Comparison of results from four linear constitutive relations in isotropic finite elasticity

We use four linear constitutive relations to study finite deformations of a biaxially loaded elastic membrane, triaxially loaded cube, and simple extensional and simple shearing deformations of an elastic body. In each case, the body is assumed to be isotropic and homogeneous. It is shown that only the neoHookean relation (a linear relation between the Cauchy stress tensor and the left Cauchy-Green tensor) and the Signorini's relation (a linear relationship between the Cauchy stress tensor and the Almansi-Hamel strain tensor) predict load-deformation curves that qualitatively agree with most of the test observations. A similar conclusion holds when the body is assumed to be incompressible. (C) 2000 Elsevier Science Ltd. All rights reserved.