This article deals with the problem of heat propagation in periodic composites described by the Cattaneo-type constitutive law. The simplest model of the macroscopic behavior of these composites can be obtained using results of the well-known asymptotic homogenization theory. However, this model is not able to describe the phenomena related to higher order motion and higher propagation speeds that play an important role in wave propagation analysis. The aim of this contribution is to propose a more general macroscopic model for the heat propagation in periodic composites that can be used for the analysis of the aforementioned phenomena and is based on the tolerance averaging of equations with functional coefficients.
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