In this paper it is first shown that the linear evolution equations for a generalized thermoelastic solid generate a C0 semigroup. Next an analysis of the long time evolution behaviour yields the some results known for classical thermoelasticity: generically, the natural state is asymptotically stable.
Most three dimensional constitutive relations that have been developed to describe the behavior of bodies are correlated against one dimensional and two dimensional experiments. What is usually lost sight of is the fact that infinity of such three dimensional models may be able to explain these experiments that are lower dimensional. Recently, the notion of maximization of the rate of entropy production has been used to obtain constitutive relations based on the choice of the stored energy and rate...
One of the main question arising in Extended Thermodynamics concerns the physical meaning of the temperature far from equilibrium. Some authors define thermodynamic temperature the inverse of the coefficient linking the entropy flux with the heat flux. Other authors, instead, define non-equilibrium temperature the inverse of the partial derivative of entropy with respect to energy, at density and heat flux constant. The aim of this paper is to determine the expression of entropy flux in some...
We performe an exponential decay analysis for a Timoshenko-type system under the thermal effect by constructing the Lyapunov functional. More precisely, this thermal effect is acting as a mechanism for dissipating energy generated by the bending of the beam, acting only on the vertical displacement equation, different from other works already existing in the literature. Furthermore, we show the good placement of the problem using semigroup theory.
The constitutive equations of rate type for a class of thermo-hypo-elastic materials are derived within the framework of the extended irreversible thermodynamics.
It is shown, in the context of the Thermomechanics of simple materials with memory, that frame indifference and, equivalently, rotation invariance are necessary consequences of the laws of classical Mechanics and the definition of the stress matrix and heat flux vector.
We characterize the general solutions to certain symmetric systems of linear partial differential equations with tensor functionals as unknowns. Then we determine the solutions that are physically meaningful in suitable senses related with the constitutive functionals of two simple thermodynamic bodies with fading memory that are globally equivalent, i.e. roughly speaking that behave in the same way along processes not involving cuts. The domains of the constitutive functionals are nowhere dense...