平面问题各向同性弹性非线性本构方程

The Isotropic Non-linear Elastic Constitutive Equations of Plane Problem

基于张量函数得到的非线性各向同性材料的本构方程是完备的,不可约的。张量不变量、标量不变量表示的张量本构方程虽然在任意坐标系下都成立、具有普适性,但是实际应用仍需要转换到特定坐标系,才能和几何方程、平衡方程一起,组成完备的方程组求解弹性力学问题。将不变量表示的各向同性非线性本构方程,退化到笛卡尔直角坐标系下,推导出各向同性材料平面问题(平面应力与平面应变)的应力-应变方程,得到的本构方程是非线性的,并且将方程退化为线性与胡克定律比较研究。

The non-linear constitutive equation of isotropie material on the basis of tensor functions is complete and irreducible. The function expressed by tensor invariants and scalar invariants is correct and universal in arbitrary coordinate. It still needs to be converted into a specific coordinate system, if we want to solve the problems in the practical application. Tensor constitutive equation is degenerated to Cartesian rectangular coordinate system. The stress and strain relationship about the plane problem （plane stress and plane strain） of isotropic materials is de- rived. These constitutive equations are nonlinear, and these equations are reduced to linear and compared with Hookeg law.