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Elastic lattices: equilibrium, invariant laws and homogenization

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Abstract

In the recent years, lattice modelling proved to be a topic of renewed interest. Indeed, fields as distant as chemical modelling and biological tissue modelling use network models that appeal to similar equilibrium laws. In both cases, obtaining an equivalent continuous model allows to simplify numerical procedures. We define the basic properties of lattices: elasticity, frame-indifference, hyperelasticity. We determine rigorously the form that constitutive laws undertake under frame-indifference and hyperelasticity assumptions. Finally, we describe an homogenization technique designed for discrete structures that provides a limit continuum mechanics model and, in the special case of hexagonal lattices, we investigate the symmetry properties of the limit constitutive law.

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Authors and Affiliations

  1. Laboratoire MAP5, Université Paris Descartes and CNRS, 45 rue des Saints Pères, 75270, Paris Cedex 06, France

    Annie Raoult

  2. Laboratoire 3S-R, Université de Grenoble and CNRS, BP 53, 38041, Grenoble Cedex 9, France

    Denis Caillerie

  3. Université Libanaise, Beyrouth, Lebanon

    Ayman Mourad

Authors
  1. Annie Raoult
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  2. Denis Caillerie
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  3. Ayman Mourad
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Correspondence to Annie Raoult.

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Raoult, A., Caillerie, D. & Mourad, A. Elastic lattices: equilibrium, invariant laws and homogenization. Ann. Univ. Ferrara 54, 297–318 (2008). https://doi.org/10.1007/s11565-008-0054-0

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  • DOI: https://doi.org/10.1007/s11565-008-0054-0

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