Abstract
The equations governing the equilibrium of a finitely deformed elastic solid are derived from the Principle of Minimum Potential Energy. The possibility of the deformation gradient and the stresses being discontinuous across certain surfaces in the body — “equilibrium shocks” — is allowed for. In addition to the equilibrium equations, natural boundary conditions and traction continuity condition, a supplementary jump condition which is to hold across the surface of discontinuity is derived. This condition is shown to imply that a stable equilibrium shock must necessarily be dissipation-free.
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The results reported in this paper were obtained in the course of an investigation supported in part by the National Science Foundation through Grant CME 81-06581.
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Abeyaratne, R. An admissibility condition for equilibrium shocks in finite elasticity. J Elasticity 13, 175–184 (1983). https://doi.org/10.1007/BF00041234
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DOI: https://doi.org/10.1007/BF00041234