In this work, an elastic-perfectly plastic model in two-dimensional planar geometry is studied and a new HLLC-type approximate Riemann solver (HLLCN) is put forward. The main feature of the new approximate Riemann solver is that it almost includes all stress waves, such as elastic, plastic, longitudinal and shear waves simultaneously in the presence of elastic-plastic phase transition. The analyses of the Jacobian matrix of governing equations are carried out for elasticity and plasticity separately, and the complicate order in the light of magnitude of characteristic speeds is simplified when constructing the approximate Riemann solver. The radial return mapping algorithm originally proposed by Wilkins is not only applied for the plastic correction in the discretization of the constitutive law, but also used to determine the elastic limit state in the approximate Riemann solver. A cell-centered Lagrangian method equipped with this new HLLC-type approximate Riemann solver is developed. Typical and new devised test cases are provided to demonstrate the performance of proposed method.

在这项工作中，研究了二维平面几何中的弹塑性模型，并提出了一种新的 HLLC 型近似黎曼求解器 (HLLCN)。新的近似黎曼求解器的主要特点是在存在弹塑性相变的情况下，它几乎同时包含了所有应力波，例如弹性波、塑性波、纵波和剪切波。控制方程的雅可比矩阵分别对弹性和塑性进行分析，构造近似黎曼求解器时，根据特征速度的大小简化了复杂的阶次。Wilkins最初提出的径向回归映射算法不仅应用于本构律离散化中的塑性修正，但也用于确定近似黎曼求解器中的弹性极限状态。开发了配备这种新的 HLLC 型近似黎曼求解器的以单元格为中心的拉格朗日方法。提供了典型的和新设计的测试用例来证明所提出方法的性能。