Transient thermal stresses in a medium with a circular cavity with surface effects

A two-dimensional, transient, uncoupled thermoelastic problem of an infinite medium with a circular nano-scale cavity is considered. The analysis is based on the generalized Gurtin and Murdoch model [Murdoch, A.I., 2005. Some fundamental aspects of surface modelling. Journal of Elasticity 80, 33–52.] where the surface of the cavity possesses its own surface tension and thermomechanical properties. A semi-analytical solution for the problem is obtained using a complex variable boundary integral equation method and the Laplace transform. Several examples are presented to study the significance of surface thermomechanical properties and surface tension, and to compare the results obtained using the generalized Gurtin and Murdoch model and a thin interphase layer model.