Wave propagation and transient heat transfer in thermoelastic composites

We revisit the pioneering works by Ene [1] and Francfort [2] which give the macroscopic equivalent model for wave propagations and transient heat transfers in thermoelastic composite media, by using the method of asymptotic expansions. The obtained model (denoted as model I in the following) shows a similar structure to the classical thermoelastic system which couples the inertial wave equation with the transient heat equation. By analyzing the dimensionless description at the heterogeneity scale and by estimating the dimensionless numbers herein, we show that two very different characteristic frequencies are present. At the higher one, the obtained model (model II) describes wave propagation with memory effects whereas macroscopic transient heat transfers are absent. At the lower frequency, model III describes transient heat transfers while the composite material undergoes a quasi-static deformation. Model III is similar to model I where the inertial term is neglected. Model II is not reducible to model I.