Elastic perturbance due to a rigid inclusion embedded in an infinite homogeneous and isotropic medium exerting a remote uniform heat flux

Abstract

The problem of an infinite homogeneous isotropic medium with a rigid inclusion and exerting a uniform remote heat flux is deeply studied. The previous solutions without considering the rigid-body displacement of the rigid inclusion relative to the matrix cannot strictly satisfy the boundary condition of displacement and/or the resultant moment constraint around the rigid inclusion. In this paper, the analytical solution due to the remote heat flux is revisited when the shape of the rigid inclusion is characterized by the Laurent polynomial with finite terms, and the relative rigid-body displacement of the rigid inclusion is introduced to make the boundary condition and constraint satisfied accurately. The obtained results are compared with some reported results, and effects of rigid-body displacement and remote heat flux direction are discussed. The caused stress concentration and rigid-body displacement of the rigid inclusion would be valuable in theory and engineering application.