Stability and well-posedness of a rate-dependent strain-softening plasticity model

This paper presents an investigation of the stability and well-posedness of a simple rate-dependent model for strain-softening materials. The model contains key features found in several advanced constitutive models that are currently used for damage and failure of materials. The stability and well-posedness of the model are studied by examining the behaviour of dynamic perturbations to the steady-state solution of a simple shear problem. It is shown that the introduction of strain-rate dependency makes the problem well-posed as dynamic perturbations with all wave lengths remain bounded for finite times. The effect of viscosity on the rate of growth of dynamic perturbations of different wave lengths is shown. It is found that the rate of growth for perturbations with short wave length is severely retarded by the material viscosity.