Dynamic homogenization and emergent bianisotropy in thermoelasticity

Abstract

We formulate a theory for the macroscopic response of heterogeneous thermoelastic media. The formulation employs independent driving fields and a Green-function representation, yielding exact nonlocal constitutive relations between the effective fields. Our theory predicts emergent cross-couplings between the elastic and thermal fields that are absent from the microscopic constitutive relations. We show that spatial inversion determines which of these couplings are permitted in the local limit, while spatial dispersion can retain inversion-odd couplings. For periodic laminates, a Fourier implementation shows that the effective model reproduces both acoustic-like and thermal-like Bloch dynamics, and that the emergent mixed couplings can strongly modify acoustic attenuation by altering the thermoelastic polarization of the modes. Finally, a generalized thermoelastic impedance reveals orientation-dependent thermoelastic conversion. Our framework provides a general homogenization route for uncovering emergent cross-couplings in other heterogeneous systems where propagating and diffusive fields coexist.