Thermodynamic admissibility of continuum damage representations

Representations of continuum damage mechanics introduce internal damage parameters into the constitutive stress–strain relations to account for the growth of microscopic flaws and the loss of material strength. Nominally elastic materials are characterized by their elasticity parameters, such as Young’s modulus and Poisson’s ratio, which become dependent on the internal damage parameters. An increase of internal damage involves an energy release similar to the well-known energy release rate in fracture mechanics. This energy release must satisfy the second law of thermodynamics. The implications for the representations of the elasticity parameters in terms of the internal damage parameters are investigated. Necessary conditions for the thermodynamic admissibility of the continuum damage representations are derived based on theoretical models. Several possibilities are given for materials with isotropic or with orthotropic elastic behaviour in the damaged state.