We study how and to what extent the existence of non-local diffusion affects the transport of chemical species in a composite medium. For our purposes, we prescribe the mass flux to obey a two-scale, non-local constitutive law featuring derivatives of fractional order, and we employ the asymptotic homogenisation technique to obtain an overall description of the species’ evolution. As a result, the non-local effects at the micro-scale are ciphered in the effective diffusivity, while at the macro-scale the homogenised problem features an integro-differential equation of fractional type. In particular, we prove that in the limit case in which the non-local interactions are neglected, classical results of asymptotic homogenisation theory are re-obtained. Finally, we perform numerical simulations to show the impact of the fractional approach on the overall diffusion of species in a composite medium. To this end, we consider two simplified benchmark problems, and report some details of the numerical schemes based on finite element methods.
Two-scale, non-local diffusion in homogenised heterogeneous media / Ramírez-Torres, Ariel; Penta, Raimondo; Grillo, Alfio. - In: ARCHIVE OF APPLIED MECHANICS. - ISSN 0939-1533. - (In corso di stampa).
|Titolo:||Two-scale, non-local diffusion in homogenised heterogeneous media|
|Data di pubblicazione:||Being printed|
|Digital Object Identifier (DOI):||http://dx.doi.org/10.1007/s00419-020-01880-3|
|Appare nelle tipologie:||1.1 Articolo in rivista|
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