叠加型A-F类随动强化模型塑性应变的数值计算法

Numerical algorithm of plasticity with superposed A-F kinematic hardening rule

以Chaboche随动强化模型为例,在M isses屈服准则及正交流动准则的前提下,推导了叠加型A rm-strong-F rederick(A-F)类随动强化模型塑性应变的数值计算法,联合利用四阶龙格-库塔法与径向返回法实现数值计算中的内部平衡迭代。同时推导了统一切向矩阵以便确定每一平衡迭代后的试算应变。利用AN SY S提供的U PF s将算法嵌入到AN SY S有限元程序,实现了叠加型A-F类随动强化模型塑性应变的数值计算,并利用四边形单元模拟了单轴循环加载时的棘轮应变,计算结果能够很好地与实验值吻合。

Taking Chaboche kinematic hardening rule as example, numerical algorithm of plasticity with superposed several Armstrong-Frederick （A-F） kinematic hardening rule was developed under the assumption of von Misses yield criterion and normal plasticity flow rule. Internal iteration was successfully implemented by combining the radial return mapping algorithm with the fourth-order Runge-Kuta algorithm. The consistent tangent matrix was also deduced to determine the trial strain at the end of every internal iteration. The algorithm was inserted into the FEA code ANSYS by its User Programmable Features（UPFs）, which allow user to write his own plasticity laws. The algorithm and the UPFs code were verified by a single square element which can represent the situation of uniaxial cyclic loading. The stress and strain hysteresis loop was worked out, and the ratcheting strain was in good agreement with that obtained from experiments.