A natural generalization of linear isotropic relations with seth-Hill strain tensors to transversely isotropic materials at finite strains
type: Item
instance of: scholarly article
title: A natural generalization of linear isotropic relations with seth-Hill strain tensors to transversely isotropic materials at finite strains
zbMATH Open document ID: 1400.74004
DOI: 10.1155/2016/7473046
author: Zhi-Qiao Wang
author: Yu Wang
published in: Mathematical Problems in Engineering
publication date: 2018-10-12T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 74A20
zbMATH DE Number: 6953543
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2016/7473046
OpenAlex ID: W2514529571
Wikidata QID: Q59141182
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description: scientific article; zbMATH DE number 6953543