Center for                           Nonlinear Analysis CNA Home People Seminars Publications Workshops and Conferences CNA Working Groups Summer Schools Summer Undergraduate Institute PIRE Cooperation Graduate Topics Courses Positions Contact Publication 08-CNA-12 Homogenization of Fiber Reinforced Microstructures: The Extremal Cases Marco Barchiesi Department of Mathematical Sciences Carnegie Mellon University Pittsburgh, PA 15213 marcob@andrew.cmu.edu and Gianni Dal Maso SISSA Trieste, Italy dalmaso@sissa.it Abstract: We analyze the as umptotic behavior of the antiplane deformations of a fragile material reinforced by a reticulated elastic structure. The microscopic geometry of this material is described by means of two small'' parameters: The size of the periodic grid and the ratio between the thickness of each of the fibers and their period of distribution. We show that this behavior depends dramatically on the relative size of the parameters. Indeed, in the two considered cases, i.e. and , we obtain two different limit models: a perfectly elastic model and an elastic model with macroscopic cracks, respectively. Get the paper in its entirety as Back to CNA Publications