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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 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 of finite element libraries. We establish the well-posedness and convergence properties of the method, and illustrate its behavior with numerical experiments. [ABSTRACT FROM AUTHOR]

In a previous paper [F. Chouly, P. Hild and Y. Renard, A Nitsche finite element method for dynamic contact. 1. Space semi-discretization and time-marching schemes. ESAIM: M2AN 49 (2015) 481-502.], we adapted Nitsche's method to the approximation of the linear elastodynamic unilateral contact problem. The space semi-discrete problem was analyzed and some schemes (è-scheme, Newmark and a new hybrid scheme) were proposed and proved to be well-posed under appropriate CFL conditions. In the present paper we look at the stability properties of the above-mentioned schemes and we proceed to the corresponding numerical experiments. In particular we prove and illustrate numerically some interesting stability and (almost) energy conservation properties of Nitsche's semi-discretization combined to the new hybrid scheme. [ABSTRACT FROM AUTHOR]

This paper presents a new approximation of elastodynamic frictionless contact problems based both on the finite element method and on an adaptation of Nitsche's method which was initially designed for Dirichlet's condition. A main interesting characteristic is that this approximation produces well-posed space semi-discretizations contrary to standard finite element discretizations. This paper is then mainly devoted to present an analysis of the space semi-discretization in terms of consistency, well-posedness and energy conservation, and also to study the well-posedness of some time-marching schemes (θ-scheme, Newmark and a new hybrid scheme). The stability properties of the schemes and the corresponding numerical experiments can be found in a second paper [F. Chouly, P. Hild and Y. Renard, A Nitsche finite element method for dynamic contact. 2. Stability analysis and numerical experiments. ESAIM: M2AN 49 (2015) 503-528.]. [ABSTRACT FROM AUTHOR]