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.
Second-order Effects in Elasticity, Plasticity and Fluid Dynamics, ed. M. Reiner, Macmillan, New York, 1964.
2.
Truesdell, C.Das ungelöste Hauptproblem der endlichen Elastizitätstheorie", Zeitschrift für Angewandte Mathematik Mechanik (ZAMM) 36, 97-103 (1956). English translation in Foundations of Elasticity Theory, Gordon and Breach, New York, 1965.
3.
Baker, M. and Ericksen, J.L.Inequalities restricting the form of the stress-deformation relations for isotropic elastic solids and Reiner-Rivlin fluids, Journal of the Washington Academy of Science 44, 33-35 (1954). Reprinted in Foundations of Elasticity Theory, Gordon and Breach, New York , 1965.
4.
Batra, R.Comparison of results from four linear constitutive relations in isotropic finite elasticity, International Journal of Non-Linear Mechanics36, 421-432 (2001).
5.
Truesdell, C. and Noll, W.The Non-linear Field Theories of Mechanics, Handbuch der Physik III/3, Springer, Berlin, 1965.
