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• W2017025711 abstract "This article is devoted to the study of the asymptotic behavior of a class of energies defined on stochastic lattices. Under polynomial growth assumptions, we prove that the energy functionals $${F_varepsilon}$$ stored in the deformation of an $${{varepsilon}}$$ -scaling of a stochastic lattice Γ-converge to a continuous energy functional when $${{varepsilon}}$$ goes to zero. In particular, the limiting energy functional is of integral type, and deterministic if the lattice is ergodic. We also generalize, to systems and nonlinear settings, well-known results on stochastic homogenization of discrete elliptic equations. As an application of the main result, we prove the convergence of a discrete model for rubber towards the nonlinear theory of continuum mechanics. We finally address some mechanical properties of the limiting models, such as frame-invariance, isotropy and natural states." @default.
• W2017025711 created "2016-06-24" @default.
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• W2017025711 date "2010-10-05" @default.
• W2017025711 modified "2023-09-25" @default.
• W2017025711 title "Integral Representation Results for Energies Defined on Stochastic Lattices and Application to Nonlinear Elasticity" @default.
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• W2017025711 doi "https://doi.org/10.1007/s00205-010-0378-7" @default.
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