论文标题
不可压缩物体中有限变形的相互定理
A Reciprocal Theorem for Finite Deformations in Incompressible Bodies
论文作者
论文摘要
麦克斯韦和贝蒂的相互定理是力学的基础，但迄今为止限于弹性体中的无限变形。在本手稿中，我们提出了一个相互定理，该定理将特定的大变形边界值问题的解决方案与不可压缩的身体相关。这些解决方案显示出相同满足麦克斯韦 - 贝蒂定理的满足。该定理具有多种潜在的应用，例如开发替代方便的实验设置，用于研究通过散装和界面空化来研究材料故障，并利用更容易的数值实现等效辅助边界价值问题。注意到定理的以下显着特征：（i）它适用于静态功能，（ii）它允许大变形，（iii）具有多个潜在孔的通用身体形状，以及（iv）任何一般的边界条件类型。
The reciprocal theorems of Maxwell and Betti are foundational in mechanics but have so far been restricted to infinitesimal deformations in elastic bodies. In this manuscript, we present a reciprocal theorem that relates solutions of a specific class of large deformation boundary value problems for incompressible bodies; these solutions are shown to identically satisfy the Maxwell-Betti theorem. The theorem has several potential applications such as development of alternative convenient experimental setups for the study of material failure through bulk and interfacial cavitation, and leveraging easier numerical implementation of equivalent auxiliary boundary value problems. The following salient features of the theorem are noted: (i) it applies to dynamics in addition to statics, (ii) it allows for large deformations, (iii) generic body shapes with several potential holes, and (iv) any general type of boundary conditions.
