On coaxiality of stress and strain fields and stationarity of elastic energy in anisotropic solids

Coaxiality of the stress and strain tensors is a necessary condition for the stationarity of the strain energy density in linearly elastic anisotropic solids. This condition is exploited to explicitly evaluate the critical points of the energy, for a given state of strain, when a material element is rotated respect to the principal directions of strain. The complete solution, in terms of critical points and classification of the corresponding energy values, is given for solids endowed with cubic, hexagonal-5 and tetragonal-6 symmetry. Some preliminary results concerning the more general case of orthorhombic symmetry are also presented.