Constitutive singularities of combined elastic degradation and plasticity

The combination of plasticity and elastic degradation results in a tangent stiffness operator with two rank-one updates of the current elastic tensor when both dissipation mechanisms are active. The singularity of the tangent operator determines failure in the form of loss of uniqueness of the incremental response. This failure condition is investigated by studying the general eigenproblem for n rank-one updates of the m×m identity matrix. The general analytic solution of such an eigenproblem is specialized to two rank-one updates when applied to combined plasticity and elastic degradation. It will be shown that the interaction of the two dissipation processes destabilizes the tangent operator and may activate the limit point singularity when both processes are hardening.