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 stored in the deformation of an ε-scaling of a stochastic lattice Γ -converge to a continuous energy functional when ε 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.

Integral representation results for energies defined on stochastic lattices and application to nonlinear elasticity

ALICANDRO, Roberto;
2011

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 stored in the deformation of an ε-scaling of a stochastic lattice Γ -converge to a continuous energy functional when ε 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.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11580/16567
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