Localization analysis of constitutive models for elastic degradation

Failure indicators in continuum mechanics distinguish among continuous failure, which is associated with a singularity of the 4th order tangent stiffness tensor, and discontinuous failure, which is detected by a singularity of the 2nd order localization tensor. These failure indicators may be applied to any rate constitutive model when the tangent stiffness operator is properly defined. A broad class of constitutive models for elastic degradation can be cast into such form [1]. This paper addresses general conditions for continuous and discontinuous failure for elastic degradation models which encompasses Continuum damage mechanics descriptions as a special case. When a scalar variable describes the stiffness degradation, discontinuous failure analysis is simplified and the plasticity analytical solutions can be used. The paper presents analytic results for critical localization directions and hardening parameters for different loading cases, which are confirmed by the geometric representation of localization in the Mohr plane.