On a class of implicit constitutive relations for nonlinear elastic bodies

If an elastic body is defined as one that does not dissipate energy into heat, the classes of elastic bodies not only include the Green elastic solid, but also some types of implicit constitutive relations recently presented in the literature. In this paper one of such new implicit relations is stud...

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Bibliographic Details
Published inInternational journal of engineering science Vol. 200; p. 104089
Main Authors Shariff, M.H.B.M., Bustamante, R.
Format Journal Article
LanguageEnglish
Published Elsevier Ltd 01.07.2024
Subjects
Isotropic solid
Large elastic deformations
Spectral invariants
Transversely isotropic elastic solid
Two directions elasticity
Isotropic solid
Spectral invariants
Transversely isotropic elastic solid
Two directions elasticity
Large elastic deformations
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Summary:If an elastic body is defined as one that does not dissipate energy into heat, the classes of elastic bodies not only include the Green elastic solid, but also some types of implicit constitutive relations recently presented in the literature. In this paper one of such new implicit relations is studied in detail, wherein the energy function depend on the second Piola–Kirchhoff stress tensor and the Green Saint-Venant strain tensor. It is assumed that the function is anisotropic having two directions of anisotropy, thus the case of a transversely isotropic body and an isotropic body are special cases of the above function. Spectral invariants are used and explicit expressions for some second derivatives of the energy function are found. Such second derivatives appear in the implicit constitutive relation.
ISSN:0020-7225
1879-2197
DOI:10.1016/j.ijengsci.2024.104089