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A second and third gradient material with torsion resulting from the homogenization of a highly contrasted rigid fibre-reinforced composite

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Abstract

We study the homogenization of an elastic material made of an elastic matrix in contact with highly contrasted three-dimensional elastic rigid fibres with circular cross section. The interaction between the matrix and the fibres is described by a local interface adhesion law. Assuming that the Lamé constants in the fibres and the stiffness coefficient of the adhesive have appropriate orders of magnitude, we derive a class of deformation energies involving second gradient functionals, third gradient functionals, and a functional energy associated with inner torsion.

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  1. LMA, FST of Tangier, Abdelmalek Essaâdi University, B.P. 416, Tangier, Morocco

    Mustapha El Jarroudi

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  1. Mustapha El Jarroudi
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Correspondence to Mustapha El Jarroudi.

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El Jarroudi, M. A second and third gradient material with torsion resulting from the homogenization of a highly contrasted rigid fibre-reinforced composite. Continuum Mech. Thermodyn. 36, 471–502 (2024). https://doi.org/10.1007/s00161-024-01278-4

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