The aim of this paper is to study the problem of regularity of displacement solutions in Hencky plasticity. Here, a non-homogeneous material is considered, where the elastic-plastic properties change discontinuously. In the first part, we have found the extremal relation between the displacement formulation defined on the space of bounded deformation and the stress formulation of the variational problem in Hencky plasticity.
In the second part, we prove that the displacement solution belongs to the appropriate Sobolev space (if the stress solution belongs to the interior of a set of admissible stresses, at each point). Then we deduce a regularity theorem for displacement solutions in composite materials.