This article is cited in 3 papers

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

E. V. Vtorushin

M. A. Lavrent'ev Institute of Hydrodynamics

Abstract: 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.

Key words: crack, non-penetration, ideal elastoplasticity (Henky model), variational inequalities, FEM, Udzava algorithm.

UDC: 519.632

Received: 24.06.2005