Strong influence of a small fiber on shear stress in fiber-reinforced composites

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In stiff fiber-reinforced composites, it has been known that the shear stress increases at the rate of 1/root epsilon as the distance e between adjacent fibers approaches 0. This paper reveals a strong influence of a combination of a triple fiber, as well as the distance between a pair of fibers, on the blow-up so that the stress concentration can be significantly accelerated by adding a small fiber in-between fibers. Specifically, if a fiber J(2) with a small diameter delta is located in-between fibers J(1) and J(3), epsilon(1) = dist(J(1), J(2)) and epsilon(2) = dist(J(2), J(3)), then the stress blows up at the exact rates of 1/root delta epsilon(1) and 1/root delta epsilon(2) between J(1) and J(2) and between J(2) and J(3), respectively. This estimate still holds even when a part of J(2) overlaps with J(3). The magnification factor 1/root delta yields the enormous increase in the stress that greatly surpasses the expectancy by previous methods. (C) 2011 Elsevier Inc. All rights reserved.
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Issue Date
2011-03
Language
English
Article Type
Article
Keywords

CONDUCTIVITY PROBLEM

Citation

JOURNAL OF DIFFERENTIAL EQUATIONS, v.250, no.5, pp.2402 - 2439

ISSN
0022-0396
DOI
10.1016/j.jde.2010.12.024
URI
http://hdl.handle.net/10203/97007
Appears in Collection
MA-Journal Papers(저널논문)
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