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EnglishThis 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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| Titolo: | Integral representation results for energies defined on stochastic lattices and application to nonlinear elasticity |
| Autori: | |
| Data di pubblicazione: | 2011 |
| Rivista: | |
| 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. |
| Handle: | http://hdl.handle.net/11580/16567 |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
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