Nonlinear Elasticity in a Deforming Ambient Space

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• 作者：Arash Yavari ; Arkadas Ozakin ; Souhayl Sadik
• 关键词：Geometric mechanics ; Nonlinear elasticity ; Deforming ambient space
• 刊名：Journal of Nonlinear Science
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：26
• 期：6
• 页码：1651-1692
• 全文大小：919 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics
  Analysis
  Mathematical and Computational Physics
  Mechanics
  Applied Mathematics and Computational Methods of Engineering
  Economic Theory
  
• 出版者：Springer New York
• ISSN：1432-1467
• 卷排序：26

文摘

In this paper, we formulate a nonlinear elasticity theory in which the ambient space is evolving. For a continuum moving in an evolving ambient space, we model time dependency of the metric by a time-dependent embedding of the ambient space in a larger manifold with a fixed background metric. We derive both the tangential and the normal governing equations. We then reduce the standard energy balance written in the larger ambient space to that in the evolving ambient space. We consider quasi-static deformations of the ambient space and show that a quasi-static deformation of the ambient space results in stresses, in general. We linearize the nonlinear theory about a reference motion and show that variation of the spatial metric corresponds to an effective field of body forces.