Homogenization of quadratic complementary energies: a duality example

Hélia Serrano

Displaying similar documents to “Homogenization of quadratic complementary energies: a duality example”

The nonlinear membrane model : a Young measure and varifold formulation

Med Lamine Leghmizi, Christian Licht, Gérard Michaille (2005)

ESAIM: Control, Optimisation and Calculus of Variations

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We establish two new formulations of the membrane problem by working in the space of $W_{Γ_{0}}^{1, p} (Ω, 𝐑^{3})$ -Young measures and $W_{Γ_{0}}^{1, p} (Ω, 𝐑^{3})$ -varifolds. The energy functional related to these formulations is obtained as a limit of the $3 d$ formulation of the behavior of a thin layer for a suitable variational convergence associated with the narrow convergence of Young measures and with some weak convergence of varifolds. The interest of the first formulation is to encode the oscillation informations on the gradients minimizing...

Admissible functions in two-scale convergence.

Valadier, Michel (1997)

Portugaliae Mathematica

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Asymptotic behaviour and correctors for linear Dirichlet problems with simultaneously varying operators and domains

Gianni Dal Maso, François Murat (2004)

Annales de l'I.H.P. Analyse non linéaire

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Γ-convergence approach to variational problems in perforated domains with Fourier boundary conditions

Valeria Chiadò Piat, Andrey Piatnitski (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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The work focuses on the Γ-convergence problem and the convergence of minimizers for a functional defined in a periodic perforated medium and combining the bulk (volume distributed) energy and the surface energy distributed on the perforation boundary. It is assumed that the mean value of surface energy at each level set of test function is equal to zero. Under natural coercivity and -growth assumptions on the bulk energy, and the assumption that the surface energy satisfies -growth...

A generalized strange term in Signorini’s type problems

Carlos Conca, François Murat, Claudia Timofte (2003)

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

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The limit behavior of the solutions of Signorini’s type-like problems in periodically perforated domains with period $ε$ is studied. The main feature of this limit behaviour is the existence of a critical size of the perforations that separates different emerging phenomena as $ε \to 0$ . In the critical case, it is shown that Signorini’s problem converges to a problem associated to a new operator which is the sum of a standard homogenized operator and an extra zero order term (“strange term”) coming...

Homogenization of evolution problems for a composite medium with very small and heavy inclusions

Michel Bellieud (2005)

ESAIM: Control, Optimisation and Calculus of Variations

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We study the homogenization of parabolic or hyperbolic equations like $ρ_{ε} \frac{\partial^{n} u_{ε}}{\partial t^{n}} - div (a_{ε} \nabla u_{ε}) = f in Ω \times (0, T) + boundary conditions, n \in {1, 2},$ when the coefficients $ρ_{ε}$ , $a_{ε}$ (defined in $Ø$ ) take possibly high values on a $ε$ -periodic set of grain-like inclusions of vanishing measure. Memory effects arise in the limit problem.

The method of Rothe and two-scale convergence in nonlinear problems

Jiří Vala (2003)

Applications of Mathematics

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Modelling of macroscopic behaviour of materials, consisting of several layers or components, cannot avoid their microstructural properties. This article demonstrates how the method of Rothe, described in the book of K. Rektorys The Method of Discretization in Time, together with the two-scale homogenization technique can be applied to the existence and convergence analysis of some strongly nonlinear time-dependent problems of this type.