On the constitutive relations for second sound in elastic solids

1992 ◽  
Vol 121 (1) ◽  
pp. 87-99 ◽  
Author(s):  
T. Sabri Öncü ◽  
T. Bryant Moodie
Keyword(s):  
Constitutive Relations ◽  
Second Sound ◽  
Elastic Solids

Propagation of thermoelastic waves across an interface with consideration of couple stress and second sound

2017 ◽  
Vol 24 (1) ◽  
pp. 235-257 ◽  
Author(s):  
Yueqiu Li ◽  
Peijun Wei ◽  
Changda Wang
Keyword(s):  
Couple Stress ◽  
Constitutive Relations ◽  
Elastic Solid ◽  
Free Energy Density ◽  
Second Sound ◽  
Elastic Solids ◽  
Reflection And Transmission ◽  
Dispersive Waves ◽  
Interfacial Conditions ◽  
Thermoelastic Waves

The reflection and transmission of thermoelastic waves across an interface between two different couple stress solids are studied based on the thermoelastic Green–Naghdi theory with consideration of second sound. First, some thermodynamic equations of a couple stress elastic solid are formulated and the function of free energy density is postulated. Second, equations of thermal motion and heat conduction of the couple stress elasticity are derived and constitutive relations with thermoelastic coupled effects are obtained. From these equations, four kinds of dispersive waves, namely, thermal-mechanically coupled MT1 wave and MT2 wave, uncoupled SV wave, and an evanescent wave that becomes the surface waves at interface, are derived. Then, the interfacial conditions of couple stress elastic solids with consideration of force stress, couple stress, and thermal effects are used to determine the amplitude ratios of the reflection and transmission waves with respect to the incident wave. The numerical results are validated by consideration of energy conservation.

scholarly journals Stretching of the mechanical-geometric model and two common nonlinear elastic solids

2021 ◽  
Vol 273 ◽  
pp. 07019
Author(s):  
Daniil Azarov
Keyword(s):  
Geometric Modeling ◽  
Strain Energy ◽  
Geometric Model ◽  
Constitutive Relations ◽  
Theory Of Elasticity ◽  
Elastic Solids ◽  
Hyperelastic Materials ◽  
Deformation Properties ◽  
Nonlinear Elastic ◽  
Nonlinear Theory Of Elasticity

The variety of hyperelastic materials and the design of new modifications and technical applications requires the development of a description of nonlinear deformation properties. The most commonly used constitutive relations of the Mooney-Rivlin and Yeoh models are based on polynomial decompositions. Mechanical-geometric modeling (hereinafter - MGM) is a new way of constructing constitutive relations and strain energy densities within the nonlinear theory of elasticity. In this paper, a comparison of the deformation behavior of MGM with the traditional Mooney-Rivlin and Yeoh models was carried out. Comparative analysis is accompanied by diagrams for uniaxial and biaxial stretching. The effectiveness of the new model was proved.

An implicit constitutive relation for describing the small strain response of porous elastic solids whose material moduli are dependent on the density

2021 ◽  
pp. 108128652110214
Author(s):  
KR Rajagopal
Keyword(s):  
Constitutive Relation ◽  
Constitutive Relations ◽  
Deformation Gradient ◽  
Short Note ◽  
Small Strain ◽  
Cauchy Stress ◽  
Porous Metals ◽  
Elastic Solids ◽  
Elastic Bodies ◽  
Implicit Equations

In this short note, we develop a constitutive relation that is linear in both the Cauchy stress and the linearized strain, by linearizing implicit constitutive relations between the stress and the deformation gradient that have been put into place to describe the response of elastic bodies (Rajagopal, KR. On implicit constitutive theories. Applications of Mathematics 2003; 28: 279–319), by assuming that the displacement gradient is small. These implicit equations include the classical linearized elastic constitutive approximation as well as some classes of constitutive relations that imply limiting strain in tension, as special subclasses. Moreover, the constitutive relations that are developed allow the material moduli to depend on the density; thus, they can be used to describe the response of porous materials, such as porous metals, bone, rocks, and concrete undergoing small deformations.

scholarly journals Implicit Type Constitutive Relations for Elastic Solids and Their Use in the Development of Mathematical Models for Viscoelastic Fluids

Fluids ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 131
Author(s):  
Vít Průša ◽  
K. R. Rajagopal
Keyword(s):  
Free Energy ◽  
Mathematical Models ◽  
Constitutive Relations ◽  
Viscoelastic Fluids ◽  
Elastic Response ◽  
Elastic Solids ◽  
New Models ◽  
Energy Storage Properties ◽  
New Perspective ◽  
Implicit Constitutive Relations

Viscoelastic fluids are non-Newtonian fluids that exhibit both “viscous” and “elastic” characteristics in virtue of the mechanisms used to store energy and produce entropy. Usually, the energy storage properties of such fluids are modeled using the same concepts as in the classical theory of nonlinear solids. Recently, new models for elastic solids have been successfully developed by appealing to implicit constitutive relations, and these new models offer a different perspective to the old topic of the elastic response of materials. In particular, a sub-class of implicit constitutive relations, namely relations wherein the left Cauchy–Green tensor is expressed as a function of stress, is of interest. We show how to use this new perspective in the development of mathematical models for viscoelastic fluids, and we provide a discussion of the thermodynamic underpinnings of such models. We focus on the use of Gibbs free energy instead of Helmholtz free energy, and using the standard Giesekus/Oldroyd-B models, we show how the alternative approach works in the case of well-known models. The proposed approach is straightforward to generalize to more complex settings wherein the classical approach might be impractical or even inapplicable.

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