\( \usepackage{euler} % must be loaded before fontspec for the whole doc (below); this must be kept for pngmath, however \usepackage{hyperref} \usepackage{amsmath} \usepackage{amsbsy} %\usepackage{mathabx} \usepackage{underscore} \usepackage[all]{xy} % Metadata of the pdf output \hypersetup{pdftitle={Yade Documentation}} \hypersetup{pdfauthor={Smilauer, V., et al.}} \hypersetup{pdfkeywords={Discrete element method, granular materials, contact law, hydromechanical coupling}} % symbols \renewcommand{\mat}{\boldsymbol} \renewcommand{\vec}{\boldsymbol} \renewcommand{\tens}{\boldsymbol} %normalized and locfram here \def\normalized#1{\widehat{#1}} \def\locframe#1{\widetilde{#1}} % timestep \def\Dt{\Delta t} \def\Dtcr{\Dt_{\rm cr}} % algorithm complexity \def\bigO#1{{\mathcal{O}(#1)}} % variants for greek symbols \let\epsilon\varepsilon \let\theta\vartheta \let\phi\varphi % shorthands \let\sig\sigma \let\eps\epsilon % variables at different points of time \def\prev#1{#1^-} \def\pprev#1{#1^\ominus} \def\curr#1{#1^{\circ}} \def\nnext#1{#1^\oplus} \def\next#1{#1^+} % shorthands for geometry \def\currn{\curr{\vec{n}}} \def\currC{\curr{\vec{C}}} \def\uT{\vec{u}_T} \def\curruT{\curr{\vec{u}}_T} \def\prevuT{\prev{\vec{u}}_T} \def\currn{\curr{\vec{n}}} \def\prevn{\prev{\vec{n}}} % motion \def\pprevvel{\pprev{\dot{\vec{u}}}} \def\nnextvel{\nnext{\dot{\vec{u}}}} \def\curraccel{\curr{\ddot{\vec{u}}}} \def\prevpos{\prev{\vec{u}}} \def\currpos{\curr{\vec{u}}} \def\nextpos{\next{\vec{u}}} \def\curraaccel{\curr{\dot{\vec{\omega}}}} \def\pprevangvel{\pprev{\vec{\omega}}} \def\nnextangvel{\nnext{\vec{\omega}}} \def\loccurr#1{\curr{\locframe{#1}}} \def\numCPU{n_{\rm cpu}} \DeclareMathOperator{\Align}{Align} \DeclareMathOperator{\sign}{sgn} % sorting algorithms \def\isleq#1{\currelem{#1}\ar@/^/[ll]^{\leq}} \def\isnleq#1{\currelem{#1}\ar@/^/[ll]^{\not\leq}} \def\currelem#1{\fbox{$#1$}} \def\sortSep{||} \def\sortInv{\hbox{\phantom{||}}} \def\sortlines#1{\xymatrix@=3pt{#1}} \def\crossBound{||\mkern-18mu<} \)

DEM formulation¶

The DEM formulation is presented in earlier chapter 2.1 DEM formulation as a common ground for all DEM calculations.

DEM formulation¶

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