Hyperelasticity models extending Hooke's law from the region of small strains to moderate ones

Abstract

Lagrangian formulations of Hill's linear isotropic hyperelastic material models based on the one-parameter (r) ltskov family of strain tensors are developed. These formulations are based on the use of pairs of conjugate Lagrangian stress and strain tensors. Fourth-order elasticity tensors are obtained for these material models. The developed formulations of isotropic hypere- lastic material models are implemented into the commercial finite element MSC.Marc code. lt is shown that the Pelzer isotropic hyperelastic material model is competitive with the Mooney-Rivlin material model.