粘塑性统一本构方程数值积分方法研究

A Numerical Integration Method for Unified Viscoplastic Constitutive Equations

本文提出了对粘塑性统一本构方程的隐式欧拉积分进行牛顿—拉夫森迭代的数值积分方法。推导出该数值积分的统一迭代格式;给出自动选取步长以及迭代收敛的准则;并对Miller的统一本构方程进行了数值求解。该法不但非常有效地克服了由于常微分方程组的刚性带来的数值困难,而且还易于控制数值误差。计算结果表明:本文所提出的方法是十分有效的。

The paper presents an implicit Euler's numerical integration method with Newton- Raphson iterations to integrate unified viscoplastic constitutive equations. The method not only can effectively overcome the numerical difficulty due to the stiff character of the ordinary differential equations, but also can easily control the numerical errors. A unified iterative scheme of the numerical integrations is derived, and the criteria of choosing automatically time steps and of iterative convergence are introduced. The numerical solution procedures are operated for Miller's unified viscoplatic constitutive equations, with results showing the effectiveness of method.