Summary
It is shown that a compressible elastic body — not necessarily homogeneous or isotropic — is hyperelastic provided the work done by all external forces acting on an arbitrary part of the body vanishes for every sufficiently smooth cyclic motion in which each material point returns to its initial position with a velocity equal to its initial velocity.
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References
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John, F, Plane Elastic Waves of Finite Amplitude Hadamard Materials and Harmonic Materials, Communications on Pure and Applied Mathematics, Volume XIX, 309 (1966).
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The results communicated in this paper were obtained in the course of an investigation supported by Contract N00014-75-C-0196 with the Office of Naval Research in Washington, D.C.
Dedicated to Clifford Truesdell on his 60 th Birthday
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Sternberg, E., Knowles, J.K. On the existence of an elastic potential for a simple material without memory. Arch. Rational Mech. Anal. 70, 19–30 (1979). https://doi.org/10.1007/BF00276379
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DOI: https://doi.org/10.1007/BF00276379