Symmetry groups in nonlinear elasticity: an exercise in vintage mathematics
Annie Raoult
Communications on Pure & Applied Analysis 2009, 8(1): 435-456 doi: 10.3934/cpaa.2009.8.435
This manuscript aims at characterizing energy densities and constitutive laws of transversely isotropic materials, orthotropic elastic materials and materials with non orthogonal families of fibers. It makes explicit references to results that are scattered over the literature and, although said to be well-known, are not always easy to locate. Direct proofs that are thought to be new and simplified expressions of constitutive laws for materials with two preferred directions are given.
keywords: fibers symmetry groups transverse isotropy constitutive laws orthotropy anisotropy Nonlinear elasticity
Homogenization of hexagonal lattices
Hervé Le Dret Annie Raoult
Networks & Heterogeneous Media 2013, 8(2): 541-572 doi: 10.3934/nhm.2013.8.541
We characterize the macroscopic effective mechanical behavior of a graphene sheet modeled by a hexagonal lattice of elastic bars, using $\Gamma$-convergence.
keywords: Cauchy-Born rule. homogenization $\Gamma$-convergence Graphene sheet atomistic-to-continuum

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