Optimal bounds for the effective energy of a mixture of isotropic, incompressible, elastic materials

DOI10.1007/BF00251534zbMath0662.73012OpenAlexW2054706759WikidataQ108773067 ScholiaQ108773067MaRDI QIDQ1114470

Robert V. Kohn, Robert P. Lipton

Publication date: 1988

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00251534

zbMATH Keywords

quadratic formhomogenizationoptimal lower boundHashin-Shtrikman variational principleeffective strain energyeffective stress-strain tensorelliptical systemmixing two incompressible, isotropic, lineary elastic solidsperiodic mixture

Mathematics Subject Classification ID

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Cites Work

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• G-closure of some particular sets of admissible material characteristics for the problem of bending of thin elastic plates
• Improved rigorous bounds on the effective elastic moduli of a composite material
• Homogenization and optimal bounds in linear elasticity
• A variational approach to the theory of the elastic behaviour of multiphase materials
• Non-homogeneous media and vibration theory
• Regularization of optimal design problems for bars and plates. I
• Bounds and self-consistent estimates for the overall properties of anisotropic composites
• \(G\)-closure of a set of anisotropically conducting media in the two-dimensional case
• On the existence of solutions to some problems of optimal design for bars and plates
• The Overall Elastic Response of Composite Materials
• Analysis of Composite Materials—A Survey
• Exact estimates of conductivity of composites formed by two isotropically conducting media taken in prescribed proportion
• Optimization and nonsmooth analysis
• Optimal design and relaxation of variational problems, I
• Exact estimates of the conductivity of a binary mixture of isotropic materials
• Optimal Bounds and Microgeometries for Elastic Two-Phase Composites
• AVERAGING ANDG-CONVERGENCE OF DIFFERENTIAL OPERATORS
• On the effective elasticity of a two-dimensional homogenised incompressible elastic composite
• Long-wave elastic anisotropy produced by horizontal layering
• On the Trace of Matrix Products
• Extremum principles for slow viscous flows with applications to suspensions

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