Thermodynamics and the constitutive relations for second sound in crystals

2005 ◽  
pp. 20-43 ◽  
Author(s):  
Bernard D. Coleman ◽  
Mauro Fabrizio ◽  
David R. Owen
Keyword(s):  
Constitutive Relations ◽  
Second Sound

Thermodynamics and the Constitutive Relations for Second Sound in Crystals

1986 ◽  
pp. 171-185 ◽  
Author(s):  
B. D. Coleman ◽  
M. Fabrizio ◽  
D. R. Owen
Keyword(s):  
Constitutive Relations ◽  
Second Sound

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.

Second sound

AccessScience ◽  
2015 ◽  
Keyword(s):  
Second Sound

Time-domain finite element analysis of viscoelastic structures with fractional derivatives constitutive relations

AIAA Journal ◽  
1997 ◽  
Vol 35 ◽  
pp. 1630-1637
Author(s):  
Mikael Enelund ◽  
B. L. Josefson
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Time Domain ◽  
Fractional Derivatives ◽  
Constitutive Relations ◽  
Element Analysis

Normal Fluid Density, Second Sound, and Fourth Sound in an Anisotropic Superfluid

1973 ◽  
Vol 31 (14) ◽  
pp. 870-873 ◽  
Author(s):  
W. M. Saslow
Keyword(s):  
Second Sound ◽  
Fluid Density ◽  
Normal Fluid ◽  
Fourth Sound

scholarly journals Phase-field gradient theory

2021 ◽  
Vol 72 (2) ◽  
Author(s):  
Luis Espath ◽  
Victor Calo
Keyword(s):  
Free Energy ◽  
Field Equation ◽  
Field Gradient ◽  
Phase Field ◽  
Constitutive Relations ◽  
The Body ◽  
Second Grade ◽  
Gradient Theory ◽  
Boundary Edge ◽  
Field Equations

AbstractWe propose a phase-field theory for enriched continua. To generalize classical phase-field models, we derive the phase-field gradient theory based on balances of microforces, microtorques, and mass. We focus on materials where second gradients of the phase field describe long-range interactions. By considering a nontrivial interaction inside the body, described by a boundary-edge microtraction, we characterize the existence of a hypermicrotraction field, a central aspect of this theory. On surfaces, we define the surface microtraction and the surface-couple microtraction emerging from internal surface interactions. We explicitly account for the lack of smoothness along a curve on surfaces enclosing arbitrary parts of the domain. In these rough areas, internal-edge microtractions appear. We begin our theory by characterizing these tractions. Next, in balancing microforces and microtorques, we arrive at the field equations. Subject to thermodynamic constraints, we develop a general set of constitutive relations for a phase-field model where its free-energy density depends on second gradients of the phase field. A priori, the balance equations are general and independent of constitutive equations, where the thermodynamics constrain the constitutive relations through the free-energy imbalance. To exemplify the usefulness of our theory, we generalize two commonly used phase-field equations. We propose a ‘generalized Swift–Hohenberg equation’—a second-grade phase-field equation—and its conserved version, the ‘generalized phase-field crystal equation’—a conserved second-grade phase-field equation. Furthermore, we derive the configurational fields arising in this theory. We conclude with the presentation of a comprehensive, thermodynamically consistent set of boundary conditions.

Stability conditions for thermodiffusion Timoshenko system with second sound

2021 ◽  
Vol 72 (4) ◽  
Author(s):  
Moncef Aouadi ◽  
Anderson Ramos ◽  
Alberto Castejón
Keyword(s):  
Stability Conditions ◽  
Second Sound ◽  
Timoshenko System

scholarly journals Polyconvex hyperelastic modeling of rubberlike materials

2021 ◽  
Vol 43 (7) ◽  
Author(s):  
Cyprian Suchocki ◽  
Stanisław Jemioło
Keyword(s):  
Experimental Data ◽  
Power Law ◽  
Curve Fitting ◽  
Constitutive Relations ◽  
Data Sets ◽  
Power Law Model ◽  
Stored Energy ◽  
Data Approximation ◽  
Exponential Power ◽  
Hyperelastic Models

AbstractIn this work a number of selected, isotropic, invariant-based hyperelastic models are analyzed. The considered constitutive relations of hyperelasticity include the model by Gent (G) and its extension, the so-called generalized Gent model (GG), the exponential-power law model (Exp-PL) and the power law model (PL). The material parameters of the models under study have been identified for eight different experimental data sets. As it has been demonstrated, the much celebrated Gent’s model does not always allow to obtain an acceptable quality of the experimental data approximation. Furthermore, it is observed that the best curve fitting quality is usually achieved when the experimentally derived conditions that were proposed by Rivlin and Saunders are fulfilled. However, it is shown that the conditions by Rivlin and Saunders are in a contradiction with the mathematical requirements of stored energy polyconvexity. A polyconvex stored energy function is assumed in order to ensure the existence of solutions to a properly defined boundary value problem and to avoid non-physical material response. It is found that in the case of the analyzed hyperelastic models the application of polyconvexity conditions leads to only a slight decrease in the curve fitting quality. When the energy polyconvexity is assumed, the best experimental data approximation is usually obtained for the PL model. Among the non-polyconvex hyperelastic models, the best curve fitting results are most frequently achieved for the GG model. However, it is shown that both the G and the GG models are problematic due to the presence of the locking effect.

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