CONSTITUTIVE STRUCTURE OF RATE THEORY OF DAMAGE IN BRITTLE ELASTIC SOLIDS

This paper presents a rate-type constitutive analysis applicable to brittle elastic materials whose elastic properties degrade in the course of deformation due to evolution of many microcracks. Thermodynamic analysis is used to identify the appropriate damage tensors and their conjugate forces (affinities). It is shown that the introduced damage potentials are dual: for the damage fluxes in the space of affinities, and for the damage strain and stress rates in the corresponding stress and strain spaces. Rate constitutive equations are derived, providing explicit representations of the tangent stiffness and compliance tensors. General results are specialized in the case of some simple, physically appealing choices of damage functions, analogous to those used in other damage and pressure-dependent plasticity models.