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

翻译：我们分析了描述标准弹性—理想塑性响应的新型系统数值格式。该弹性—理想塑性响应通过率型方程描述，未使用传统弹塑性分解，且模型无需引入变分不等式。此外，该模型自然包含温度演化方程。我们提出基于有限元法的低阶离散化方案。在网格满足特定约束条件下，证明了离散解的存在性，并讨论了数值格式的稳定性性质。分析辅以计算示例加以验证。