Work

Mixed finite elements of higher-order in elastoplasticity

Year: 2024

Type: article

Abstract: In this paper a higher-order mixed finite element method for elastoplasticity with linear kinematichardening is analyzed. Thereby, the non-differentiability of the involved plasticity functionalis resolved by a Lagrange multiplier leading to a three field formulation. The finite elementdiscretization is conforming in the displacement field and the plastic strain but potentially non-conforming in the Lagrange multiplier as its Frobenius norm is only constrained in a certain setof Gauss quadrature points. A discrete inf-sup condition with constant 1 and the well posednessof the discrete mixed problem are shown. Moreover, convergence and guaranteed convergencerates are proved with respect to the mesh size and the polynomial degree, which are optimal forthe lowest order case. Numerical experiments underline the theoretical results.

Source: Applied Numerical Mathematics

DOI: 10.1016/j.apnum.2024.11.008

Authors: Patrick Bammer, Lothar Banz, Andreas Schröder

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $1,560

Funder: Bundesministerium für Bildung, Wissenschaft und Forschung

Award: G3096427437