有限变形的三维粘弹性本构模型(英文)

A Three-dimensional Viscoelastic Constitutive Model of Finite Deformation

遗传积分形式与弹性元件和粘壶串并联表示的微分形式可以描述高聚物小变形情况下的粘弹性特性.文章以这些小变形的本构模型为起点,推出有限变形下的本构模型.一个有限变形过程分解成一系列微小变形子过程.小变形子过程中,应力的转动变化由弹性本构方程确定,主应力的变化由弹性元件和粘壶串并联结构的模型确定,这样提出了一个满足客观性原理的有限变形的粘弹性本构模型.模型材料参数随应变率而变,所以模型适合于从准静态到冲击载荷的较宽应变率范围.作为应用,计算了简单剪切有限变形,就建议的模型与现有的模型进行了比较,结果表明建议的模型能够描述高聚物有限变形情况下的粘弹性性质.

Hereditary integral formulations and differential formulations identified with spring and dashpot constructions can express the viscoelastic behaviors of polymeric materials at small deformations. In this paper, the models of small deformation serve as a starting point for the development of the viscoelastic constitutive models of finite deformation. A process of finite deformation is decomposed into a series of sub-processes of small deformation. The rotations of stress in sub-processes are determined by elastic constitutive equation. The changes in the principal stress are calculated using the spring and dashpot constructions. Then, a viscoelastic constitutive model, which satisfies the principle of objectivity, is presented. Such form of constitutive model in principle can be suitable for a range of strain-rates, e.g. either for quasi-static loading or for impact loading, with different material parameters in different strain-rates. As an application example, the simple shear deformation is computed to show that the proposed model can adequately well describe the viscoelastic behavior for polymers at finite deformations.