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

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Abstract

We consider elastic materials containing rigid micro-inclusions located along self-similar fractals. We use \(\Gamma \)-convergence methods in order to study the asymptotic behaviour of the structure with respect to vanishing parameters describing the thickness of the inclusions. We derive effective elastic behaviours of the elastic materials with boundary conditions describing discontinuities in the tractions across the self-similar fractal interfaces.

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Authors and Affiliations

  1. FST Tanger Laboratoire Mathématiques et Applications, Université Abdelmalek Essaâdi, B.P. 416, Tangier, Morocco

    Mustapha El Jarroudi & Mustapha Er-Riani

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  1. Mustapha El Jarroudi
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  2. Mustapha Er-Riani
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Correspondence to Mustapha El Jarroudi.

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Communicated by Andreas Öchsner.

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El Jarroudi, M., Er-Riani, M. Homogenization of elastic materials containing self-similar rigid micro-inclusions. Continuum Mech. Thermodyn. 31, 457–474 (2019). https://doi.org/10.1007/s00161-018-0700-4

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