Dynamic behavior of structures composed of strain and workhardening visco-plastic materials

Abstract

A dynamic convergence thereon is proven for a class of visco-plastic constitutive equations involving internal state variables, which provides an extension of a result due to Martin[1]. The class of constitutive equation, which includes the Malvern material when effective plastic strain is adopted as the state variable, is expressed in terms of a flow potential. For a simple model structure both convergence and divergence is demonstrated. The example also demonstrates that the theorem provides a sufficient but not a necessary condition for convergence, as convergence can occur even when the conditions of the theorem are not satisfied.