THE NEUMANN SIEVE PROBLEM AND DIMENSIONAL REDUCTION: A MULTISCALE APPROACH

DOI10.1142/S0218202507002078zbMath1120.74040arXivmath/0605769OpenAlexW1976894771MaRDI QIDQ5297212

Jean-François Babadjian, Nadia Ansini, Caterina Ida Zeppieri

Publication date: 18 July 2007

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0605769

zbMATH Keywords

nonlinear elasticitygamma-convergencebilayer thin film

Mathematics Subject Classification ID

Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics (74G10) Energy minimization in equilibrium problems in solid mechanics (74G65) Thin films (74K35) Homogenization in equilibrium problems of solid mechanics (74Q05)

Related Items (7)

The mathematics of thin structures ⋮ A variational model for fracture and debonding of thin films under in-plane loadings ⋮ Effective Helmholtz problem in a domain with a Neumann sieve perforation ⋮ Reduced models for linearly elastic thin films allowing for fracture, debonding or delamination ⋮ The periodic unfolding method for perforated domains and Neumann sieve models ⋮ Homogenization via unfolding in periodic layer with contact ⋮ A variational model of interaction between continuum and discrete systems

Cites Work

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• The thick Neumann's sieve
• An asymptotic study of the debonding of thin films
• Asymptotic analysis of periodically-perforated nonlinear media.
• Heterogeneous thin films of martensitic materials
• A theory of thin films of martensitic materials with applications to microactuators
• Homogenization of free discontinuity problems
• Analyse limite d'équations variationnelles dans un domaine contenant une grille
• Equi-integrability results for 3D-2D dimension reduction problems
• Brittle thin films

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