Elastic lattices: equilibrium, invariant laws and homogenization |
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Authors: | Annie Raoult Denis Caillerie Ayman Mourad |
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Institution: | (1) Laboratoire MAP5, Université Paris Descartes and CNRS, 45 rue des Saints Pères, 75270 Paris Cedex 06, France;(2) Laboratoire 3S-R, Université de Grenoble and CNRS, BP 53, 38041 Grenoble Cedex 9, France;(3) Université Libanaise, Beyrouth, Lebanon |
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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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Keywords: | Lattices Homogenization Finite elasticity Molecular mechanics Graphene sheets |
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