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.
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