## Preprint 2022-32

## Franz Chouly, Tom Gustafsson, Patrick Hild:

### A Nitsche method for the elastoplastic torsion problem

### Abstract:

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 well-posedness and convergence properties of the method, and illustrate its behavior with numerical experiments.