OPTIMIZATION OF THE STORED ENERGY AND COAXIALITY OF STRAIN AND STRESSIN FINITE ELASTICITY

The strain energy density of a hyperelastic anisotropic body which is rotated before being subjected to a given but arbitrary deformation is viewed as a smooth function defined on the group of rotations, parame trized by the deformation gradient. It is shown that the critical poin ts of this function correspond to rotations which, when composed with the prescribed deformation, yield a total strain tensor which is coaxi al with the corresponding stress. For any type of material symmetry, t here are at least two such rotations. Coaxiality of stress and strain for all deformations is shown to be a sufficient condition for the iso tropicity of hyperelastic materials.