Localization Analysis of Elastic Degradation with Application to Scalar Damage

Abstract

The present paper extends the results of discontinuous bifurcation analysis of elastoplastic solids to materials that exhibit elastic degradation. As a starting point, the concepts of elastic degradation are formulated in terms of a secant relationship, a threshold function, and an elastic stiffness degradation rule. Differentiation of the secant law renders the governing tangent operator for both stress- or strain-based formulations of elastic degradation. Scalar- and tensor-valued proposals in continuum damage mechanics are particular cases of this unified formulation of elastic degradation, when a reduced set of damage variables is considered. The traditional (1 −