ M^{\Omega+}_{eb}\ddot{u}^0_b+K^{\Omega+}_{eb}u^0_b\end{array}\right\}
    \end{eqnarray*}





%\vspace*{-2.0cm}
\end{frame}





%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Other...}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{frame}
 \frametitle{Other Related (more or less) Work}


 \begin{itemize}
   \item Plastic Domain Decomposition (PDD) method
     
\vspace*{0.5cm}

   \item Stochastic Elastic--Plastic Finite Element Method

\vspace*{0.5cm}

   \item Visualization for Earthquake Engineering
   Simulations (VEES) system driver 
   (computational steering, 
   pre-- and post--processing)



 \end{itemize}

\end{frame}







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\section{Deliverables: People, Implementation and Documents}



%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\begin{frame}
 \frametitle{Documentation: Literate Programming}

   \begin{itemize}

     \item Implementation follows formulation
\vspace*{0.3cm}

     \item Formulation follows mechanics and numerics

\vspace*{0.3cm}
     \item Methodology goal: low Kolmogorov (program--size) complexity

\vspace*{0.3cm}
     \item Verification, Validation and 
     Prediction 

\vspace*{0.3cm}
     \item Open Source (GPL)


   \end{itemize}

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




%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\subsection{Theory Manual}

\begin{frame}
 \frametitle{Theory Manual}

   \begin{itemize}

     \item Detailed theoretical background
\vspace*{0.3cm}
     \item 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}

%\vspace*{0.5cm}
\vspace*{0.3cm}
     \item Support for literate programming (DEK)

   \end{itemize}

\end{frame}
%- 
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
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\subsection{Implementation Manual}

\begin{frame}
 \frametitle{Implementation Manual}

   \begin{itemize}

     \item Application Programming Interface (API)

       \begin{itemize}
%\vspace*{0.3cm}
         \item Public API is forever (asset, liability)
%\vspace*{0.5cm}
%\vspace*{0.3cm}
         \item Realistically, API evolves
%\vspace*{0.3cm}
         \item API design is tough (perfection is unachievable, but try anyway)

       \end{itemize}


\vspace*{0.3cm}
     \item Literate programming drives API

   \end{itemize}

\end{frame}

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\subsection{Examples Manual}

\begin{frame}
 \frametitle{Examples Manual}

   \begin{itemize}

     \item Basic validation examples,
     (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.})
%\vspace*{0.5cm}
     \item Advanced, practical, real life predictive examples
      (Prediction:  use  of  computational  model  to foretell the state
         of a physical system under consideration under conditions for which the
         computational model has not been validated.)

    \item Command manual part of examples manual   

   \end{itemize}

\end{frame}
%- 
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\section*{Conclusions}

\begin{frame}
 \frametitle{Conclusions}
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

\begin{itemize}
%\vspace*{0.5cm}


\item     A rich variety of models, elements and procedures have been 
   \begin{itemize}

\vspace*{0.5cm}

\item   Theories,  formulations, implementation details, as well as   verification,
validation and application examples are available at:
        \texttt{http://sokocalo.engr.ucdavis.edu/$\tilde{~}$jeremic/}




\end{itemize}



\end{frame}



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\end{document}


