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Mathematics and Mechanics of Solids
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Must Elastic Materials be Hyperelastic?

M.M. Carroll

Department of Mechanical Engineering and Materials Science, Rice University, Houston, TX 77251-1892, USA

Rivlin's observation that elastic stress response that does not derive from a strain energy (Cauchy elasticity) admits negative work in closed cycles of deformations is demonstrated for specific isotropic stress responses and for a simple closed cycle of deformation. It is concluded that elastic materials must be hyperelastic.

Key Words: finite elasticity • Cauchy elasticity • hyperelasticity • strain energy

This version was published on June 1, 2009

Mathematics and Mechanics of Solids, Vol. 14, No. 4, 369-376 (2009)
DOI: 10.1177/1081286508099385
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