Some Restrictions on Constitutive Equations; Discussion Paper

Abstract

This paper presents a clear and concise discussion of concepts associated with the stability of equilibrium configurations of an elastic body subjected to dead-loading conditions which generate finite deformations. Thermal effects are not specifically included, although analogous considerations will arise in the extension to the more general problem of thermodynamic equilibrium. The development of the Hadamard stability condition is presented in terms of the strain energy density, U, a function of the deformation gradient tensor x_i,A of the deformed position, x_i, with respect to the reference position, X_A. It is shown that the Hadamard condition constitutes a local convexity condition in the neighbourhood of the equilibrium configuration at each material point of the body.