Thermoelasticity of inclusions with interface stress revisited: modified boundary condition and nonlinear response
摘要
We revisit the thermo-elastic problem of an inclusion with small-scale interface effects in the context of plane deformations. The interface effects involve interface heat conduction and interface thermoelasticity with interface tension. Following the essential idea in the original Gurtin-Murdoch surface model, we propose a modified boundary condition in which the deformation-caused change in the configuration of the interface is taken into account for evaluating the traction (acting on the bulk surrounding the interface) induced by not only the interface tension but also the temperature-related interface stress. We establish the complex variable boundary value formulation corresponding to the modified boundary condition for an arbitrary shape of the inclusion. We then apply the boundary value formulation to the case of a circular inclusion embedded in an elastic matrix subjected to a remote heat flux, and present some numerical results for the heat flux-induced thermal stress field. Interestingly, it is shown that the thermal stress field in the composite structure increases nonuniformly with increasing remote heat flux, demonstrating a typical nonlinear response of the structure to external thermal loadings and an apparent asymmetric distribution relative to the structural geometric midline, which is in sharp contrast to the classical case when the original Gurtin-Murdoch-type boundary condition (incorporating interface thermal expansion) is used. The modified boundary condition and corresponding boundary value formulation would be useful in the prediction of nonlinear thermo-elastic behavior of unidirectional fibrous micro- or nano-composites under high-flux thermal environment.