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Journal of Engineering Mathematics
Published in: Journal of Engineering Mathematics 1/2021

01-04-2021

A class of transversely isotropic non-linear elastic bodies that is not Green elastic

Authors: R. Bustamante, K. R. Rajagopal

Published in: Journal of Engineering Mathematics | Issue 1/2021

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Abstract

An implicit constitutive relation is proposed to study transversely isotropic bodies. The relation is obtained assuming the existence of a Gibbs potential that depends on the second Piola–Kirchhoff stress tensor, from which the Green Saint-Venant strain tensor is obtained as the derivative with respect to the stress. The responses of unconstrained as well as inextensible bodies are studied, and some boundary value problems are analysed. An inextensible body, where the constraint of inextensibility appears only in tension is also considered.
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Appendix
Available only for authorised users
Footnotes
1
In several such works, exact solutions have been found for isotropic bodies that are inextensible in a specific direction [16], or else for bodies that are incompressible and inextensible in a specific direction [10].
 
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Metadata
Title
A class of transversely isotropic non-linear elastic bodies that is not Green elastic
Authors
R. Bustamante
K. R. Rajagopal
Publication date
01-04-2021
Publisher
Springer Netherlands
Published in
Journal of Engineering Mathematics / Issue 1/2021
Print ISSN: 0022-0833
Electronic ISSN: 1573-2703
DOI
https://doi.org/10.1007/s10665-021-10094-7

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