非线性横观各向同性弹性材料的本构方程及其势函数

Nonlinear Constitutive Equations and Potential Function of Transversely Isotropy Elastic Materials

研究了非线性Green弹性材料弹性张量独立分量,归纳推导出横观各向同性Green弹性材料、各向同性非线性弹性材料独立的弹性常数个数。从张量函数出发,用含有高阶弹性张量的张量多项式,推导出四阶非线性横观各向同性,各向同性材料Green弹性材料本构方程及其势函数。并将本构方程及其势函数用张量不变量,标量不变量表示。证明了方程是完备的,不可约的,满足张量函数表示定理。

The independent components of elastic tensor in nonlinear Green elastic materials were studied. The numbers of independent elastic constants were derived for transversely isotropy and isotropy Green elastic materials. From tensor function, the constitutive equations and Potential Function of 4th order transversely isotropy nonlinear Green elastic materials and isotropy Green elastic materials were derived by tensor polynomial with high order elasticity tensor. The constitutive equations and potential functions can be expressed as tensor invariant and scalar invariant. The equations are proved complete and irreducible, and satisfy the law of tensor function expressions.