Feeble interfaces in bimaterials

Summary In the present paper, the thermal and thermo-elastic response of a bi-material to temperature changes is analyzed, when its interface exhibits a simultaneous weakness in traction transferring and heat flow conducting (feeble interface). Such a pathological behavior of an interface is described by two sets of constitutive relationships relating the heat flow passing through the interface to the temperature jump and the interfacial components of the traction to those of the displacement jump. The bimaterial model considered is that of a circular inhomogeneity in an elastic matrix with linear forms of the constitutive relationships. When the solutions of both heat conduction and thermoelastic problems with a perfect interface are known, the corresponding problems with a feeble interface are reduced to the solution of two dislocation problems: a heat conduction problem with an appropriate temperature dislocation applied across the interface, and an elasticity problem with an appropriate displacement dislocation of Somigliana type acting across the interface. For both dislocation problems, general representations of their solutions in terms of two-phase potential functions of complex variables are provided. Detailed analytical results are given for a circular inhomogeneity with a feeble interface disturbing a linear distribution of the temperature change in the matrix. In this case, the stress field within the inhomogeneity has a linear distribution and it vanishes for the limiting case of a sliding interface. For a specific value of the interface parameter H, which characterizes the thermal imperfection, there are no shear stresses within the inhomogeneity. Finally, since the constitutive laws describing the thermal and mechanical interface behavior correlate tensors of different order, the resulting fields in the system are drastically affected by the inhomogeneity size.