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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 (onedimensional) 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)

- Marco Barchiesi, Giuliano Lazzaroni, Caterina Ida Zeppieri
- SIAM J. Math. Analysis
- 2016

- Nadia Ansini, Caterina Ida Zeppieri
- SIAM J. Math. Analysis
- 2012

We study the asymptotic behavior of a sequence of Dirichlet problems for second order linear operators in divergence form where the matrix (σε) ⊂ L∞(Ω;Rn×n) is uniformly elliptic and possibly nonsymmetric. Because of the variational principle of Cherkaev and Gibiansky [Math. Phys., 35 (1994), pp. 127–145], we are able to prove a variational characterization… (More)

- Lucia Scardia, Caterina Ida Zeppieri
- SIAM J. Math. Analysis
- 2012

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… (More)

- Martin Burger, Teresa Esposito, Caterina Ida Zeppieri
- Multiscale Modeling & Simulation
- 2015

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