Homogenization of Fiber Reinforced Microstructures: the Extremal Cases
نویسنده
چکیده
We analyze the asymptotic 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 ε of the periodic grid and the ratio δ 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., ε ≪ δ and ε ≫ δ, we obtain two different limit models: a perfectly elastic model and an elastic model with macroscopic cracks, respectively.
منابع مشابه
Homogenization of Fiber Reinforced Brittle Materials: The Extremal Cases
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 ε of the grid and the ratio δ between the thickness of the fibers and the period ε. We show that the asymptotic behavior as ε → 0 and δ → 0 depends dramatically ...
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