We propose a thermodynamic model describing the thermoelastic behavior of composition graded materials. The compatibility of the model with second law of thermodynamics is explored by applying a generalized Coleman-Noll procedure. We calculate the speeds of coupled first- and second-sound pulses, propagating either trough nonequilibrium or trough equilibrium states. We characterize several different types of perturbations, depending on the value of the material coefficients. Under the assumption that the deformation of the body can produce changes in its stoichiometry, altering locally the material composition, the possibility of propagation of pure stoichiometric waves is pointed out. Thermoelastic perturbations generated by the coupling of stoichiometric and thermal effects are analyzed as well.

In this paper, we propose a modeling method based on peridynamics for ductile fracture at high temperatures. A thermoelastic coupling model combining peridynamics and classical continuum mechanics is used to limit the peridynamics calculations to the failure region of a given structure, thereby reducing computational costs. Then, a plastic constitutive model of peridynamic bonds is developed to capture the ductile-fracture process of the structure. Furthermore, an iterative algorithm for ductile-fracture calculation is presented. Finally, several numerical examples are shown. Particularly, the fracture processes of a superalloy structure under 800℃ and 900℃ environments are simulated and compared with experimental results. Our comparisons show that the crack modes captured by the proposed model are similar to experimental observations, which verifies the validity of the proposed model.

In this paper, we study the global existence and exponential decay for a dynamic contact problem between a Timoshenko beam with second sound and two rigid obstacles, of which the heat flux is given by Cattaneo's law instead of the usual Fourier's law. The main difficulties arise from the irregular boundary terms, from the low regularity of the weak solution and from the weaker dissipative effects of heat conduction induced by Cattaneo's law. By considering related penalized problems, proving some a priori estimates and passing to the limit, we prove the global existence of the solutions. By considering the approximate framework, constructing some new functionals and applying the perturbed energy method, we obtain the exponential decay result for the approximate solution, and then prove the exponential decay rate to the original problem by utilizing the weak lower semicontinuity arguments.

The major goal of this work is to present a novel fractional temperature-dependent boundary element model (BEM) for solving thermoelastic wave propagation problems in smart nanomaterials. The computing performance of the suggested methodology was demonstrated by using stable communication avoiding S-step – generalized minimal residual method (SCAS-GMRES) to solve discretized linear BEM systems. The benefits of SCAS-GMRES are investigated and compared to those of other iterative techniques. The numerical results are graphed to demonstrate the influence of fractional, piezoelectric, and length scale characteristics on total force-stresses. These findings also demonstrate that the BEM methodology is practical, feasible, effective, and has superiority over domain methods. The results of the present paper help to develop the industrial uses of smart nanomaterials.

Besides the Lagrangian and the Eulerian descriptions, the motion of a body can also be expressed relative to the present configuration of the body, known as the relative motion description. It is interesting to consider such a relative motion description in general to formulate the basic system of field equations for solid bodies. In doing so, when the time increment from the present state is small enough, the nonlinear constitutive equations can be linearized relative to the present state so that the resulting system becomes linear. This will be done for thermoelastic materials with a brief comment on the exploitation of entropy principle in general. Relative Lagrangian formulation is based on the well-known ``small-on-large'' idea, and can be implemented for solving problems with large deformation in successive incremental manner. Some applications of such a formulation in numerical simulations are briefly reviewed.