Transient responses of multi-layered structures with interfacial conditions in the generalized thermoelastic diffusion theory

We present a theoretical framework to study the thermoelastic diffusion responses of multi-layered structures. A multi-layered structure with a permeating substance in contact with its surface is considered in the context of generalized thermoelastic diffusion with one relaxation time. For each elastic homogeneous layer, the differential equations describing the wave-like hyperbolic heat conduction and mass diffusion are solved in Laplace domain. Solutions accounting for proper interfacial and boundary conditions and material parameters are first presented to describe the thermoelastic diffusion behavior of the multi-layered structure. Transient concentration, chemical potential, temperature, displacement and stress are obtained in time domain via Laplace inversion. We then apply the solutions obtained to a one-dimensional bi-layered medium and study the effects of interfacial conditions and material parameters on the thermoelastic diffusion responses.