The equations of coupled thermoelasticity are considered in the case of stationary vibrations. The dimensional and order-of-magnitude analysis of the parameters occurring within these equations prompts the introduction of the new non-dimensionalisation scheme, highlighting the nearly-adiabatic nature of the resulting motions. The departure from the purely adiabatic regime is characterised by a ...

The recently introduced Finite Cell Method (FCM) combines the fictitious domain idea with the benefits of high-order Finite Elements. While previous publications concentrated on single-field applications, this paper demonstrates that the advantages of the method carry over to the multi-physical context of linear thermoelasticity. The ability of the method to converge with exponential rates is i...

In this work, we consider the coupled systems of linear unsteady partial differential equations, which arise in the modeling of poroelasticity processes. Stability estimates of weighted difference schemes for the coupled system of equations are presented. Approximation in space is based on the finite element method. We construct splitting schemes and give some numerical comparisons for typical ...

In this paper we propose some thermodynamic theories of materials with internal variables. In concrete, we extend the arguments of the theories of the thermoelasticity of type I, II and III proposed by Green and Naghdi to the case of materials with internal variables. We state the system of equations in the linear case when the material is centrosymmetric. We end with an existence and uniquenes...

This system arises from a model of the nonlinear thermoelastic coupled vibration structure with the clamped ends for simultaneously considering the medium damping, the viscous effect and the nonlinear constitutive relation and thermoelasticity based on a theory of non-Fourier heat flux laws. By considering the case where the internal (structural) damping is present, for 0≤ ι < 1, we show that t...

In the present paper is concerned with study of thermoelastic interaction in an infinite KelvinVoigt type viscoelastic, thermally conducting solid bordered with viscous liquid half-spaces/layers of varying temperature. Complex secular equations in closed and isolated mathematical conditions for Rayleigh wave propagation in completely separate terms are derived. The results for coupled and uncou...

A Lagrangian-Hamiltonian variational formulation is proposed for the thermoelasticity of heat conductors and its generalization to anelasticity described by means of internal-state variablesby using a gauge-theoretical technique (introduction of an additional variable of state the gradient of thermacy that renders the system apparently Hamiltonian). Projecting the equations resulting from the E...

An interpretation of the Gough-Joule-Effect from an atomistic point of view is given by a special investigation of lattice vibrations using a non-interacting model. The calculations are restricted to crystals with ideal crystal structure built up of only one kind of particles. Approximate analytical formulas are derived. A comparison between the classical macroscopic theory and the here present...