Elastic moduli of two-dimensional composite continua with elliptical inclusions

Michael Thorpe, P. N. Sen

Research output: Contribution to journalArticle

57 Citations (Scopus)

Abstract

The elastic field around an elliptical inclusion in two dimensions is obtained. This result is then used to compute the effective moduli of a composite medium containing many randomly positioned and oriented elliptical objects. Two different self-consistent methods are described and the special cases of voids and rigid reinforcement are considered in detail. The asymmetric self-consistent method shows that the Young's modulus E goes to zero as E = E1(p - p(c))/(1 - p(c)), where 1 - p is the concentration of the voids and subscript one denotes the void free material. The Poisson ratio σ is also linear in p and goes to a value σ(c) at p(c) that is independent of the initial value of Poisson's ratio σ1. Unlike the corresponding three-dimensional case, the two elastic moduli decouple in this special case. The corresponding elastic threshold is p(c) = [1 + ab /(a2 + b2)], where a and b are the major semiaxes. The symmetric self-consistent method yields a different p(c) = 2[1 + √2(a + b2)2/(a2 + b1)]-1 and a different concentration dependence of the effective moduli. Both methods give the same result for circular inclusions and both methods give p(c) + σ(c) = 1 for all aspect ratios. Similar results are presented for the case of rigid reinforcements.

Original languageEnglish (US)
Pages (from-to)1674-1680
Number of pages7
JournalJournal of the Acoustical Society of America
Volume77
Issue number5
StatePublished - 1985
Externally publishedYes

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voids
modulus of elasticity
Poisson ratio
inclusions
continuums
reinforcement
composite materials
aspect ratio
thresholds
Elastic Modulus
Inclusion
Voids
Reinforcement

ASJC Scopus subject areas

  • Acoustics and Ultrasonics

Cite this

Elastic moduli of two-dimensional composite continua with elliptical inclusions. / Thorpe, Michael; Sen, P. N.

In: Journal of the Acoustical Society of America, Vol. 77, No. 5, 1985, p. 1674-1680.

Research output: Contribution to journalArticle

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