Homogenization of a quasilinear elliptic problem in a fractal-reinforced structure

Jarroudi, Mustapha El

doi:10.1007/s40324-021-00250-5

Cited by 4 publications

(1 citation statement)

References 32 publications

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“…The limit problems consist in second order transmission problems. Problems involving thin highly conductive fractal inclusions have been addressed in a series of papers (see for instance [39], [31], [12], [14], and [19]). The obtained mathematical models are elliptic or parabolic boundary value problems involving transmission conditions of order two on the interfaces.…”

Section: Introductionmentioning

confidence: 99%

Asymptotic analysis of an elastic material reinforced with thin fractal strips

Jarroudi¹,

Filali²,

Lahrouz³

et al. 2022

NHM

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<p style='text-indent:20px;'>We study the asymptotic behavior of a three-dimensional elastic material reinforced with highly contrasted thin vertical strips constructed on horizontal iterated Sierpinski gasket curves. We use <inline-formula><tex-math id="M1">\begin{document}$ \Gamma $\end{document}</tex-math></inline-formula>-convergence methods in order to study the asymptotic behavior of the composite as the thickness of the strips vanishes, their Lamé constants tend to infinity, and the sequence of the iterated curves converges to the Sierpinski gasket in the Hausdorff metric. We derive the effective energy of the composite. This energy contains new degrees of freedom implying a nonlocal effect associated with thin boundary layer phenomena taking place near the fractal strips and a singular energy term supported on the Sierpinski gasket.</p>

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