弹塑性大变形率问题的变分原理和应用

VARIATIONAL PRINCIPLE OF RATE PROBLEM OF ELASTICPLASTIC LARGE DEFORMATION AND IT'S APPLICATION

本文根据Hiil(1958,1959)一般变分原理,采用流动坐标导出了弹塑性大变形及非线性率问题的,分别以初始和现时构形为参考状态的,适合于有限元计算的变分方程,并用根据该变分方程建立起来的有限元公式对处于平面应变条件下的,带有微小缩颈状初始几何缺陷的聚合物板的缩颈过程作了分析,分析时考虑了材料的硬化,本文所导出的变分方程适于分析包括金属塑性成形在内的弹塑性大变形过程。

In this paper, based on Hill's general variational principle(l958-1959), a variational equation in intitial configuration ( reference configuration) and current configuration ( reference configuration ) is derived using convetced coordinates.The derived variational equation is for large elastoplastic, double nonlinear rate problem and is suited for finite element caculation.As an applied example of the derived variational equation, necking of a plane strain ploymer sheet with a initial geometric inperfection ( initial neck ) is analysed using the finite formulation based on the derived variational equation. Work hardening of materials is considered.The derived variational equation in this paper is suitable for analysing large elastoplastic deformation problem including metal forming processes.