Article Dans Une Revue ESAIM: Mathematical Modelling and Numerical Analysis Année : 2023

A Nitsche method for the elastoplastic torsion problem

Résumé

This study is concerned with the elastoplastic torsion problem, in dimension n ≥ 1, and in a polytopal, convex or not, domain. In the physically relevant case where the source term is a constant, this problem can be reformulated using the distance function to the boundary. We combine the aforementioned reformulation with a Nitsche-type discretization as in [Burman, Erik, et al. Computer Methods in Applied Mechanics and Engineering 313 (2017): 362-374]. This has two advantages: 1) it leads to optimal error bounds in the natural norm, even for nonconvex domains; 2) it is easy to implement within most of finite element libraries. We establish the wellposedness and convergence properties of the method, and illustrate its behavior with numerical experiments.

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hal-03891827 , version 1 (09-12-2022)

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Franz Chouly, Tom Gustafsson, Patrick Hild. A Nitsche method for the elastoplastic torsion problem. ESAIM: Mathematical Modelling and Numerical Analysis, 2023, 57 (3), pp.1731 - 1746. ⟨10.1051/m2an/2023034⟩. ⟨hal-03891827⟩
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