EMMC14.

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diff --git a/ECCOMAS_2012/figures/2particles_with_kinks.tikz b/ECCOMAS_2012/figures/2particles_with_kinks.tikz
diff --git a/ECCOMAS_2012/figures/4particle_rve.tikz b/ECCOMAS_2012/figures/4particle_rve.tikz
diff --git a/ECCOMAS_2012/figures/evolve_data.txt b/ECCOMAS_2012/figures/evolve_data.txt
diff --git a/ECCOMAS_2012/figures/gbpm_example.png b/ECCOMAS_2012/figures/gbpm_example.png
diff --git a/ECCOMAS_2012/figures/s_mean_fixed_1.txt b/ECCOMAS_2012/figures/s_mean_fixed_1.txt
diff --git a/ECCOMAS_2012/figures/s_mean_fixed_3.txt b/ECCOMAS_2012/figures/s_mean_fixed_3.txt
diff --git a/ECCOMAS_2012/figures/s_mean_fixed_5.txt b/ECCOMAS_2012/figures/s_mean_fixed_5.txt
diff --git a/ECCOMAS_2012/figures/s_mean_shear_1.txt b/ECCOMAS_2012/figures/s_mean_shear_1.txt
diff --git a/ECCOMAS_2012/figures/s_mean_shear_3.txt b/ECCOMAS_2012/figures/s_mean_shear_3.txt
diff --git a/ECCOMAS_2012/figures/s_mean_shear_5.txt b/ECCOMAS_2012/figures/s_mean_shear_5.txt
diff --git a/ECCOMAS_2012/figures/sintering_rve.tikz b/ECCOMAS_2012/figures/sintering_rve.tikz
diff --git a/ECCOMAS_2012/figures/surface_stress_plane.tikz b/ECCOMAS_2012/figures/surface_stress_plane.tikz
diff --git a/ECCOMAS_2012/figures/topologyboundaries.tikz b/ECCOMAS_2012/figures/topologyboundaries.tikz
diff --git a/EMMC14/EMMC14_MikaelOEhman.pdf b/EMMC14/EMMC14_MikaelOEhman.pdf
diff --git a/EMMC14/EMMC14_MikaelOEhman.tex b/EMMC14/EMMC14_MikaelOEhman.tex
diff --git a/ICMM2/ICMM2_abstract_EL_ME.tex b/ICMM2/ICMM2_abstract_EL_ME.tex
diff --git a/NSCM-23/Avancez_black.pdf b/NSCM-23/Avancez_black.pdf
diff --git a/NSCM-23/Avancez_gold.pdf b/NSCM-23/Avancez_gold.pdf
diff --git a/NSCM-23/NSCM-23-Presentation.tex b/NSCM-23/NSCM-23-Presentation.tex
diff --git a/NSCM-23/beamerthemechalmers.sty b/NSCM-23/beamerthemechalmers.sty
diff --git a/NSCM-23/figures/4particle_rve.tikz b/NSCM-23/figures/4particle_rve.tikz
diff --git a/NSCM-23/figures/4particles_deformed.tikz b/NSCM-23/figures/4particles_deformed.tikz
diff --git a/NSCM-23/figures/Sintering_5x5_000.png b/NSCM-23/figures/Sintering_5x5_000.png
diff --git a/NSCM-23/figures/Sintering_5x5_114.png b/NSCM-23/figures/Sintering_5x5_114.png
diff --git a/NSCM-23/figures/connectivity_edge.dat b/NSCM-23/figures/connectivity_edge.dat
diff --git a/NSCM-23/figures/connectivity_tri2.dat b/NSCM-23/figures/connectivity_tri2.dat
diff --git a/NSCM-23/figures/fig081.jpeg b/NSCM-23/figures/fig081.jpeg
diff --git a/NSCM-23/figures/matlab_convert.m b/NSCM-23/figures/matlab_convert.m
diff --git a/NSCM-23/figures/nodes_1.dat b/NSCM-23/figures/nodes_1.dat
diff --git a/NSCM-23/figures/nodes_1_mat.txt b/NSCM-23/figures/nodes_1_mat.txt
diff --git a/NSCM-23/figures/nodes_200.dat b/NSCM-23/figures/nodes_200.dat
diff --git a/NSCM-23/figures/nodes_200_mat.txt b/NSCM-23/figures/nodes_200_mat.txt
diff --git a/NSCM-23/figures/nodes_50.dat b/NSCM-23/figures/nodes_50.dat
diff --git a/NSCM-23/figures/nodes_50_mat.txt b/NSCM-23/figures/nodes_50_mat.txt
diff --git a/NSCM-23/figures/pressure_1.dat b/NSCM-23/figures/pressure_1.dat
diff --git a/NSCM-23/figures/pressure_1_mat.txt b/NSCM-23/figures/pressure_1_mat.txt
diff --git a/NSCM-23/figures/pressure_200_mat.txt b/NSCM-23/figures/pressure_200_mat.txt
diff --git a/NSCM-23/figures/pressure_50_mat.txt b/NSCM-23/figures/pressure_50_mat.txt
diff --git a/NSCM-23/figures/rve_evolve.pdf b/NSCM-23/figures/rve_evolve.pdf
diff --git a/NSCM-23/figures/sinter_1-crop.pdf b/NSCM-23/figures/sinter_1-crop.pdf
diff --git a/NSCM-23/figures/sinter_2-crop.pdf b/NSCM-23/figures/sinter_2-crop.pdf
diff --git a/NSCM-23/firstpage.pdf b/NSCM-23/firstpage.pdf
diff --git a/NSCM-23/nordic.cls b/NSCM-23/nordic.cls
diff --git a/NSCM-23/nordic.tex b/NSCM-23/nordic.tex
diff --git a/NSCM-23/nscm-abstract-extended.tex b/NSCM-23/nscm-abstract-extended.tex
diff --git a/NSCM-23/nscm-abstract.tex b/NSCM-23/nscm-abstract.tex
diff --git a/NSCM-23/references.bib b/NSCM-23/references.bib
diff --git a/NSCM-23/references_extended.bib b/NSCM-23/references_extended.bib
diff --git a/NSCM-23/tensortyping.sty b/NSCM-23/tensortyping.sty
diff --git a/Prag/figures/2particles_with_kinks.tikz b/Prag/figures/2particles_with_kinks.tikz
diff --git a/Prag/figures/4particle_rve.tikz b/Prag/figures/4particle_rve.tikz
diff --git a/Prag/figures/sinter_1-crop.pdf b/Prag/figures/sinter_1-crop.pdf
diff --git a/Prag/figures/sinter_2-crop.pdf b/Prag/figures/sinter_2-crop.pdf
diff --git a/Prag/figures/sintering_rve.tikz b/Prag/figures/sintering_rve.tikz
diff --git a/Prag/figures/surface_stress_plane.tikz b/Prag/figures/surface_stress_plane.tikz
diff --git a/Prag/figures/topologyboundaries.tikz b/Prag/figures/topologyboundaries.tikz
diff --git a/VCCH_incompressible_elastic/SwissCheese.tex b/VCCH_incompressible_elastic/SwissCheese.tex
diff --git a/VCCH_incompressible_elastic/SwissCheeseFig.pdf b/VCCH_incompressible_elastic/SwissCheeseFig.pdf
diff --git a/VCCH_incompressible_elastic/VCCH_incompressible_elasticity.tex b/VCCH_incompressible_elastic/VCCH_incompressible_elasticity.tex
@@ -509,7 +509,7 @@ \subsection{VMS-ansatz and scale separation}
 \end{align}
 %----------------------------------------------------------------------------
 
-In the spirit of the Variational MultiScale method (VMS) \cite{larsson_variationally_2010}, we introduce the \emph{ansatz} that the fields $\ta{u}\in\set{U}$ and $p\in\set{P}$ can be decomposed into macroscale (smooth) and subscale (fluctuating) parts inside each RVE via the unique orthogonal split $\set{U} = \set{U}^\macro \oplus \set{U}^\fluct$ and $\set{P} = \set{P}^\macro \oplus \set{P}^\fluct$.
+In the spirit of the Variational MultiScale method (VMS) \cite{larsson_variationally_2010}, we introduce the \emph{ansatz} that the fields $\ta{u}\in\set{U}$ and $p\in\set{P}$ can be decomposed into macroscale (smooth) and subscale (fluctuating) parts inside each RVE via the unique hierarchical split $\set{U} = \set{U}^\macro \oplus \set{U}^\fluct$ and $\set{P} = \set{P}^\macro \oplus \set{P}^\fluct$.
 As a result, we may assume that it is possible solve for the fluctuation fields $\ta{u}^\fluct\in\set{U}^\fluct$ and $p^\fluct\in\set{P}^\fluct$ as ``local approximations'' on each RVE for given macroscale solutions $\ta{u}^\macro\in\set{U}^\macro$ and $p^\macro\in\set{P}^\macro$, i.e.\ we construct the complete solution on each RVE as\footnote{Curly brackets $\{(\bullet)\}$ indicate implicit and/or nonlocal functional dependence on $(\bullet)$.}.
 %------------------------------------------------------------------------------------------------------------
 \begin{subequations}\label{eq4}

diff --git a/VCCH_incompressible_elastic/VCHomogen_elasticity_incompressible.tex b/VCCH_incompressible_elastic/VCHomogen_elasticity_incompressible.tex
diff --git a/VCCH_incompressible_elastic/contmech.sty b/VCCH_incompressible_elastic/contmech.sty
diff --git a/VCCH_porosity/SwissCheese.tex b/VCCH_porosity/SwissCheese.tex
diff --git a/VCCH_porosity/SwissCheeseFig.pdf b/VCCH_porosity/SwissCheeseFig.pdf
diff --git a/VCCH_porosity/contmech.sty b/VCCH_porosity/contmech.sty
diff --git a/VCCH_porosity/figures/2particles_with_kinks.tikz b/VCCH_porosity/figures/2particles_with_kinks.tikz
diff --git a/VCCH_porosity/figures/4particle_rve.tikz b/VCCH_porosity/figures/4particle_rve.tikz
diff --git a/VCCH_porosity/figures/sintering_rve.tikz b/VCCH_porosity/figures/sintering_rve.tikz
diff --git a/VCCH_porosity/figures/surface_stress_plane.tikz b/VCCH_porosity/figures/surface_stress_plane.tikz
diff --git a/VCCH_porosity/figures/topologyboundaries.tikz b/VCCH_porosity/figures/topologyboundaries.tikz
diff --git a/WCCM14/WCCM14_MikaelOEhman.pdf b/WCCM14/WCCM14_MikaelOEhman.pdf
diff --git a/WCCM14/WCCM14_MikaelOEhman.tex b/WCCM14/WCCM14_MikaelOEhman.tex
@@ -17,7 +17,7 @@
 \usepackage{pgfplots}
 
 %\pgfplotsset{compat=newest}
-\pgfplotsset{compat=1.6}
+%\pgfplotsset{compat=1.6}
 \usetikzlibrary{shapes,arrows}
 
 \newcommand{\highlight}[1]{{\color{red}#1}}
@@ -62,7 +62,7 @@
 
 \usetheme[titleflower=true]{chalmers}
 \title{
-Computational homogenization of incompressible microstructures
+On computational modeling of incompressible microstructures
 }
 \author[Mikael \"Ohman WCCM-ECCM  --- 2014-07-22]{Mikael \"Ohman\\Kenneth Runesson\\Fredrik Larsson}
 \institute{Department of Applied Mechanics\\ Chalmers University of Technology\\
@@ -107,15 +107,53 @@ \section{Title page}
 % \end{center}
 %\end{frame}
 
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}
+ \frametitle{Motivation}
+  \begin{itemize}
+  \item Challenge in computational homogenization: Seamless transition of macroscale compressibility $\rightarrow$ incompressibility.
+   \item Practical application: Meltphase sintering of hardmetal producs: Porosity vanishes
+\begin{center}
+ \includegraphics[scale=0.1]{figures/evolve_free_a}
+\hspace{1em}
+ \includegraphics[scale=0.1]{figures/evolve_free_b}
+ \hspace{1em}
+\includegraphics[scale=0.1]{figures/evolve_free_d}
+\\
+ \includegraphics[scale=0.1]{figures/evolve_shear_a}
+\hspace{1em}
+ \includegraphics[scale=0.1]{figures/evolve_shear_b}
+ \hspace{1em}
+\includegraphics[scale=0.1]{figures/evolve_shear_d}
+\end{center}
+  \end{itemize}
+\end{frame}
+
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+\begin{frame}
+ \frametitle{Motivation}
+  \begin{itemize}
+  \item Prototype problem (this presentation): Solid phase microstructure with heterogeneous subscale compressibility.
+ \\
+ Extreme situation: Uniform incompressibility $\rightarrow$ macroscale incompressibility
+
+ \item Need for comprehensive variational framework for homogenization.
+     Reference: Öhman et al.
+    \textit{On \ the variationally consistent computational homogenization of elasticity in the incompressible limit}.
+     AMSE (2014). Conditionally accepted
+  \end{itemize}
+\end{frame}
+
 \section{Outline}
 \begin{frame}
  \frametitle{Outline}
-
 \begin{itemize}
  \item Mixed formulation for incompressible elasticity
- \item Problem with traditional boundary conditions
+ \item Variationally consistent homogenization
  \item Macroscale problem
- \item Weakly periodic boundary condition
+ \item Subscale problem
+ \item Numerical examples
  \item Conclusions
 \end{itemize}
 \end{frame}
@@ -133,14 +171,14 @@ \section{Theory}
     \\
     \hat{e}(p) - \ta u\cdot\ta\nabla &= 0\text{ in } \Omega%, \quad \Omega = \cup_\alpha \Omega_\alpha
   \end{align*}
-  \item Example material model, isotropic linear elasticity
+  \item Prototype material model: isotropic linear elasticity
   \begin{gather*}
    \hat{\ts\sigma}_\dev(\ts\epsilon_\dev) \defeq 2 G \ts\epsilon_\dev\\
    \hat{\ts\sigma}_\dev(\ts\epsilon_\dev) = \ts\sigma + p\ts I,\quad \ts\epsilon_\dev \defeq [\ta u\outerp \diff]_\dev^\sym
    \\
    \hat{e}(p) \defeq -C\,p
   \end{gather*}
-  \item For compressible cases, the bulk modulus is $ K = C^{-1}$
+  \item In the case of local compressibility, the bulk modulus is $ K = C^{-1}$
   \item Subscript $\dev$ denotes deviatoric tensor: $\bullet_\dev = \bullet - \frac13 [\bullet:\ts I]\ts I$
  \end{itemize}
 \end{frame}
@@ -162,24 +200,6 @@ \section{Theory}
  \end{itemize}
 \end{frame}
 
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}
- \frametitle{Problem with classical boundary conditions}
-  \begin{itemize}
-   \item As $C\to 0$, the volumetric part of the macroscopic strain can no longer be controlled in an RVE. Classical (Dirichlet and Neumann) boundary conditions for homogenization breaks down.
-   \item Solution presented:
-    \begin{center}
-    %\fullcite{ohman_variationally_2014}
-     Mikael Öhman, Kenneth Runesson, and Fredrik Larsson.
-     \\%[1em]
-    \textit{On the variationally consistent computational homogenization of elasticity in the incompressible limit}.
-     \\%[1em]
-     Advanced Modeling and Simulation in Engineering Sciences (2014). Under review
-    \end{center}
-  \end{itemize}
-\end{frame}
-
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}
  \frametitle{Variationally Consistent Homogenization (VCH)}
@@ -197,62 +217,22 @@ \section{Theory}
   p = p^\macro + p^\fluct
  \end{align*}
  \item Variationally Consistent Homogenization $\leadsto$ macroscale problem
-\end{itemize}
-\end{frame}
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\begin{frame}
- \frametitle{Variationally Consistent Macrohomogenity Condition}
-\begin{itemize}
- \item Variationally Consistent Macrohomogeneity condition (VCMC):
- \begin{center}
-  \input{figures/VCMC.tikz}
- \end{center}
- \item $\leadsto$ restrictions on microscale boundary conditions
- \item $z = (\ta u, p)$
- \item A generalized Hill-Mandel condition
+ \item Generalized Hill-Mandel condition $\leadsto$ subscale modeling requirements
 \end{itemize}
 \end{frame}
 
 
-% \section{Paper}
-% \subsection{A}
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% \begin{frame}
-%  \frametitle{Choice of prolongation}
-% \begin{itemize}
-%  \item First order Taylor expansion of the velocity, and no macroscale pressure
-% \begin{align*}
-%  \ta u^\macro &= \bar{\ta u} + [\bar{\ta u}\outerp\diff]\cdot[\ta x - \bar{\ta x}]
-% \\
-%  p^\macro &= 0
-% \end{align*}
-% \item Constraint on the fluctuation $\ta u^\fluct$ within each RVE via the condition
-% \begin{align*}
-%  \frac{1}{\volume} \int_{\Gamma_\rve} \ta u\outerp\ta n \dif S &= \bar{\ta u}\outerp\diff
-% \end{align*}
-% \item \textbf{Remark}: $\bar{\ta u}\outerp\diff$ represents the ``effective'' volume average for a porous domain
-% \end{itemize}
-% \end{frame}
-
-%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% \begin{frame}
-%  \frametitle{Paper A summarized}
-% \begin{center}
-%  \input{figures/box1.tikz}
-% \end{center}
-% \end{frame}
-
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}
- \frametitle{Hierarchical split}
+ \frametitle{Variationally Consistent Homogenization (VCH)}
 \begin{itemize}
  \item First order Taylor expansion of the displacement, and zeroth order expansion of the pressure
 \begin{align*}
  \ta u^\macro &= \bar{\ta u} + [\bar{\ta u}\outerp\diff]\cdot[\ta x - \bar{\ta x}]
 \\
  p^\macro &= \bar{p}
 \end{align*}
+where $(\bar{\ta u}, \bar{p})$ are macroscale fields with induced regularity requirements.
  \item Constraints on the fluctuations $\ta u^\fluct$ and $p^\fluct$ within each RVE via the conditions
 \begin{align*}
  \homgen{\ta u\outerp\diff} &= \bar{\ta u}\outerp\diff
@@ -282,6 +262,28 @@ \section{Theory}
 \end{itemize}
 \end{frame}
 
+
+\begin{frame}
+ \frametitle{Weak periodicity on RVE}
+\begin{center}
+\begin{tikzpicture}
+%\tikzstyle{every node}=[font=\Large]
+\node [inner sep=0pt,above right]{
+   \includegraphics[scale=.3]{figures/SwissCheeseFig}
+   };
+\draw[<-, line width=.4mm] (5.0,4.0) to[out=0,in=-120] (6.0,5.0) node[right=1pt,black]{$\Gamma_\rve^+$};
+\draw[<-, line width=.4mm] (4.0,5.0) to[out=60,in=120] (6.0,5.0);
+\draw[<-, line width=.4mm] (0.0,1.0) to[out=180,in=60] (-1.0,0.0) node[left=1pt,black]{$\Gamma_\rve^-$};
+\draw[<-, line width=.4mm] (1.0,0.0) to[out=-120,in=-60] (-1.0,0.0);
+\draw[<-, line width=.6mm] (0.0,2.4) to[out=15,in=165] (5.0,2.4) node[right]{$\ta{\varphi}_\per$} ;
+%\draw[<-, line width=.4mm] (4.6,1.7) .. controls +(right:0.5cm) and +(left:0.5cm) .. (6.0,1.0) node[right=1pt,black,text width=3cm,text badly ragged]{$\partial\Omega_{\rve,i}^\text{p}$};
+\end{tikzpicture}
+\end{center}
+\begin{itemize}
+ \item $\jump{\bullet} = $ difference of $\bullet$ between $\Gamma_\rve^+$ and $\Gamma_\rve^-$ (mirror point)
+\end{itemize}
+\end{frame}
+
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}
  \frametitle{RVE problem --- Weakly Periodic b.c.}
@@ -308,27 +310,31 @@ \section{Theory}
 &
   \forall\;\delta\bar{e} \in \set R
 \end{flalign*}
- \item $\jump{\bullet} = $ difference of $\bullet$ between $\Gamma_\rve^+$ and $\Gamma_\rve^-$ (mirror point)
 \end{itemize}
 \end{frame}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}
- \frametitle{RVE problem --- Dirichlet and Neumann b.c.}
+ \frametitle{RVE problem}
 \begin{itemize}
- \item For given macroscale variables $\bar{\ts\epsilon}_\dev$ and $\bar{p}$ obtain $\bar{\ts\sigma}_\dev$ and $\bar{e}$:
+ \item For given macroscale variables $\bar{\ts\epsilon}_\dev$ and $\bar{p}$, obtain $\bar{\ts\sigma}_\dev$ and $\bar{e}$ as output from the RVE problem:
  \begin{itemize}
-  \item Dirichlet b.c.: find ($\ta{u},p,\bar{e})\in\set{U}'_\rve\times\set{P}_\rve\times\set R$
+  \item Dirichlet b.c.: find ($\ta{u},p,\bar{e})\in\set{U}^{D'}_\rve\times\set{P}_\rve\times\set R$
   \begin{itemize}
-    \item Similar implementation to traditional Dirichlet b.c. only $\bar{e}$ is not controlled.
-    \item $\bar{\ts\sigma}_\dev$ response is post-processed reaction forces on RVE-boundary.
+    \item Note: $\bar{e}$ (volumetric part of macroscopic strain) is not controlled.
+    \item $\bar{\ts\sigma}_\dev$ is obtained from post-processing reaction forces on RVE-boundary.
   \end{itemize}
   \item Neumann b.c.: find ($\ta{u},p,\bar{\ts\sigma}_\dev)\in\set{U}_\rve\times\set{P}_\rve\times\set{R}^{3\times 3}_\dev$.
   \begin{itemize}
-    \item Similar implementation to traditional Neumann b.c. only $\bar{p}$ is controlled.
-    \item $\bar{e}$ response is post-processed from displacement on RVE-boundary.
+    \item Note: $\bar{p}$ (volumetric part of macroscopic stress) is controlled.
+    \item $\bar{e}$ is obtained from post-processing displacements on RVE-boundary.
   \end{itemize}
  \end{itemize}
+ \item Remarks:
+ \begin{itemize}
+  \item Dirichlet/Neumann b.c. represent upper/lower bound of macroscale strain energy
+  \item Weakly periodic b.c. has been enforced approximately by polynomial basis for tractions in $\set{T}_\rve$ (costly, implemented but no results shown in this presentation).
+ \end{itemize}
 \end{itemize}
 \end{frame}
 
@@ -340,9 +346,10 @@ \section{Theory}
 \end{center}
 \end{frame}
 
+\section{Numerical examples}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}
- \frametitle{Statistical Volume Element (SVE)}
+ \frametitle{Numerical examples}
 \begin{center}
  \hspace{1cm}
  \includegraphics[scale=0.05]{figures/rve6.png}
@@ -358,7 +365,7 @@ \section{Theory}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \begin{frame}
- \frametitle{Homogenized shear and bulk modulus}
+ \frametitle{Numerical examples}
 \begin{center}
 %\input{figures/meanG.tikz}
 \includegraphics[width=0.4\linewidth]{figures/meanG}
@@ -384,9 +391,9 @@ \section{Theory}
  \begin{itemize}
  \item Multiscale problem derived from fine-scale problem with VCH
  \item Seamless transition to macroscopic incompressibility
- \item Methodology is extensible to include pores and surface tension
+ \item Methodology is extendable to include pores and surface tension
  %\item Modified Neumann-b.c. at no additional computational cost
- \item Implementation of boundary conditions is available in the open source code OOFEM \texttt{www.oofem.org}
+ \item Implementation of RVE boundary conditions is available in the open source code OOFEM \texttt{www.oofem.org}
  \end{itemize}
 \end{frame}
 

diff --git a/WCCM14/figures/2particles_with_kinks.tikz b/WCCM14/figures/2particles_with_kinks.tikz
diff --git a/WCCM14/figures/4particle_rve.tikz b/WCCM14/figures/4particle_rve.tikz
diff --git a/WCCM14/figures/beam_multiscale.tikz b/WCCM14/figures/beam_multiscale.tikz
diff --git a/WCCM14/figures/evolve_free.tikz b/WCCM14/figures/evolve_free.tikz
diff --git a/WCCM14/figures/sintering_rve.tikz b/WCCM14/figures/sintering_rve.tikz
diff --git a/WCCM14/figures/surface_stress_plane.tikz b/WCCM14/figures/surface_stress_plane.tikz
diff --git a/WCCM14/figures/topologyboundaries.tikz b/WCCM14/figures/topologyboundaries.tikz