Homogenization of elastic materials containing self-similar rigid micro-inclusions

Jarroudi, Mustapha El; Er‐Riani, Mustapha

doi:10.1007/s00161-018-0700-4

Cited by 3 publications

(2 citation statements)

References 31 publications

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“…Due to the physical characteristics of the inclusions, singular energy forms containing fractal energies are obtained in these articles as the limit of non-singular full-dimensional energies. On the other hand, the effective properties of elastic materials fixed on rigid thin self-similar micro-inclusions disposed along two and three dimensional Sierpinski carpet fractals have been recently obtained in [20].…”

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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Section: Introductionmentioning

confidence: 99%

Asymptotic analysis of an elastic material reinforced with thin fractal strips

Jarroudi¹,

Filali²,

Lahrouz³

et al. 2022

NHM

Self Cite

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“…Multiple spatial scales are also studied within scenarios of fractal or self‐similar microstructures. Recent examples for this include the analytical homogenization of the elastic properties in the presence of fractal pores 9 or (without assumed separation of scales) fractal interfaces 10,11 . Such considerations are motivated, for example, by geology or fracture mechanics.…”

Section: Introductionmentioning

confidence: 99%

Many‐scale finite strain computational homogenization via Concentric Interpolation

Kunc

Fritzen

2020

Numerical Meth Engineering

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A method for efficient computational homogenization of hyperelastic materials under finite strains is proposed. Multiple spatial scales are homogenized in a recursive procedure: starting on the smallest scale, few high fidelity FE computations are performed. The resulting fields of deformation gradient fluctuations are processed by a snapshot POD resulting in a reduced basis (RB) model. By means of the computationally efficient RB model, a large set of samples of the homogenized material response is created. This data set serves as the support for the Concentric Interpolation (CI) scheme, interpolating the effective stress and stiffness. Then, the same procedure is invoked on the next larger scale with this CI surrogating the homogenized material law. A three-scale homogenization process is completed within few hours on a standard workstation. The resulting model is evaluated within minutes on a laptop computer in order to generate fourth-scale results. Open source code is provided.

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

Jarroudi

2021

SeMA

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Homogenization of elastic materials containing self-similar rigid micro-inclusions

Cited by 3 publications

References 31 publications

Asymptotic analysis of an elastic material reinforced with thin fractal strips

Asymptotic analysis of an elastic material reinforced with thin fractal strips

Many‐scale finite strain computational homogenization via Concentric Interpolation

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

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