Wave propagation and transient heat transfer in thermoelastic composites

摘要

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 frequen cies are present. At the higher one, the obtained model (model Ⅱ) describes wave propagation with mem ory 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.