Second-order homogenization of periodic materials based on asymptotic approximation of the strain energy: formulation and validity limits

DOI10.1007/s11012-014-9906-0zbMath1396.74089arXiv1401.7855OpenAlexW2073520457WikidataQ64016850 ScholiaQ64016850MaRDI QIDQ2510333

Andrea Bacigalupo

Publication date: 1 August 2014

Published in: Meccanica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1401.7855

zbMATH Keywords

overall elastic modulisecond-order Taylor expansionmacro-homogeneity conditionsecond-order equivalent continuumthree-phase orthotropic material

Mathematics Subject Classification ID

Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics (74G10) Homogenization in equilibrium problems of solid mechanics (74Q05) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27)

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Cites Work

• Computational two-scale homogenization of periodic masonry: characteristic lengths and dispersive waves
• Homogenization of spectral problems in bounded domains with doubly high contrasts
• Boundary conditions for the high order homogenized equation: laminated rods, plates and composites
• Rayleigh scattering in elastic composite materials
• Asymptotic homogenization of elastic composite materials with a regular structure
• Microstructural effects in elastic composites
• A micromechanical approach of nonlocal modeling for media with periodic microstructures
• On rigorous derivation of strain gradient effects in the overall behaviour of periodic heterogeneous media
• Cosserat overall modeling of heterogeneous materials
• Multipolar continuum mechanics
• Multi-scale second-order computational homogenization of multi-phase materials: a nested finite element solution strategy
• Micro-structure in linear elasticity
• Generalized continua and non-homogeneous boundary conditions in homogenisation methods
• Second‐order computational homogenization of heterogeneous materials with periodic microstructure
• On spectrum gaps of some divergent elliptic operators with periodic coefficients
• Higher order asymptotic homogenization and wave propagation in periodic composite materials
• High-frequency homogenization for periodic media
• Multiscale Modeling of Elastic Waves: Theoretical Justification and Numerical Simulation of Band Gaps
• Scale transition and enforcement of RVE boundary conditions in second-order computational homogenization
• Homogenization and Two-Scale Convergence
• On an extension of the method of two-scale convergence and its applications
• Multi‐scale constitutive modelling of heterogeneous materials with a gradient‐enhanced computational homogenization scheme
• Homogenization methods and mechanics of generalized continua - part 2
• High-frequency asymptotics for microstructured thin elastic plates and platonics
• Tabu search for a class of single-machine scheduling problems

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