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, in which the eigenvector id hydrostatic. The main finding is that pressure and volumetric strain must be redefined as effective quatities. Using this idea, an energy decomposition that exactly separates deviatoric and volumetric energy follows.