Material anisotropy and work strain characterized by stationary values of strain energy density function

Stationary values of the strain energy density function are used to determine the relative position of the material symmetry axes and those of principal stress and strain. The minima and maxima would determine the directions of orthotropy for which the body would exhibit the stiffest or softest response. Variational principle is applied to formulate the orthotropic linear elastic problem in three dimensions. Solutions are obtained for a cubic and transversely isotropic material such that the principal axes of stress and strain are aligned with the axes of orthotropy according to the stationary values of the strain energy density. Similar considerations are given to the plane state of stress where the variational process would also involve the material coefficients as independent variables.