Extremal overall elastic response of polycrystalline materials

Polycrystalline materials comprised of grains obtained from a single anisotropic material are considered in the framework of linear elasticity. No assumptions on the symmetry of the polycrystal are made. We subject the material to independent external strain and stress fields with prescribed mean values. We show that the extremal overall elastic response is always achieved by a configuration consisting of a single properly oriented crystal. This result is compared to results for isotropic polycrystals. (C) 1997 Elsevier Science Ltd.