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Thick fibrous composite reinforcements behave as special second-gradient materials: three-point bending of 3D interlocks

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Abstract

In this paper, we propose to use a second gradient, 3D orthotropic model for the characterization of the mechanical behavior of thick woven composite interlocks. Such second-gradient theory is seen to directly account for the out-of-plane bending rigidity of the yarns at the mesoscopic scale which is, in turn, related to the bending stiffness of the fibers composing the yarns themselves. The yarns’ bending rigidity evidently affects the macroscopic bending of the material and this fact is revealed by presenting a three-point bending test on \({0 ^{\circ}/90 ^{\circ} \,\,{\rm and}\,\, \pm45 ^{\circ}}\) specimens of composite interlocks. These specimens differ one from the other for the different relative direction of the yarns with respect to the edges of the sample itself. Both types of specimens are independently seen to take advantage of a second-gradient modeling for the correct description of their macroscopic bending modes. The results presented in this paper are essential for the setting up of a correct continuum framework suitable for the mechanical characterization of composite interlocks. The few second-gradient parameters introduced by the present model are all seen to be associated with peculiar deformation modes of the mesostructure (bending of the yarns) and are determined by inverse approach. Although the presented results undoubtedly represent an important step toward the complete characterization of the mechanical behavior of fibrous composite reinforcements, more complex hyperelastic second-gradient constitutive laws must be conceived in order to account for the description of all possible mesostructure-induced deformation patterns.

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Authors and Affiliations

  1. LGCIE, INSA, Université de Lyon, 20 Avenue Albert Einstein, 69621, Villeurbanne Cedex, France

    Angela Madeo

  2. International Research Center M&MoCS, Università dell’Aquila, L’Aquila, Italy

    Angela Madeo & Francesco dell’Isola

  3. LaMCoS, INSA-CNRS, Université de Lyon, 20 Avenue Albert Einstein, 69621, Villeurbanne Cedex, France

    Manuel Ferretti & Philippe Boisse

  4. DICEAA, Università dell’Aquila, L’Aquila, Italy

    Manuel Ferretti

  5. DISG, Università di Roma ”La Sapienza”, Rome, Italy

    Francesco dell’Isola

Authors
  1. Angela Madeo
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  2. Manuel Ferretti
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  3. Francesco dell’Isola
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  4. Philippe Boisse
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Corresponding author

Correspondence to Angela Madeo.

Additional information

The authors thank INSA-Lyon for the financial support assigned to the project BQR 2013-0054 “Matériaux Méso et Micro-Hétérogènes: Optimisation par Modèles de Second Gradient et Applications en Ingénierie”. The second author thanks the Rhône-Alpes Région for partial funding of this project. The first and the last authors thank CRNS-INSIS for support to the PEPS project “Modélisation en Second Gradient des Renforts Fibreux de Composites”.

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Madeo, A., Ferretti, M., dell’Isola, F. et al. Thick fibrous composite reinforcements behave as special second-gradient materials: three-point bending of 3D interlocks. Z. Angew. Math. Phys. 66, 2041–2060 (2015). https://doi.org/10.1007/s00033-015-0496-z

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  • DOI: https://doi.org/10.1007/s00033-015-0496-z

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