| 非线性弹性材料的三阶本构方程 |
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| 引用本文： | 王寿梅,徐明,李宁.非线性弹性材料的三阶本构方程[J].北京航空航天大学学报,2002,28(4):402-404. |
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| 作者姓名： | 王寿梅 徐明 李宁 |
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| 作者单位： | 北京航空航天大学飞行器设计与应用力学系 |
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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.
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| 关 键 词： | 非线性 应变能 本构方程 |
| 文章编号： | 1001-5965(2002)04-0402-03 |
| 收稿时间： | 2000-10-30 |
| 修稿时间： | 2000年10月30日 |
Third-Order Constitutive Law for Nonlinear Elastic Materials |
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| WANG Shou-mei,XU Ming,LI Ning.Third-Order Constitutive Law for Nonlinear Elastic Materials[J].Journal of Beijing University of Aeronautics and Astronautics,2002,28(4):402-404. |
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| Authors: | WANG Shou-mei XU Ming LI Ning |
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| Institution: | Beijing University of Aeronautics and Astronautics, Dept. of Flight Vehicle Design and Applied Mechanics |
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| 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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| Keywords: | non-linear strain energy constitutive equations |
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