Nonlinear Elasticity in a Deforming Ambient Space

作者：Yavari Arash^*; Ozakin Arkadas; Sadik Souhayl

来源：Journal of Nonlinear Science, 2016, 26(6): 1651-1692.

DOI：10.1007/s00332-016-9315-8

• Geometric mechanics
• Nonlinear elasticity
• Deforming ambient space

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.

• 出版日期2016-12