Homogeneização Assintótica e Cálculo Fracionário na modelagem de meios micro-heterogêneos: uma introdução com o caso de uma barra funcionalmente graduada, microperiódica e linear

Roberto Martins da Silva Décio Júnior; Adriano De Cezaro; Leslie Darien Pérez-Fernández

doi:10.14295/vetor.v32i1.13759

Authors

Roberto Martins da Silva Décio Júnior Programa de Pós-Graduação em Modelagem Computacional - Universidade Federal de Rio Grande
Adriano De Cezaro Instituto de Matemática, Estatística e Física (IMEF) - Universidade Federal do Rio Grande (FURG)
Leslie Darien Pérez-Fernández Instituto de Física e Matemática, Universidade Federal de Pelotas (UFPel) https://orcid.org/0000-0002-4452-264X

DOI:

https://doi.org/10.14295/vetor.v32i1.13759

Keywords:

Asymptotic Homogenization, Fractional Calculus, Conformable Derivatives, Functionally Graduated Materials

Abstract

The study of materials with complex structure, like the functionally graded, is a field of increasing interest, what happens mostly because the importance of these materials in the industry. In this work, the Asymptotic Homogenization Method and Fractional Calculus are both applied in a problem which models the behaviour of a micro-heterogeneous material, like the functionally graded. The goal of this work is the study of the association possibilities between these two tools, since which one are providing important results in the mathematical modelling of complex structures. The results show that each methodology reproduce a different aspect of the phenomenon: the Homogenization stays in the microstructure details and the fractional derivative takes care of a macroscopic behaviour, which nature is possibly dissipative. Here are important information, but a deeper and more diverse approach is necessary to provide strong e more general statements about this theme.

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