Inverse problem of deformation of a physically nonlinear inhomogeneous medium

An isotropic linear-elastic (viscoelastic) plane containing various physically nonlinear elliptic inclusions is considered. It is assumed that the distances between the centers of the inclusions are much greater than their dimensions. The problem is to determine the orientation of the inclusions and the loads applied at infinity which ensure a specified value of the principal shear stress in each inclusion. Necessary and sufficient conditions of existence of the solution of the problem are formulated for a plane strain of an incompressible inhomogeneous medium.