ANNALI DELL'UNIVERSITA' DI FERRARA

, Volume 54, Issue 2, pp 297–318 | Cite as

Elastic lattices: equilibrium, invariant laws and homogenization

Article

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.

Keywords

Lattices Homogenization Finite elasticity Molecular mechanics Graphene sheets 

Mathematics Subject Classification (2000)

70G75 74B15 74B20 74K15 74Q15 

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Copyright information

© Università degli Studi di Ferrara 2008

Authors and Affiliations

  1. 1.Laboratoire MAP5Université Paris Descartes and CNRSParis Cedex 06France
  2. 2.Laboratoire 3S-RUniversité de Grenoble and CNRSGrenoble Cedex 9France
  3. 3.Université LibanaiseBeyrouthLebanon

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