Functionally Graded Media
Cedric M. Campos, Marcelo Epstein, Manuel de Leon
TL;DR
This paper reviews the concepts of uniformity and homogeneity in elastic materials using advanced mathematical frameworks and extends these ideas to functionally graded media, deriving conditions for their homogeneity.
Contribution
It introduces a Lie groupoid and frame bundle framework to analyze homogeneity in functionally graded media, expanding the theoretical understanding of these materials.
Findings
Derived homogeneity conditions for functionally graded media
Extended Lie groupoid framework to graded materials
Provided mathematical characterization of material uniformity
Abstract
The notions of uniformity and homogeneity of elastic materials are reviewed in terms of Lie groupoids and frame bundles. This framework is also extended to consider the case Functionally Graded Media, which allows us to obtain some homogeneity conditions.
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