Summary
This article is concerned with the theoretical problem of predicting the effective properties of a dense suspension of stiff elastic rods in an elastic matrix. The rods have large bending stiffness so that if they are straight in the stress-free configuration they will remain straight in the deformed configuration. Furthermore, in the limit of high volume fraction of the fibers one can equate the transversal mobility of the fiber to zero relative to its longitudinal mobility. A constitutive relation for the suspension can thus be derived, giving useful information on the effective mechanical properties of the composite material.
Zusammenfassung
Dieser Artikel befaßt sich mit dem theoretischen Problem der Voraussage der wirklichen Eigenschaften einer dichten Lösung von steifen elastischen Fasern in einer elastischen Matrix. Die Fasern haben große Beugesteifigkeit, sodaß sie im unbeanspruchten, wie auch im beanspruchten Fall gerade bleiben. Zusätzlich kann man im Grenzfall von hohen Volumenbruchteilen der Fasern die transversale Mobilität der Stränge relativ zu der longitudinalen gleich null setzen. Eine konstitutive Beziehung für die Lösung kann daher abgeleitet werden, die nützliche Information über die wirklichen mechanischen Eigenschaften des zusammengesetzten Materials ergibt.
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This work was done while N. P-T. was a Visiting Fulbright Scholar at Caltech. He wishes to thank the Australian-American Educational Foundation for providing support.
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Phan-Thien, N., Leal, L.G. A constitutive equation for a concentrated suspension of bendable rods in an elastic matrix. Z. angew. Math. Phys. 34, 754–759 (1983). https://doi.org/10.1007/BF00948813
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DOI: https://doi.org/10.1007/BF00948813