Coupled problems of gradient thermoelasticity for periodic structures

We have considered the most general from the point of view of coupled processes a linear model of reversible thermomechanical processes, in which gradient thermoelasticity and stationary thermal conductivity are coupled processes. Mathematical statements for the model including the gradient equilibrium equations of the fourth order, generalized thermal gradient conductivity equation, and the boundary value problems as a whole are considered, the structure of the fundamental solutions is studied, and the general solution is established in analytical form for the one-dimensional problems. We study the influence of both couple effects and scale effects on the deformation process, temperature distribution, and effective mechanical properties of the periodic inhomogeneous structures. Thermal resistance is also taken into account. We show that an analytical solution predicts the possible abnormal effects due to couple and scale effects for diapason of the parameters allowed by the positive definition constraints. Certainly the possible realization of these effects for the inhomogeneous structures is dependent on the real diapason parameters, which must be determined from the experimental data.

Automated summary

This paper considers a linear model describing a reversible thermomechanical process with coupled gradient thermoelasticity and stationary thermal conductivity. The mathematical statements and analytical solutions of the model are presented, and the influence of couple effects and scale effects on periodic inhomogeneous structures is studied.