01152nas a2200121 4500008004300000245007700043210006900120260000900189520075400198100002100952700002100973856003600994 2009 en_Ud 00aHomogenization of fiber reinforced brittle materials: the extremal cases0 aHomogenization of fiber reinforced brittle materials the extrema bSIAM3 aWe 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.1 aBarchiesi, Marco1 aDal Maso, Gianni uhttp://hdl.handle.net/1963/2705