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The combined effect of fine heterogeneities and small gradient perturbations is analyzed by means of an asymptotic development by Γ-convergence for a family of energies related to (one-dimensional) phase transformations. We show that multi-scale effects add up to the usual sharp-interface limit, due to the homogenization of microscopic interfaces, internal(More)
In the framework of linear elasticity, we study the limit of a class of discrete free energies modeling strain-alignment-coupled systems by a rigorous coarse-graining procedure, as the number of molecules diverges. We focus on three paradigmatic examples: magnetostrictive solids, ferroelectric crystals and nematic elastomers, obtaining in the limit three(More)
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 2 |∆u| 2 dx, where ω is a random parameter and ε > 0 denotes a typical length-scale associated with the variations in the elastic(More)
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