LOCALIZATION ANALYSIS OF ELASTIC DEGRADATION WITH APPLICATION TO SCALAR DAMAGE

The present paper extends the results of discontinuous bifurcation ana lysis of elastoplastic solids to materials that exhibit elastic degrad ation. As a starting point, the concepts of elastic degradation are fo rmulated in terms of a secant relationship, a threshold function, and an elastic stiffness degradation rule. Differentiation of the secant l aw renders the governing tangent operator for both stress- or strain-b ased formulations of elastic degradation. Scalar- and tenser-valued pr oposals in continuum damage mechanics are particular cases of this uni fied formulation of elastic degradation, when a reduced set of damage variables is considered. The traditional (1 - D) approach of scalar da mage describes the stiffness degradation by a single variable, whereby all components of the secant stiffness are affected in a self-similar manner. The paper presents general analytic results for distributed a nd localized failure of elastic-degrading materials, further specializ ed for the traditional (1 - D) scalar damage model, when it is subject ed to specific loading scenarios. For illustration, a geometric locali zation criterion is introduced to highlight the features of localized failure in the Mohr coordinates.