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Nonlinear Elasticity in a Deforming Ambient Space

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  • Arash Yavari, Georgia Institute of Technology
  • ,
  • Arkadas Ozakin, Skytree, Inc.
  • ,
  • Souhayl Sadik

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.

Original languageEnglish
JournalJournal of Nonlinear Science
Pages (from-to)1651-1692
Number of pages42
Publication statusPublished - Dec 2016
Externally publishedYes

    Research areas

  • Deforming ambient space, Geometric mechanics, Nonlinear elasticity

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