On constitutive models of finite elasticity with possible zero apparent Poisson’s ratio

Abstract

The idea in this paper is to build a class of constitutive equations for highly compressible isotropic materials that, among others, are capable to describe a zero apparent Poisson’s ratio in the whole finite strain range, not only for moderate straining. This remarkable property is, for instance, observed in many soft materials with micro-structures such as sponges and polymeric foams with high porosities. It would then be suitable to describe their behavior within a macroscopic modeling framework. More specifically, herein by means of elementary considerations, we deduce adequate forms of strain-energy functions that are a priori decomposed into purely volumetric and volume-preserving parts. A class of compressible hyperelastic materials of the general Odgen type is obtained. It can consequently be specialized, for instance, to neo-Hookean, Mooney–Rivlin, and Varga’s model types as well. Furthermore, for the elastic parameters, a connection with the limiting case of linear elasticity is made whenever possible, in particular with the classical Poisson’s ratio, and with the bulk to shear moduli ratio.