Wave propagation modeling in periodic elasto-thermo-diffusive materials via multifield asymptotic homogenization

A multifield asymptotic homogenization technique for periodic thermo-diffusive elastic materials is
provided in the present study. Field equations for the first-order equivalent medium are derived and
overall constitutive tensors are obtained in closed form. These lasts depend upon the micro constitutive
properties of the different phases composing the composite material and upon periodic perturbation
functions, which allow taking into account the effects of microstructural heterogeneities. Perturbation
functions are determined as solutions of recursive non homogeneous cell problems emanated from the
substitution of asymptotic expansions of the micro fields in powers of the microstructural characteristic
size into local balance equations. Average field equations of infinite order are also provided, whose formal
solution can be obtained through asymptotic expansions of the macrofields. With the aim of investigating
dispersion properties of waves propagating inside the medium, proper integral transforms are applied to
governing field equations of the homogenized medium. A quadratic generalized eigenvalue problem
is thus obtained, whose solution characterizes the complex valued frequency spectrum of the first-order
equivalent material. The validity of the proposed technique has been confirmed by the very good matching
obtained between dispersion curves of the homogenized medium and the lowest frequency ones relative
to the heterogeneous material. These lasts are computed from the resolution of a quadratic generalized
eigenvalue problem over the periodic cell subjected to Floquet-Bloch boundary conditions. An illustrative
benchmark is conducted referring to a Solid Oxide Fuel Cell (SOFC)-like material, whose microstructure
can be modeled through the spatial tessellation of the domain with a periodic cell subjected to thermo-
diffusive phenomena.