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Analysis of Nonlinear Wave Propagation in Hyperelastic Network Materials

  • Hilal RedaEmail author
  • Khaled ElNady
  • Jean-François Ganghoffer
  • Nikolas Karathanasopoulos
  • Yosra Rahali
  • Hassan Lakiss
Part of the Advanced Structured Materials book series (STRUCTMAT, volume 90)

Abstract

We analyze the acoustic properties of microstructured repetitive network material undergoing configuration changes leading to geometrical nonlinearities. The effective constitutive law of the homogenized network is evaluated successively as an effective first nonlinear 1D continuum, based on a strain driven incremental scheme written over the reference unit cell, taking into account the changes of the lattice geometry. The dynamical equations of motion are next written, leading to specific dispersion relations. The inviscid Burgers equation is obtained as a specific wave propagation equation for the first order effective continuum when the expression of the energy includes third order contributions, whereas a perturbation method is used to solve the dynamical properties for the effective medium including fourth order terms. This methodology is applied to analyze wave propagation within different microstructures, including the regular and reentrant hexagons, and plain weave textile pattern.

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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Hilal Reda
    • 1
    • 2
    Email author
  • Khaled ElNady
    • 1
  • Jean-François Ganghoffer
    • 5
  • Nikolas Karathanasopoulos
    • 3
  • Yosra Rahali
    • 4
  • Hassan Lakiss
    • 2
  1. 1.LEMTAUniversité de LorraineVandoeuvre-les-NancyFrance
  2. 2.Faculty of Engineering, Section IIICampus Rafic Hariri, Lebanese UniversityBeirutLebanon
  3. 3.Institute for Computational Science, ETH ZurichZurichSwitzerland
  4. 4.Institut Préparatoire aux Études d’Ingénieur de BizerteBizerteTunisia
  5. 5.LEM3Université de Lorraine CNRSMetz CedexFrance

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