Homogenization of elliptic problems in a fiber reinforced structure. Non local effects

Michel Bellieud; Guy Bouchitté

Displaying similar documents to “Homogenization of elliptic problems in a fiber reinforced structure. Non local effects”

External approximation of first order variational problems estimates

Cesare Davini, Roberto Paroni (2008)

ESAIM: Control, Optimisation and Calculus of Variations

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Here we present an approximation method for a rather broad class of first order variational problems in spaces of piece-wise constant functions over triangulations of the base domain. The convergence of the method is based on an inequality involving $W^{- 1, p}$ norms obtained by Nečas and on the general framework of -convergence theory.

Some remarks on two-scale convergence and periodic unfolding

Jan Franců, Nils E M Svanstedt (2012)

Applications of Mathematics

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The paper discusses some aspects of the adjoint definition of two-scale convergence based on periodic unfolding. As is known this approach removes problems concerning choice of the appropriate space for admissible test functions. The paper proposes a modified unfolding which conserves integral of the unfolded function and hence simplifies the proofs and its application in homogenization theory. The article provides also a self-contained introduction to two-scale convergence and gives...

Spatial heterogeneity in 3D-2D dimensional reduction

Jean-François Babadjian, Gilles A. Francfort (2005)

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 et al. (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...

-convergence of functionals on divergence-free fields

Nadia Ansini, Adriana Garroni (2007)

ESAIM: Control, Optimisation and Calculus of Variations

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We study the stability of a sequence of integral functionals on divergence-free matrix valued fields following the direct methods of -convergence. We prove that the -limit is an integral functional on divergence-free matrix valued fields. Moreover, we show that the -limit is also stable under volume constraint and various type of boundary conditions.

Asymptotic behaviour and correctors for Dirichlet problems in perforated domains with homogeneous monotone operators

Gianni Dal Maso, François Murat (1997)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Asymptotic behavior of nonlinear systems in varying domains with boundary conditions on varying sets

Carmen Calvo-Jurado, Juan Casado-Díaz, Manuel Luna-Laynez (2009)

ESAIM: Control, Optimisation and Calculus of Variations

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 For a fixed bounded open set $Ω \subset ℝ^{N}$ , a sequence of open sets $Ω_{n} \subset Ω$ and a sequence of sets $Γ_{n} \subset \partial Ω \cap \partial Ω_{n}$ , we study the asymptotic behavior of the solution of a nonlinear elliptic system posed on $Ω_{n}$ , satisfying Neumann boundary conditions on $Γ_{n}$ and Dirichlet boundary conditions on $\partial Ω_{n} ∖ Γ_{n}$ . We obtain a representation of the limit problem which is stable by homogenization and we prove that this representation depends on $Ω_{n}$ and $Γ_{n}$ locally. 