Stress, strain and energy splittings for anisotropic elastic solids under volumetric constraints
We define stress and strain splittings appropriate to linearly elastic anisotropic materials with volumetric constraints. The treatment includes rigidtropic materials, which develop no strains under a stress pattern that is a null eigenvector of the compliance matrix. This model includes as special case incompressible materials, for which the eigenvector is hydrostatic stress. The main finding is that pressure and volumetric strain must be redefined as effective quantities. Using this idea, an energy decomposition that exactly separates deviatoric and volumetric energy follows.
splitting elasticity volumetric constraints compliance incompressibility deviatoric anisotropy rigidtropy isochoricity stability constitutive equation