非线性弹性大变形问题的率型解法

A Rate Type Method for Large Deformation Problems of Nonllnear Elasticity

摘要: 本文分别采用Jaumann应力率、Truesdell应力率和Green-Naghdi应力率导出了非线性各向同性弹性体的率型本构表达形式,通过对Mooney-Rivlin材料的简单剪切大变形分析表明,三种率型的本构关系均与全量本构关系相等价。文中还给出了相应的率型变分原理,并采应Ritz法,数值求解了受单轴拉伸的矩形橡皮薄膜的大变形问题。
- 非线性弹性 /
- 次弹性 /
- 大变形 /
- 应力率张量
Abstract: In this paper, we obtain the rate-tvpe constitutive expressions of the nonlinear isotropic elastieity by using the Jaumann, Truesdell and Green-Naghdi stress rate respectively,Through analysing the simple shear deformation for Mooney-Rivlin material,three kinds of rate-type constitutive equations are verified to be equivalent to the original equation.Rate-type variational prineiples are also presented, and the Ritzmethod is used to obtain the numerical solution of a reetangular rubber membrane under uniaxial stretch.
- nonlinear elasticity /
- hypoelasticity /
- large deformation /
- stress rate tensor

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