Asymptotics of the homogenized moduli for the elastic chess-board composite

Leonid V. Berlyand, S. M. Kozlov

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

We find the asymptotic behavior of the homogenized coefficients of elasticity for the chess-board structure. In the chess board white and black cells are isotropic and have Lamé constants (λ, μ,) and (δλ, δμ) respectively. We assume that the black cells are soft, so δ →0. It turns out that the Poisson ratio for this composite tends to zero with δ.

Original languageEnglish (US)
Pages (from-to)95-112
Number of pages18
JournalArchive for Rational Mechanics and Analysis
Volume118
Issue number2
DOIs
StatePublished - Jun 1992

Fingerprint

Poisson ratio
Elasticity
Modulus
Composite
Poisson's Ratio
Cell
Composite materials
Asymptotic Behavior
Tend
Zero
Coefficient

All Science Journal Classification (ASJC) codes

  • Mathematics (miscellaneous)
  • Mathematics(all)
  • Mechanics of Materials
  • Computational Mechanics

Cite this

@article{8d3100b650954dbca63d68c4f11aea1a,
title = "Asymptotics of the homogenized moduli for the elastic chess-board composite",
abstract = "We find the asymptotic behavior of the homogenized coefficients of elasticity for the chess-board structure. In the chess board white and black cells are isotropic and have Lam{\'e} constants (λ, μ,) and (δλ, δμ) respectively. We assume that the black cells are soft, so δ →0. It turns out that the Poisson ratio for this composite tends to zero with δ.",
author = "Berlyand, {Leonid V.} and Kozlov, {S. M.}",
year = "1992",
month = "6",
doi = "10.1007/BF00375091",
language = "English (US)",
volume = "118",
pages = "95--112",
journal = "Archive for Rational Mechanics and Analysis",
issn = "0003-9527",
publisher = "Springer New York",
number = "2",

}

Asymptotics of the homogenized moduli for the elastic chess-board composite. / Berlyand, Leonid V.; Kozlov, S. M.

In: Archive for Rational Mechanics and Analysis, Vol. 118, No. 2, 06.1992, p. 95-112.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Asymptotics of the homogenized moduli for the elastic chess-board composite

AU - Berlyand, Leonid V.

AU - Kozlov, S. M.

PY - 1992/6

Y1 - 1992/6

N2 - We find the asymptotic behavior of the homogenized coefficients of elasticity for the chess-board structure. In the chess board white and black cells are isotropic and have Lamé constants (λ, μ,) and (δλ, δμ) respectively. We assume that the black cells are soft, so δ →0. It turns out that the Poisson ratio for this composite tends to zero with δ.

AB - We find the asymptotic behavior of the homogenized coefficients of elasticity for the chess-board structure. In the chess board white and black cells are isotropic and have Lamé constants (λ, μ,) and (δλ, δμ) respectively. We assume that the black cells are soft, so δ →0. It turns out that the Poisson ratio for this composite tends to zero with δ.

UR - http://www.scopus.com/inward/record.url?scp=0026989582&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0026989582&partnerID=8YFLogxK

U2 - 10.1007/BF00375091

DO - 10.1007/BF00375091

M3 - Article

AN - SCOPUS:0026989582

VL - 118

SP - 95

EP - 112

JO - Archive for Rational Mechanics and Analysis

JF - Archive for Rational Mechanics and Analysis

SN - 0003-9527

IS - 2

ER -