A Natural Generalization of Linear Isotropic Relations with Seth-Hill Strain Tensors to Transversely Isotropic Materials at Finite Strains

Hooke’s law was naturally generalized to finite strains by Hill in 1978, 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...

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Bibliographic Details
Published inMathematical problems in engineering Vol. 2016; no. 2016; pp. 1 - 9
Main Authors Zhi-qiao, Wang, Yu, Wang
Format Journal Article
LanguageEnglish
Published Cairo, Egypt Hindawi Publishing Corporation 01.01.2016
Hindawi Limited
Subjects
Conjugates
Constitutive equations
Constitutive relationships
Deformation
Elasticity
Hookes law
Isotropic material
Mathematical analysis
Mathematical models
Shear stress
Softening
Stiffening
Strain
Studies
Tensors
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Summary:Hooke’s law was naturally generalized to finite strains by Hill in 1978, 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.
Bibliography:ObjectType-Article-1
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ISSN:1024-123X
1563-5147
DOI:10.1155/2016/7473046