Abstract
We study mathematical properties of the model that has been proposed to explain the phenomenon of hardening due to cyclic loading. The model considers two elastic plastic materials, soft and hard, that co-exist while the soft material can be transformed into the hard material.
Regarding elastic responses we remain in a simplified framework of linearized elasticity. Incorporating tools such as variational inequalities, penalty approximations and Sobolev spaces, we prove the existence of weak solution to the corresponding boundary-value problem and investigate its uniqueness and regularity.