Reflection and transmission of thermo-elastic waves without energy dissipation at the interface of two dipolar gradient elastic solids

The reflection and transmission of thermal elastic waves at the interface between two different dipolar gradient elastic solids are studied based on the generalized thermo-elastic theory of Green and Naghdi (1993). J. Elasticity 31, 189-208 (type II of no energy dissipation). First, some thermodynamic formulas are generalized to a dipolar gradient elastic solid and the function of free energy density is postulated. Second, equations of thermal motion and constitutive relations in a dipolar gradient elasticity are derived. Then the nontraditional interfacial conditions are used to determine the amplitude ratio of the reflection and transmission waves with respect to the incident wave. Some numerical results of the reflection and transmission coefficients in the form of an energy flux ratio are given for different microstructure parameters while thermal parameters are fixed. The numerical results are validated by the consideration of energy conservation. It is found that there are a total of five modes of dispersive waves, namely, coupled MT1 wave, coupled MT2 wave, coupled MT3 wave, SV wave, and one evanescent wave which reduces to the surface waves at an interface, namely, SS wave. The thermal parameters mainly affect the coupled MT2 wave while the microstructure parameters affect not only the coupled waves but also the SS surface waves.