Stability and well-posedness of a rate-dependent damage model for brittle materials based on crack mechanics

This paper presents an investigation of the stability and well-posedness of a rate-dependent damage model for brittle materials. The model is based on the response of an ensemble of distributed microcracks under a general, three-dimensional state of stress. The stability and well-posedness of the model are studied by examining the behavior of dynamic perturbations to the steady-state solution of uniaxial-stress loading. It is shown that as a result of incorporating the strain-rate effect in the model, perturbations of all wave lengths remain bounded for finite times, making the problem well-posed. It is also shown that the corresponding rate-independent model is ill-posed in that perturbations grow unbounded with the wave number, even for finite times.