Displaying similar documents to “Two-scale homogenization for a model in strain gradient plasticity”

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 [ (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.

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...

A brief introduction to homogenization and miscellaneous applications

Grégoire Allaire (2012)

ESAIM: Proceedings

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This paper is a set of lecture notes for a short introductory course on homogenization. It covers the basic tools of periodic homogenization (two-scale asymptotic expansions, the oscillating test function method and two-scale convergence) and briefly describes the main results of the more general theory of −  or −convergence. Several applications of the method are given: derivation of Darcy’s law for flows in porous media, derivation...