Comparison of results from four linear constitutive relations in isotropicfinite elasticity

We use four linear constitutive relations to study finite deformations of a biaxially loaded elastic membrane, triaxially loaded cube, and simple exte nsional 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 r elationship between the Cauchy stress tensor and the Almansi-Hamel strain t ensor) predict load-deformation curves that qualitatively agree with most o f the test observations. A similar conclusion holds when the body is assume d to be incompressible. (C) 2000 Elsevier Science Ltd. All rights reserved.