The paper presents the strategy for automatic generating a plastic region in the parametric integral equation system (PIES) and its spread during the incremental process of solving elastoplastic problems. Instead of some preliminary research on the not known a priori plastic zone, it is found automatically on the basis of stresses on the boundary and then it propagates considering the current stress state. The presented strategy requires the PIES method as an efficient approach for solving boundary value problems and several algorithms of computational geometry. The effectiveness of PIES comes from the lack of discretization of the plastic zone, which is defined globally by surface patches known from computer graphics. Several examples provided confirm the validity of the proposed approach.

本文提出了一种在参数积分方程系统（PIES）中自动生成塑性区域的策略，以及在解决弹塑性问题的增量过程中其可扩展性的策略。代替对未知的先验塑性区的一些初步研究，它是根据边界上的应力自动找到的，然后考虑当前应力状态进行传播。提出的策略要求使用PIES方法作为解决边值问题的有效方法，并且需要使用几种计算几何算法。PIES的有效性来自于缺乏塑料区的离散化，而塑料区的离散化是由计算机图形学已知的表面补丁整体定义的。提供的几个例子证实了该方法的有效性。