Numerical investigation of a model problem for deforming an elastoplastic body with a crack under non-penetration condition

The Lamé system is considered in a two-dimensional domain with a crack. The Dirichlet and the Neuman conditions are held on the exterior boundary, and non-penetration condition is assumed to be on a crack. The convolution product of the deviator of the stress tensor is restricted by a certain constant within the domain. Thus, we have a model problem for deforming an ideal elastoplastic body with a crack (the Henky model) subject to the Mises yield criterion. Simultaneously, the non-penetration condition is held on a crack. The problem is formulated as a variational one. We find a displacement vector as solution to minimization problem for the energy functional over a convex set. Discretization of the problem is provided by a finite element method. Examples of calculation are obtained using the Udzava algorithm.