Third-Order Constitutive Law for Nonlinear Elastic Materials
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摘要: 推导了可压和不可压非线性弹性体的本构方程.应力张量,作为以单个应变张量为变量的张量值函数,用含有高阶弹性张量的张量多项式来表示.利用各种对称性来简化这些表达式,最后得到了各向同性情况下的本构方程和应变能函数.得到的表达式是完备和不可约的,满足张量函数的表示定理.Abstract: A rigorous derivation of constitutive laws for nonlinear behavior of compressible and incompressible elasticity is presented. As a tensor-valued function with a single tensor variable, i.e. strain, stress is expressed as a tensor polynomial that contains high order elasticity tensors. Various symmetric features of these tensors are then introduced to simplify the expression. Finally, for isotropic material the constitutive laws and strain energy functions are obtained. The expressions satisfy the criterion known as representation theorem for tensor functions and are complete and irreducible.
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Key words:
- non-linear /
- strain energy /
- constitutive equations
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