Homogenization of Fiber Reinforced Brittle Materials: The Extremal Cases
- 1 January 2009
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Mathematical Analysis
- Vol. 41 (5), 1874-1889
- https://doi.org/10.1137/080744372
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 ε of the grid and the ratio δ between the thickness of the fibers and the period ε. We show that the asymptotic behavior as ε → 0+ and δ → 0+ depends dramatically on the relative size of these parameters. Indeed, in the two cases considered, i.e., ε ≪ δ and ε ≫ δ, we obtain two different limit models: a perfectly elastic model and an elastic model with macroscopic cracks, respectively.Keywords
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