TY - JOUR

T1 - A consistent isotropic spectral constitutive equation

T2 - The infinitesimal strain depends nonlinearly on the stress

AU - Shariff, M. H.B.M.

AU - Bustamante, R.

N1 - Publisher Copyright:
© 2020 The Authors

PY - 2020/3

Y1 - 2020/3

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85089991748&partnerID=8YFLogxK

U2 - 10.1016/j.apples.2020.100007

DO - 10.1016/j.apples.2020.100007

M3 - Article

AN - SCOPUS:85089991748

SN - 2666-4968

VL - 1

JO - Applications in Engineering Science

JF - Applications in Engineering Science

M1 - 100007

ER -