率相关本构方程积分新算法

New Integration Algorithm of Rate Dependent Constitutive Equation

提出一种积分率相关本构方程的隐式积分新算法,引入0～1范围内的缩放因子λ对本构方程进行间接求解,可以避免直接求解等效塑性应变或等效塑性应变率时,由于其数值过大或过小而造成的收敛困难或收敛失败,实现对率相关本构方程的快速准确求解。以B-P统一本构方程及双曲正弦本构方程为例,验证了算法的可行性。结果表明,新算法对于准静态变形条件下的无硬化本构方程也可以得出准确的解。

A new implicit integration algorithm is developed to integrate the rate dependent constitutive equations quickly and accurately. The difficulties or failure of convergence during the direct solution can be effectively avoided by introducing the scaling factor λ ranging from 0 to 1. The whole integration procedure is illustrated by two examples, B-P unified constitutive equation and hyperbolic sine constitutive equation. The results show that numerical algorithm is unconditionally stable for an implicit integration method. The hyperbolic sine constitutive equation without harding behavior can also be solved successfully in the quais-static forming process.