%0 Report
%D 2015
%T A bridging mechanism in the homogenisation of brittle composites with soft inclusions
%A Marco Barchiesi
%A Giuliano Lazzaroni
%A Caterina Ida Zeppieri
%X We provide a homogenisation result for the energy-functional associated with a purely brittle composite whose microstructure is characterised by soft periodic inclusions embedded in a stiffer matrix. We show that the two constituents as above can be suitably arranged on a microscopic scale ε to obtain, in the limit as ε tends to zero, a homogeneous macroscopic energy-functional explicitly depending on the opening of the crack.
%I SISSA
%G en
%U http://urania.sissa.it/xmlui/handle/1963/7492
%1 7621
%$ Submitted by Maria Pia Calandra (calapia@sissa.it) on 2015-01-26T14:21:23Z
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%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
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