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A multifield asymptotic homogenization technique for periodicthermo-diffusive elastic materials is provided in the present study. Fieldequations for the first-order equivalent medium are derived and overallconstitutive tensors are obtained in closed form. These lasts depend upon themicro constitutive properties of the different phases composing the compositematerial and upon periodic perturbation functions, which allow taking intoaccount the effects of microstructural heterogeneities. Perturbation functionsare determined as solutions of recursive non homogeneous cell problems emanatedfrom the substitution of asymptotic expansions of the micro fields in powers ofthe microstructural characteristic size into local balance equations. Averagefield equations of infinite order are also provided, whose formal solution canbe obtained through asymptotic expansions of the macrofields. With the aim ofinvestigating dispersion properties of waves propagating inside the medium,proper integral transforms are applied to governing field equations of thehomogenized medium. A quadratic generalized eigenvalue problem is thusobtained, whose solution characterizes the complex valued frequency bandstructure of the first-order equivalent material. The validity of the proposedtechnique has been confirmed by the very good matching obtained betweendispersion curves of the homogenized medium and the lowest frequency onesrelative to the heterogeneous material. These lasts are computed from theresolution of a quadratic generalized eigenvalue problem over the periodic cellsubjected to Floquet-Bloch boundary conditions. An illustrative benchmark isconducted referring to a Solid Oxide Fuel Cell (SOFC)-like material, whosemicrostructure can be modeled through the spatial tessellation of the domainwith a periodic cell subjected to thermo-diffusive phenomena.

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