Stochastic Homogenisation of Singularly Perturbed Integral Functionals
نویسنده
چکیده
We study the relative impact of small-scale random inhomogeneities and singular perturbations in nonlinear elasticity. More precisely, we analyse the asymptotic behaviour of the energy functionals Fε(ω)(u) = ∫ A ( f ( ω, x ε ,Du ) + ε|∆u| ) dx, where ω is a random parameter and ε > 0 denotes a typical length-scale associated with the variations in the elastic properties of the body. For f stationary and ergodic, we show that when ε → 0 the randomly inhomogeneous material described by Fε(ω) behaves (almost surely) like a homogeneous deterministic material. The limit stored energy density is given in terms of an asymptotic cell formula in which the Laplacian perturbation explicitly appears.
منابع مشابه
Stochastic Homogenisation of Singularly Perturbed Integral Functionals
We study the relative impact of small-scale random inhomogeneities and singular perturbations in nonlinear elasticity. More precisely, we analyse the asymptotic behaviour of the energy functionals Fε(ω)(u) = ∫ A ( f ( ω, x ε ,Du ) + ε|∆u| ) dx, where ω is a random parameter and ε > 0 denotes a typical length-scale associated with the variations in the elastic properties of the body. For f stati...
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