统一粘塑性本构方程一致切线刚度矩阵的研究

Research on consistent tangent modulus for unified viscoplastic constitutive equations

统一粘塑性本构方程是微分或增量形式的方程组,内变量是隐式的,一致切线刚度矩阵很难给出明确的表达式.针对包含热恢复项的统一的粘塑性本构方程,在向后欧拉积分的基础上,为本构模型推导和确定了一个新的考虑率相关塑性的一致切线刚度矩阵(Consistent tangent modulus)的表达式,并在通用的有限单元分析程序MARC中实现.通过一些算例的有限元分析,检验了一致切线刚度矩阵的可行性.

Unified viscoplasticity constitutive equations are a system of integral or incremental equations with implied internal variables. So,it is difficult to provide a well-defined expression of the consistent tangent modulus. Based on the backward Euler＇s integral for unified viscoplasticity constitutive equations, a new expression of consistent tangent modulus was derived for rate-dependent plasticity. The constitutive equations and consistent tangent modulus expression were implemented in a commercial finite element code-MARC. The numerical examples of finite elements verify the feasibility of consistent tangent modulus.