A consistent isotropic spectral constitutive equation: The infinitesimal strain depends nonlinearly on the stress

Recently, there have been several developments in nonlinear infinitesimal-strain stress constitutive relations to describe the response of elastic bodies. However, some of the nonlinear constitutive equations presented in the literature are unable to model both compressible and incompressible bodies...

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Autores principales:	M.H.B.M. Shariff, R. Bustamante
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2020
Materias:	Engineering (General). Civil engineering (General) TA1-2040
Acceso en línea:	https://doaj.org/article/78b0ed04c95e4a2a96d51829067a8299
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spelling	oai:doaj.org-article:78b0ed04c95e4a2a96d51829067a82992021-12-01T05:05:18ZA consistent isotropic spectral constitutive equation: The infinitesimal strain depends nonlinearly on the stress2666-496810.1016/j.apples.2020.100007https://doaj.org/article/78b0ed04c95e4a2a96d51829067a82992020-03-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S2666496820300078https://doaj.org/toc/2666-4968Recently, there have been several developments in nonlinear infinitesimal-strain stress constitutive relations to describe the response of elastic bodies. However, some of the nonlinear constitutive equations presented in the literature are unable to model both compressible and incompressible bodies. In this paper, we develop a spectral constitutive equation, where the infinitesimal strain depends nonlinearly on the stresses, and the incompressible behaviour is simply described as a special case obtained from the compressible elastic model, by just letting the value of the Poisson’s ratio equal to a half. The constitutive equation satisfies the Baker-Ericksen inequality and a specific expression for the constitutive equation is proposed to fit experimental data for the compression of a sample of rock. Several boundary value problems with homogeneous deformations and stresses are analysed. Spectral components for the fourth order tensor that is required for the analysis of the propagation of P- and S-waves are given.M.H.B.M. ShariffR. BustamanteElsevierarticleEngineering (General). Civil engineering (General)TA1-2040ENApplications in Engineering Science, Vol 1, Iss , Pp 100007- (2020)
institution	DOAJ
collection	DOAJ
language	EN
topic	Engineering (General). Civil engineering (General) TA1-2040
spellingShingle	Engineering (General). Civil engineering (General) TA1-2040 M.H.B.M. Shariff R. Bustamante A consistent isotropic spectral constitutive equation: The infinitesimal strain depends nonlinearly on the stress
description	Recently, there have been several developments in nonlinear infinitesimal-strain stress constitutive relations to describe the response of elastic bodies. However, some of the nonlinear constitutive equations presented in the literature are unable to model both compressible and incompressible bodies. In this paper, we develop a spectral constitutive equation, where the infinitesimal strain depends nonlinearly on the stresses, and the incompressible behaviour is simply described as a special case obtained from the compressible elastic model, by just letting the value of the Poisson’s ratio equal to a half. The constitutive equation satisfies the Baker-Ericksen inequality and a specific expression for the constitutive equation is proposed to fit experimental data for the compression of a sample of rock. Several boundary value problems with homogeneous deformations and stresses are analysed. Spectral components for the fourth order tensor that is required for the analysis of the propagation of P- and S-waves are given.
format	article
author	M.H.B.M. Shariff R. Bustamante
author_facet	M.H.B.M. Shariff R. Bustamante
author_sort	M.H.B.M. Shariff
title	A consistent isotropic spectral constitutive equation: The infinitesimal strain depends nonlinearly on the stress
title_short	A consistent isotropic spectral constitutive equation: The infinitesimal strain depends nonlinearly on the stress
title_full	A consistent isotropic spectral constitutive equation: The infinitesimal strain depends nonlinearly on the stress
title_fullStr	A consistent isotropic spectral constitutive equation: The infinitesimal strain depends nonlinearly on the stress
title_full_unstemmed	A consistent isotropic spectral constitutive equation: The infinitesimal strain depends nonlinearly on the stress
title_sort	consistent isotropic spectral constitutive equation: the infinitesimal strain depends nonlinearly on the stress
publisher	Elsevier
publishDate	2020
url	https://doaj.org/article/78b0ed04c95e4a2a96d51829067a8299
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A consistent isotropic spectral constitutive equation: The infinitesimal strain depends nonlinearly on the stress

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