Continuum Dynamics on Manifolds: Application to Elasticity of Residually-Stressed Bodies

Raz Kupferman, Elihu Olami, Reuven Segev

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

This paper is concerned with the dynamics of continua on differentiable manifolds. We present a covariant derivation of the equations of motion, viewing motion as a curve in an infinite-dimensional Banach manifold of embeddings of a body manifold in a space manifold. Our main application is the motion of residually-stressed elastic bodies, where the residual stresses result from a geometric incompatibility between body and space manifolds. We then study a particular example of elastic vibrations of a two-dimensional curved annulus embedded in a sphere.

Original languageEnglish
Pages (from-to)61-84
Number of pages24
JournalJournal of Elasticity
Volume128
Issue number1
DOIs
StatePublished - 1 Jun 2017

Keywords

  • Continuum dynamics
  • Differentiable manifolds
  • Kinetic energy
  • Residual stress
  • Riemannian metric

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