A theory of hyperelasticity of multi-phase media with surface/interface energy effect
A theory of hyperelasticity of multi-phase media with surface/interface energy effect
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DOI：
10.1007/s00707-005-0286-3
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发表时间：
2006-02
期刊：
影响因子：
2.7
通讯作者：
Zhuping Huang;Jianxiang Wang
中科院分区：
文献类型：
--
作者：
Zhuping Huang;Jianxiang Wang
在求解具有表面/界面能效应的多相超弹性介质中的应力场边值问题时，除了连续介质力学中的经典控制方程外，还需要两类控制方程。第一种是界面本构关系，第二种是界面牵引力不连续条件，即Young-Laplace方程。本文在有限变形框架下，用拉格朗日描述和欧拉描述给出了界面能量形式的界面本构关系，并作为特例给出了各向同性界面的界面应力表达式。然后，通过引入一种虚拟的无应力位形，提出了具有界面能效应的多相超弹性介质的新能量泛函。泛函考虑了界面能和界面应力引起的反映材料固有物理性质的“残余”弹性场。所有的场方程，包括广义的Young-Laplace方程，都可以从这个泛函的定态条件中得到。用简单的例子说明了本理论。本文的结果为研究有限变形条件下考虑表面/界面能效应的多相超弹性体的弹性静力学问题提供了一个理论框架。
In addition to the classical governing equations in continuum mechanics, two kinds of governing equations are necessary in the solution of boundary-value problems for the stress fields in multi-phase hyperelastic media with the surface/interface energy effect. The first is the interface constitutive relation, and the second are the discontinuity conditions of the traction across the interface, namely, the Young-Laplace equations. In this paper, the interface consitutive relations are presented in terms of the interface energy in both Lagrangian and Eulerian descriptions within the framework of finite deformation, and the expressions of the interface stress for an isotropic interface are given as a special case. Then, by introducing a fictitious stress-free configuration, a new energy functional for multi-phase hyperelastic media with interface energy effect is proposed. The functional takes into account the interface energy and the interface stress-induced ``residual'' elastic field, which reflects the intrinsic physical properties of the material. All field equations, including the generalized Young-Laplace equation, can be derived from the stationary condition of this functional. The present theory is illustrated by simple examples. The results in this paper provide a theoretical framework for studying the elastostatic problems of multi-phase hyperelastic bodies that involve surface/interface energy effects at finite deformation.