On the formulation of gradient-type theory of thermoelastic solids

Abstract

The fundamental set of equations for gradient thermoelasticity is obtained. Mentioned equations take into account the effect of a local mass displacement on mechanical and thermal processes. New quantities associated with local mass displacement were introduced and we obtained for it additional balance relation. The linear equations governing the motion of thermoelastic solids within the framework of this gradient theory are set out. We obtained formula for surface energy of deformation of solids. The boundary value problem is presented to study the effect of the characteristic length parameter on mechanical fields in isotropic elastic layer and sphere. It is shown that the developed theory is capable of predicting nonlocal effects, such as the near-surface and size effects.