Towards a general formulation of elastic degradation and damage based on a loading surface

The current literature on elastic degradation and damage lacks uniform terminology and notation and takes extensive recourse to thermodynamics with little engineering insight. In this paper, an attempt is presented to develop a unified theory in this field using well known concepts of classical elastoplasticity. First, the general features of elastic degradation are considered, with evolution laws for the secant stiffness and compliance tensors. Then, elastic damage is defined as a particular case in which those secant tensors are functions of a reduced set of the damage varaibles (scalar, vectorial or tensorial). Combination of the basic constitutive equations and consistency conditions leas to the expressions for the stress and strain-based tangent operators which are very similar to the elastoplastic ones. A specific version of the general formulation is finally presented for associated scalar damage models of the (1-D) type. This particular formulation encompasses the most significant damage models found in recent literature.