A mixed finite element formulation for elastoplasticity. (22nd July 2022)

• Record Type: Journal Article
• Authors: Nagler, Michaela; Pechstein, Astrid; Humer, Alexander
• Is Part Of: International journal for numerical methods in engineering. Volume 123:Number 21(2022)
• Page Start: 5346
• Page End: 5368
• Publication Date: 2022-07-22
• Subjects: elastoplasticity -- mixed finite elements -- principle of maximum dissipation -- shear locking; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.7070
• Languages: English
• ISSNs: 0029-5981

Abstract

Abstract: 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.