Phase transformations in isotropic elastic materials induced by shear stress states

In this paper we study the stable two-phase deformations for an incompressible isotropic elastic body subjected to a homogeneous distribution of dead load tractions on the boundary with two opposite principal forces, whereas the third one is arbitrary. By considering a stored energy function with a nonconvex (rank-one) dependence on the first invariant of strain and an added linear dependence on the second invariant, we determine values of the boundary tractions which support stable two-phase deformations and discuss some kinematical properties of such solutions.