Publications Details
Bifurcations in elastic-damaging materials
Continuum damage theories describe the progressive reduction in stiffness and strength of brittle materials resulting from the initiation and growth of microcracks and microvoids. When brittle materials are loaded into the nonlinear regime, they often exhibit localized zones of intense deformation and the eventual formation of macrocracks. Criteria for diffuse and discontinuous bifurcations have previously been developed and used to study the initiation of necking and localization in elastic-plastic materials. In this investigation, the same bifurcation criteria are applied to continuum damage theories. Since the bifurcation criteria depend on the fourth-order tangent modulus tensor, the first step in this investigation is the derivation of the tangent modulus tensor for a general continuum damage theory. An eigenanalysis of the symmetric part of the tangent modulus tensor is then shown to fully characterize the potential diffuse and discontinuous bifurcations associated with a given continuum damage theory.