The evolution of anisotropies in the elastic response of an elastic-plastic material

The problem of determining the change in a material's symmetries as it undergoes an elastic-plastic deformation is considered. This is interpreted as the problem of evaluating the anisotropies of the current elastic response. The discussion is presented in the context of a particular form of constitutive equation which relates the Cauchy stress to the current value of the deformation gradient and a second order tensor quantity which is a function of the deformation gradient history. A sufficient condition is established for a transformation to be a material symmetry transformation of the current elastic response. This condition relates the minimum symmetries of the current elastic response to the initial material symmetry, the given deformation history, and the structure of the constitutive equation.