Displaying similar documents to “Homogenization of unbounded functionals and nonlinear elastomers. The case of the fixed constraints set”

Two-scale homogenization for a model in strain gradient plasticity

Alessandro Giacomini, Alessandro Musesti (2011)

ESAIM: Control, Optimisation and Calculus of Variations

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Using the tool of two-scale convergence, we provide a rigorous mathematical setting for the homogenization result obtained by Fleck and Willis [ 52 (2004) 1855–1888] concerning the effective plastic behaviour of a strain gradient composite material. Moreover, moving from deformation theory to flow theory, we prove a convergence result for the homogenization of quasistatic evolutions in the presence of isotropic linear hardening.

Homogenization of systems with equi-integrable coefficients

Marc Briane, Juan Casado-Díaz (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper we prove a H-convergence type result for the homogenization of systems the coefficients of which satisfy a functional ellipticity condition and a strong equi-integrability condition. The equi-integrability assumption allows us to control the fact that the coefficients are not equi-bounded. Since the truncation principle used for scalar equations does not hold for vector-valued systems, we present an alternative approach based on an approximation result by Lipschitz functions...

Spatial heterogeneity in 3D-2D dimensional reduction

Jean-François Babadjian, Gilles A. Francfort (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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A justification of heterogeneous membrane models as zero-thickness limits of a cylindral three-dimensional heterogeneous nonlinear hyperelastic body is proposed in the spirit of Le Dret (1995). Specific characterizations of the 2D elastic energy are produced. As a generalization of Bouchitté (2002), the case where external loads induce a density of bending moment that produces a Cosserat vector field is also investigated. Throughout, the 3D-2D dimensional reduction is viewed as a problem...

Homogenization in perforated domains with rapidly pulsing perforations

Doina Cioranescu, Andrey L. Piatnitski (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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The aim of this paper is to study a class of domains whose geometry strongly depends on time namely. More precisely, we consider parabolic equations in perforated domains with rapidly pulsing (in time) periodic perforations, with a homogeneous Neumann condition on the boundary of the holes. We study the asymptotic behavior of the solutions as the period of the holes goes to zero. Since standard conservation laws do not hold in this model, a first difficulty is to get estimates...

Two-scale homogenization for a model in strain gradient plasticity

Alessandro Giacomini, Alessandro Musesti (2011)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

Using the tool of two-scale convergence, we provide a rigorous mathematical setting for the homogenization result obtained by Fleck and Willis [ (2004) 1855–1888] concerning the effective plastic behaviour of a strain gradient composite material. Moreover, moving from deformation theory to flow theory, we prove a convergence result for the homogenization of quasistatic evolutions in the presence of isotropic linear hardening.

-convergence and absolute minimizers for supremal functionals

Thierry Champion, Luigi De Pascale, Francesca Prinari (2010)

ESAIM: Control, Optimisation and Calculus of Variations

Similarity:

In this paper, we prove that the approximants naturally associated to a supremal functional -converge to it. This yields a lower semicontinuity result for supremal functionals whose supremand satisfy weak coercivity assumptions as well as a generalized Jensen inequality. The existence of minimizers for variational problems involving such functionals (together with a Dirichlet condition) then easily follows. In the scalar case we show the existence of at least one absolute minimizer...