The aim of this paper is to develop an effective finite volume method for numerical simulation of the adiabatic shear bands (ASB) formation processes. A formation of ASB happens at high-speed shear strains of ductile materials. A numerical simulation of such problems using Lagrangian approach is associated with some problems, the main one of which is a mesh distortion at large deformations. We use Eulerian approach to describe a motion of the non-linear elasto-plastic material. More specifically, we consider a modification of a well-known hypoelastic Wilkins model. In this paper we suggest a numerical method for modeling of high-speed shear deformations on two-dimensional meshes. The method is verified on the three test problems suggested by other authors.

本文的目的是开发一种有效的有限体积方法，用于绝热剪切带（ASB）形成过程的数值模拟。在韧性材料的高速剪切应变下会形成ASB。使用拉格朗日方法对此类问题进行的数值模拟与某些问题相关，其中主要问题是大变形时的网格变形。我们使用欧拉方法来描述非线性弹塑性材料的运动。更具体地说，我们考虑对著名的低弹性威尔金斯模型的修改。在本文中，我们提出了一种用于二维网格上高速剪切变形建模的数值方法。该方法在其他作者提出的三个测试问题上得到了验证。