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We analyse a numerical scheme for a system arising from a novel descriptionof the standard elastic--perfectly plastic response. The elastic--perfectlyplastic response is described via rate-type equations that do not make use ofthe standard elastic-plastic decomposition, and the model does not require theuse of variational inequalities. Furthermore, the model naturally includes theevolution equation for temperature. We present a low order discretisation basedon the finite element method. Under certain restrictions on the mesh wesubsequently prove the existence of discrete solutions, and we discuss thestability properties of the numerical scheme. The analysis is supplemented withcomputational examples.

Numerical approximation of a thermodynamically complete rate-type model for the elastic--perfectly plastic response