TY - JOUR
T1 - Homogenization of fiber reinforced brittle materials: the extremal cases
JF - SIAM J. Math. Anal. 41 (2009) 1874-1889
Y1 - 2009
A1 - Marco Barchiesi
A1 - Gianni Dal Maso
AB - 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.
PB - SIAM
UR - http://hdl.handle.net/1963/2705
U1 - 1396
U2 - Mathematics
U3 - Functional Analysis and Applications
ER -