2020/02/11 by Francesca Fantoni, Andrea Bacigalupo, Fantoni, Francesca +1
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Composite Material Mechanics #Computational Engineering #FOS: Computer and information sciences #FOS: Physical sciences #Finance #Fluid Dynamics (physics.flu-dyn) #Materials Science (cond-mat.mtrl-sci) #Numerical methods in engineering #and Science (cs.CE)
paper · pdf · doi:10.48550/arxiv.2002.11479
openalex publication_date 2020/02/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A multifield asymptotic homogenization technique for periodic\nthermo-diffusive elastic materials is provided in the present study. Field\nequations for the first-order equivalent medium are derived and overall\nconstitutive tensors are obtained in closed form. These lasts depend upon the\nmicro constitutive properties of the different phases composing the composite\nmaterial and upon periodic perturbation functions, which allow taking into\naccount the effects of microstructural heterogeneities. Perturbation functions\nare determined as solutions of recursive non homogeneous cell problems emanated\nfrom the substitution of asymptotic expansions of the micro fields in powers of\nthe microstructural characteristic size into local balance equations. Average\nfield equations of infinite order are also provided, whose formal solution can\nbe obtained through asymptotic expansions of the macrofields. With the aim of\ninvestigating dispersion properties of waves propagating inside the medium,\nproper integral transforms are applied to governing field equations of the\nhomogenized medium. A quadratic generalized eigenvalue problem is thus\nobtained, whose solution characterizes the complex valued frequency band\nstructure of the first-order equivalent material. The validity of the proposed\ntechnique has been confirmed by the very good matching obtained between\ndispersion curves of the homogenized medium and the lowest frequency ones\nrelative to the heterogeneous material. These lasts are computed from the\nresolution of a quadratic generalized eigenvalue problem over the periodic cell\nsubjected to Floquet-Bloch boundary conditions. An illustrative benchmark is\nconducted referring to a Solid Oxide Fuel Cell (SOFC)-like material, whose\nmicrostructure can be modeled through the spatial tessellation of the domain\nwith a periodic cell subjected to thermo-diffusive phenomena.\n