A Nitsche method for the elastoplastic torsion problem

Abstract

This study is concerned with the elastoplastic torsion problem, in dimension ≥ 1, and in a polytopal, convex or not, domain. In the physically relevant case where the source term is aconstant, this problem can be reformulated using the distance function to the boundary. We combinethe aforementioned reformulation with a Nitsche-type discretization as in Burman et al. [Comput.Methods Appl. Mech. Eng. 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 offinite element libraries. We establish the well-posedness and convergence properties of the method, and illustrate its behavior with numerical experiments.