An integral equation method for the homogenization of unidirectional fibre-reinforced media; antiplane elasticity and other potential problems

DOI10.1098/rspa.2017.0080zbMath1404.74142OpenAlexW2613050483WikidataQ52384390 ScholiaQ52384390MaRDI QIDQ4647220

Duncan Joyce, William J. Parnell, I. David Abrahams, Raphaël C. Assier

Publication date: 4 January 2019

Published in: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1098/rspa.2017.0080

zbMATH Keywords

homogenizationpotential problemantiplane elasticityfibre-reinforced composite

Mathematics Subject Classification ID

Homogenization in equilibrium problems of solid mechanics (74Q05) Linear integral equations (45A05)

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Cites Work

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• The Eshelby, Hill, moment and concentration tensors for ellipsoidal inhomogeneities in the Newtonian potential problem and linear elastostatics
• On the computation of the Hashin-Shtrikman bounds for transversely isotropic two-phase linear elastic fibre-reinforced composites
• Dynamic homogenization in periodic fibre reinforced media. Quasi-static limit for SH waves
• Homogenization for wave propagation in periodic fibre-reinforced media with complex microstructure. I: Theory
• Effective properties of elastic periodic composite media with fibers
• Overall behavior of two-dimensional periodic composites.
• An integral equation method for elastostatics of periodic composites
• Effective properties of composite materials with periodic microstructure: A computational approach
• Approximations to wave propagation through a lattice of Dirichlet scatterers
• Propagation of elastic waves through a lattice of cylindrical cavities
• A new integral equation approach to elastodynamic homogenization
• Effective Properties of a Composite Half-Space: Exploring the Relationship Between Homogenization and Multiple-Scattering Theories
• High-frequency homogenization for periodic media
• Composites with periodic microstructure
• Elastic waves and homogenization in oblique periodic structures
• Long-wave elastic anisotropy produced by horizontal layering
• A Unified Model for the Properties of Composite Materials