Elastic lattices: equilibrium, invariant laws and homogenization
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.
KeywordsLattices Homogenization Finite elasticity Molecular mechanics Graphene sheets
Mathematics Subject Classification (2000)70G75 74B15 74B20 74K15 74Q15
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