%0 Journal Article
%J SIAM J. Math. Anal. 41 (2009) 1874-1889
%D 2009
%T Homogenization of fiber reinforced brittle materials: the extremal cases
%A Marco Barchiesi
%A Gianni Dal Maso
%X 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.
%B SIAM J. Math. Anal. 41 (2009) 1874-1889
%I SIAM
%G en_US
%U http://hdl.handle.net/1963/2705
%1 1396
%2 Mathematics
%3 Functional Analysis and Applications
%$ Submitted by Andrea Wehrenfennig (andreaw@sissa.it) on 2008-08-13T12:57:01Z\\nNo. of bitstreams: 1\\nmicrofibre.pdf: 236545 bytes, checksum: 53ef9ce789d27bba7dcac550930f306b (MD5)