On the adequacy of the existing restrictions on the constitutive relations to ensure reasonable elastic response of compressible bodies

Abstract

Abstract We show that even when the constitutive relations for the elastic response of compressible bodies satisfy the empirical, Baker–Ericksen and ordered forces inequalities and ellipticity restrictions, they could result in physically unrealistic response. We pick a constitutive relation that satisfies the above inequalities and is also globally elliptic but its response to both uniaxial extension and inflation at constant length is physically unrealistic, based on the available experimental observations. However, the Coleman–Noll, pressure–compression, tension–extension and invertibility of force-stretch conditions and that proposed in Carroll and McCarthy (1995) are violated by this constitutive relation.