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This work is devoted to the analysis of the interplay between internal variables and high-contrast microstructure in inelastic solids. As a concrete case-study, by means of variational techniques, we derive a macroscopic description for an…

Analysis of PDEs · Mathematics 2024-10-14 Elisa Davoli , Chiara Gavioli , Valerio Pagliari

We carry out a variational study for integral functionals that model the stored energy of a heterogeneous material governed by finite-strain elastoplasticity with hardening. Assuming that the composite has a periodic microscopic structure,…

Analysis of PDEs · Mathematics 2024-03-08 Elisa Davoli , Chiara Gavioli , Valerio Pagliari

Using an elastostatic description of crack growth based on the Griffith criterion and the principle of local symmetry, we present a stochastic model describing the propagation of a crack tip in a 2D heterogeneous brittle material. The model…

Materials Science · Physics 2007-05-23 E. Katzav , M. Adda-Bedia , B. Derrida

We consider the well-travelled problem of homogenization of random integral functionals. When the integrand has standard growth conditions, the qualitative theory is well-understood. When it comes to unbounded functionals, that is, when the…

Analysis of PDEs · Mathematics 2016-04-20 Mitia Duerinckx , Antoine Gloria

We study the homogenization of a class of non-local functionals featuring a rapidly oscillating periodic weight. By means of two-scale convergence, we explicitly evaluate the {\Gamma}-limit for constant target functions, revealing how the…

Analysis of PDEs · Mathematics 2026-05-19 Enrico Micalizio

We study the effective behavior of heterogeneous energies arising in the modeling of material voids in geometrically linear elastic materials. Specifically, we consider functionals featuring bulk terms depending on the symmetrized gradient…

Analysis of PDEs · Mathematics 2026-02-20 Stefano Almi , Antonio Flavio Donnarumma , Manuel Friedrich

This paper addresses the asymptotics of functionals with linear growth depending on the Riesz $s$-fractional gradient on piecewise constant functions. We consider a general class of varying energy densities and, as $s\to 1$, we characterize…

Analysis of PDEs · Mathematics 2025-10-07 Stefano Almi , Maicol Caponi , Manuel Friedrich , Francesco Solombrino

In this work, we demonstrate that a functional modeling the self-aggregation of stochastically distributed lipid molecules can be obtained as the $\Gamma$-limit of a family of discrete energies driven by a sequence of independent and…

Probability · Mathematics 2023-05-11 Luca Lussardi , Anderson Melchor Hernandez , Marco Morandotti

A discrete-to-continuum analysis for free-boundary problems related to crystalline films deposited on substrates is performed by $\Gamma$-convergence. The discrete model here introduced is characterized by an energy with two contributions,…

Analysis of PDEs · Mathematics 2019-02-19 Leonard Kreutz , Paolo Piovano

We determine the effective behavior of a class of composites in finite-strain crystal plasticity, based on a variational model for materials made of fine parallel layers of two types. While one component is completely rigid in the sense…

Analysis of PDEs · Mathematics 2016-04-13 Fabian Christowiak , Carolin Kreisbeck

We perform a stochastic-homogenization analysis for composite materials exhibiting a random microstructure. Under the assumptions of stationarity and ergodicity, we characterize the Gamma-limit of a micromagnetic energy functional defined…

Analysis of PDEs · Mathematics 2023-06-26 Elisa Davoli , Lorenza D'Elia , Jonas Ingmanns

This paper is on $\Gamma$-convergence for degenerate integral functionals related to homogenisation problems in the Heisenberg group. Here both the rescaling and the notion of invariance or periodicity are chosen in a way motivated by the…

Analysis of PDEs · Mathematics 2019-06-28 Nicolas Dirr , Federica Dragoni , Paola Mannucci , Claudio Marchi

In this paper, we introduce a nonlocal, variational model for thin films. We consider convolution-type functionals defined on a thin domain whose thickness is of order $\gamma$, where the effective interactions range between points is of…

Analysis of PDEs · Mathematics 2026-05-08 Nadia Ansini , Antonio Tribuzio

This work is concerned with an asymptotic analysis, in the sense of $\Gamma$-convergence, of a sequence of variational models of brittle damage in the context of linearized elasticity. The study is performed as the damaged zone concentrates…

Analysis of PDEs · Mathematics 2019-11-19 Jean-Francois Babadjian , Flaviana Iurlano , Filip Rindler

We carry out the spatially periodic homogenization of nonlinear bending theory for plates. The derivation is rigorous in the sense of Gamma-convergence. In contrast to what one naturally would expect, our result shows that the limiting…

Analysis of PDEs · Mathematics 2014-05-16 Stefan Neukamm , Heiner Olbermann

Under a suitable notion of equivalence of integral densities we prove a $\Gamma$-closure theorem for integral functionals: The limit of a sequence of $\Gamma$-convergent families of such functionals is again a $\Gamma$-convergent family.…

Analysis of PDEs · Mathematics 2013-08-06 Martin Jesenko , Bernd Schmidt

In this work, we study the effective behavior of a two-dimensional variational model within finite crystal plasticity for high-contrast bilayered composites. Precisely, we consider materials arranged into periodically alternating thin…

Analysis of PDEs · Mathematics 2019-02-01 Elisa Davoli , Rita Ferreira , Carolin Kreisbeck

We prove a compactness result with respect to $\Gamma$-convergence for a class of integral functionals which are expressed as a sum of a local and a non-local term. The main feature is that, under our hypotheses, the local part of the…

Analysis of PDEs · Mathematics 2022-12-23 Andrea Braides , Gianni Dal Maso

We study the limit behaviour of a sequence of non-convex, vectorial, random integral functionals, defined on $W^{1,1}$, whose integrands satisfy degenerate linear growth conditions. These involve suitable random, scale-dependent…

Analysis of PDEs · Mathematics 2022-10-27 Matthias Ruf , Caterina Ida Zeppieri

We study periodic homogenization by Gamma-convergence of some singular integral functionals related to nonlinear elasticity.

Analysis of PDEs · Mathematics 2009-06-29 Omar Anza Hafsa , Mohamed Lamine Leghmizi , Jean-Philippe Mandallena