A contact problem in couple stress thermoelasticity: The indentation by a hot flat punch

It is well known, that thermo-elastic effects may have significant results upon the macroscopic response in the mechanics of contact. On the other hand, as the scales in the contact system reduce progressively (micro to nano-scales), the internal material lengths become important and their effect upon the macroscopic response cannot be ignored. The present work extends the classical contact solution for a hot flat punch indenting a homogeneous elastic half-plane, where heat conduction is permitted (Comninou et al., 1981), to the analogous case of an indented microstructured solid. The behavior of the indented material is modeled through the couple-stress elasticity theory, which introduces characteristic material lengths and is appropriately modified in order to incorporate the thermal effects. The problem formulation is based on singular integral equations, resulted from a treatment of the mixed boundary value problems via integral transforms and generalized functions. The results show significant departure from the predictions of classical thermoelasticity showing that the microstructural characteristics of the material should not be ignored.