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Homogenization of fiber reinforced brittle materials: the extremal cases

TitleHomogenization of fiber reinforced brittle materials: the extremal cases
Publication TypeJournal Article
Year of Publication2009
AuthorsBarchiesi, M, Dal Maso, G
JournalSIAM J. Math. Anal. 41 (2009) 1874-1889
Abstract

We analyze the behavior of a fragile material reinforced by a reticulated elastic unbreakable structure in the case of antiplane shear. The microscopic geometry of this material is described by means of two small parameters: the period $\\\\varepsilon$ of the grid and the ratio $\\\\delta$ between the thickness of the fibers and the period $\\\\varepsilon$. We show that the asymptotic behavior as $\\\\varepsilon\\\\to0^+$ and $\\\\delta\\\\to0^+$ depends dramatically on the relative size of these parameters. Indeed, in the two cases considered, i.e., $\\\\varepsilon\\\\ll\\\\delta$ and $\\\\varepsilon\\\\gg\\\\delta$, we obtain two different limit models: a perfectly elastic model and an elastic model with macroscopic cracks, respectively.

URLhttp://hdl.handle.net/1963/2705

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