Journal ArticleDOI
On the consequences of the constraint of incompressibility with regard to a new class of constitutive relations for elastic bodies: small displacement gradient approximation
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In this article, the consequences of the constraint of incompressibility in a subclass of implicit constitutive relations are studied for Cauchy elasticity, where the deformation gradient is defined as the sum of the stress and deformation of the body.Abstract:
Recently, there has been an interest in the development of implicit constitutive relations between the stress and the deformation gradient, to describe the response of elastic bodies as such constitutive relations are capable of describing physically observed phenomena, in which classical models within the construct of Cauchy elasticity are unable to explain. In this paper, we study the consequences of the constraint of incompressibility in a subclass of such implicit constitutive relations.read more
Citations
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Journal ArticleDOI
A note on the linearization of the constitutive relations of non-linear elastic bodies
TL;DR: In this article, a proper justification can be provided for such models within the context of the new class of constitutive relations that have been developed to describe the response of elastic bodies by Rajagopal [19], and these models can be generalized to also describe the inelastic response in the small strain regime.
Book ChapterDOI
A Review of Implicit Constitutive Theories to Describe the Response of Elastic Bodies
TL;DR: In this paper, implicit constitutive relations for elastic, electro- and magneto-elastic and thermoelastic bodies are discussed for boundary-value problems confining attention to some specific forms of implicit relations.
Journal ArticleDOI
Representations for implicit constitutive relations describing non-dissipative response of isotropic materials
TL;DR: A methodology for obtaining implicit constitutive representations involving the Cauchy stress and the Hencky strain for isotropic materials undergoing a non-dissipative process is developed in this article.
Journal ArticleDOI
Implicit equations for thermoelastic bodies
TL;DR: In this article, the authors generalize the recent implicit models that have been put into place to describe the elastic response of bodies when thermal effects come into play and obtain constitutive relations that allow the linearized strain to be a non-linear function of the stress and temperature.
References
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Book
The non-linear field theories of mechanics
TL;DR: A theory aiming to describe their mechanical behavior must take heed of their deformability and represent the definite principles it obeys as mentioned in this paper, which is not the case in modern physics, since it concerns solely the small particles of matter.
Journal ArticleDOI
On Implicit Constitutive Theories
TL;DR: In this paper, the authors discuss implicit constitutive theories for the Helmholtz potential that depends on both the stress and strain, and which does not dissipate in any admissible process.
Journal ArticleDOI
The elasticity of elasticity
TL;DR: In this article, the authors argue that the usual interpretation of what one means by "elasticity" is much too insular and illustrate their thesis by introducing implicit constitutive theories that can describe the non-dissipative response of solids.