Abstract: Lagrangian formulations of Hill’s linear isotropic hyperelastic material models based on the one-parameter (r) Itskov 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 hyperelastic material models are implemented into the commercial finite element MSC.Marc code. It is shown that the Pelzer isotropic hyperelastic material model provides the best fit between the dependences of the resultant moment and the increase in the length of the rod on the twist angle and the results of computer simulation in the problem of torsion of a rod from the Mooney-Rivlin material.

Cite: Rotanova T.A. , Korobeynikov S.N. , Larichkin A.Y.
Hyperelasticity models extending Hooke's law from the region of small strains to moderate ones
17th International Conference of Numerical Analysis and Applied Mathematics 23-28 Sep 2019