A natural generalization of linear isotropic relations with seth-Hill strain tensors to transversely isotropic materials at finite strains
Summary: Hooke's law was naturally generalized to finite strains by \textit{R. Hill} [``Aspects of invariance in solid mechanics'', Adv. Appl. Mech. 18, 1--75 (1978; \url{doi:10.1016/S0065-2156(08)70264-3})], by introducing the Seth-Hill strain and its conjugate stress. This paper presents the transversely isotropic relations, which are not only a natural extension of Hill's theory from isotropic materials to transversely isotropic materials, but also the natural generalization of the transversely isotropic Hooke's law from infinitesimal strains to moderate strains. This generalization introduces a class of transversely isotropic hyperelastic models, which are adopted to investigate the uniaxial stretch and the simple shear problems. Results show that the material responses for different constitutive equations are significantly different; the stiffening or softening behaviors of materials at moderate deformations can be described by the appropriate model with proper material parameters.
scientific article; zbMATH DE number 6953543
scientific article