Linear Response in Finite Elasticity

This paper presents objective finite elastic equations that reproduce the linear stress-strain behaviour observed in uniaxial tension tests with some materials. More generally, the new equations reduce to linear elastic equations when the deformation is a pure stretch. Further, the response of the proposed equations for the case of isotropic materials in uniaxial tension-compression and simple shear is examined. It is also shown how the new equations can be considered as linear approximations of general equations of finite elasticity.