An LBB-stable tetrahedral finite element based on a Pseudo-Random Integration (PRI) method for finite strain von Mises elasto-plasticity
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The aim of this work is to propose a new nodal treatment of the pressure for tetrahedral meshes devoted to finite strain von Mises elasto-plasticity. The approach proposed has the interest of being LBB-stable for P1-type discretization. Thus, the existence of an error estimate is ensured and there is no need for a stabilization technique. The pressure is assumed to be constant on nodal sub-cells whose size is defined by means of a pseudo-random number generator. In this way, the discretization for the pressure is 'out of sync' with the one used for the kinematics. Because of this non-coincident spatial decomposition, the inf-sup test proposed by Chapelle and Bathe \cite{Chappelle} shows that the LBB condition can be ensured. Examples are presented to illustrate the relevance of the approach developed for Eulerian and Lagrangian formalisms.
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