Three-field mixed formulation of elasticity model nonlinear in the mean normal stress for the problem of non-penetrating cracks in bodies

Abstract

A class of models in the theory of elasticity is considered, where a material response between the linearized strain and the stress is assumed to be nonlinear with respect to the mean normal stress. The governing system is endowed with a mixed variational formulation treating the displacement, the deviatoric stress and the mean normal stress as three independent fields. The body contains an inner crack subjected to a non-penetration condition. The resulting problem is described as a pseudo-monotone variational inequality. Its well-posedness is established based on the Galerkin approximation, penalty regularization, and the existence theorem developed by Brézis.

Keywords

• 74B20
• 35J87
• 47J07
• 49J52