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A mixed finite element formulation for elastoplasticity
Author(s) -
Nagler Michaela,
Pechstein Astrid,
Humer Alexander
Publication year - 2022
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.7070
Subject(s) - discretization , finite element method , dissipative system , mathematics , discontinuous galerkin method , mixed finite element method , galerkin method , dissipation , linear elasticity , mathematical analysis , structural engineering , physics , engineering , quantum mechanics , thermodynamics
The present article, provides a novel mixed finite element formulation for elastoplasticity which is suitable for the discretization of thin‐walled structures using highly anisotropic volume elements. We present a thermodynamically consistent framework for the modeling of elastoplastic stress response, where dissipative effects are considered through a dissipation function instead of explicit flow rules. Along these lines, a mixed incremental principle, in which stresses are included as independent unknowns, is derived. We propose to employ tangential‐displacement normal‐normal‐stress (TDNNS) elements for a Galerkin discretization of the underlying variational problem. These elements were originally developed for linear elasticity, where it could be shown that they do not suffer from shear locking if the element's aspect ratio deteriorates. Excellent computational performance and accuracy of the proposed method are demonstrated in several benchmark problems.