Equilibrium shocks in plane deformations of incompressible elastic materials

Abstract

This paper is concerned with piecewise smooth plane deformations in an isotropic, incompressible elastic material. An explicit necessary and sufficient condition for the existence of piecewise homogeneous equilibrium states is established, and the set of all such states is precisely characterized. A particularly simple expression is derived for the “driving traction” on a surface of discontinuity in the deformation gradient.

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Abeyaratne, R., Knowles, J.K. Equilibrium shocks in plane deformations of incompressible elastic materials. J Elasticity 22, 63–80 (1989). https://doi.org/10.1007/BF00041104

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Keywords

  • Equilibrium State
  • Elastic Material
  • Deformation Gradient
  • Simple Expression
  • Plane Deformation