【摘要】 研究了非线性Green弹性材料弹性张量独立分量,归纳推导出各向异性Green弹性材料、具有一个对称面Green弹性材料、正交各向异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,推导出三阶非线性正交各向异性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。详细研究Green弹性材料势函数存在的充分和必要条件,给出并证明了具有普适性的势函数存在定理。更多还原

【Abstract】 The independent components of elastic tensor in nonlinear Green elastic materials were studied.The numbers of independent elastic constants were derived for aeolotropy Green elastic materials,Green elastic materials with a plane of symmetry and three order nonlinear orthogonal aeolotropy elastic materials.From tensor function,the constitutive equations and potential function of three order orthogonal aeolotropy nonlinear Green elastic materials were derived by tensor polynomial with high order elasticity tensor.The constitutive equations and the 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.The adequate and necessary conditions under which elastic material potential funtions exist were fully studied and the general existing principle of potential functions are presented and proved.更多还原