增量型各向异性损伤理论与数值分析

考虑到目前各向异性损伤理论存在一些不足,该文在增量型各向异性损伤理论的框架下,引入二阶对称张量,构造四阶对称有效损伤张量,建立了有效应力方程.类似于塑性流动分析方法,定义了增量弹性应力-应变关系.利用von Mises塑性屈服准则,并考虑各向异性损伤效应,推导出四阶对称的弹-塑性变形损伤刚度张量,其对称性反映了材料的固有特性.根据物体的变形和现时损伤状态,构造了材料损伤演化方程,方程中各项具有明确的物理意义.通过对Al2024-T3金属薄板单向拉伸的有限元分析,确定了损伤演化参数,验证了损伤演化方程的正确性.此外还对含孔口薄板做有限元模拟,讨论了反力-位移曲线的变化规律以及它所揭示变形性质,给出了损伤场的分布规律.

INCREMENTAL ANISOTROPIC DAMAGE THEORY AND ITS NUMERICAL ANALYSIS

Under the framework of incremental anisotropic damage theory, this paper addresses the study of construction of the effect damage tensor and the effective stress equation using second-order symmetrical damage tensor. The incremental elastic stress-strain relation is derived. The process is similar to the analysis in plastic flow. Using von Mises yield criterion with anisotropic damage involved, the fourth-order symmetrical elasto-plastic-damage stiffness tensor is obtained. It reflects the intrinsic behaviour in material deformation. The damage evolution equation is constructed which is proportional to the equivalent plastic strain and the present damage. By simulating Al2024-T3 sheet metal in uni-axial tension, the damage parameters are determined. The validity of the damage evolution is verified by comparising the computed damage values with the experimental ones. This paper also presents some discussion on the damage distribution in a rectangular plate with a center hole.