Non-Fourier thermal wave in 2D cellular metamaterials: From transient heat propagation to harmonic band gaps

Abstract

Tailoring the nano/microarchitecture of advanced materials is a new root for manipulating their behavior to attain unparalleled multifunctional properties, including guided transitional waves. Elastic , acoustic, and electromagnetic wave responses in architected materials have extensively been studied, while only few studies have been allocated to the thermal wave propagation in these engineered materials. In this article, we explore the propagation of thermal waves in cellular metamaterials as a category of rationally-designed architected materials. First, the propagation of an instantaneous heat excitation through a two-dimensional (2D) cellular medium is investigated in steady-state and transient modes by Fourier and non-Fourier (Cattaneo-Vernotte and dual-phase-lag) heat conduction theories. The effects of relative density and microarchitecture of the cellular domain on the heat propagation characteristics are investigated, connecting these traits to the effective thermal conductivity of the cellular domain using an asymptotic homogenization method. Second, by implementing the Bloch theorem for non-Fourier heat conduction models, complex dispersion curves are obtained for five alternative cellular architectures with Archimedean tilings. The cellular microstructure, on the one hand, affects the transient temperature distribution resulting from an instantaneous source and temporarily creates domains with temperatures as high as two times the applied temperature difference in the external boundaries, while on the other hand, blocks harmonic thermal excitations in a range of frequencies (thermal band gaps) from passing the material. Moreover, the relative density of cellular architectures significantly affects the characteristics of thermal band gaps; for example, the first thermal band gap width may be reduced by 80% when relative density of cellular architectures changes from 0.2 to 0.6. Our findings can pave a path towards developing architected multifunctional metamaterials with programmable thermal isolation/guiding properties.