Journal
JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
Volume 52, Issue 5, Pages 1023-1052Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.jmps.2003.09.030
Keywords
interphases; fiber reinforced composite material; Cosserat shells; shells and membranes
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This study is concerned with the modeling of interphases in elastic media in general, and in composite materials in particular. The aim is to replace a boundary value problem consisting of a three-phase configuration, say that of fiber-interphase-matrix, by a simpler problem which involves the fiber and matrix only, plus certain matching conditions which simulate the interphase. The simplest of such known representations replaces a thin interphase by a perfect contact interface (a single surface) across which the displacements and tractions are assumed to be continuous. Another classical model replaces a thin and soft interphase by a spring-type interface, across which the tractions are continuous, but the displacement field undergoes a discontinuity. In the present paper, a Cosserat shell model of the interphase is derived which successfully models the original interphase in a unified manner, for the full range of its material parameters relative to those of the neighboring media. The model is derived in the setting of three-dimensional linear elasticity with small deformations and displacements. Comparisons with an existing exact solution of a coated fiber in an infinite matrix show that it performs extremely well even for moderately thick interphases. (C) 2003 Elsevier Ltd. All rights reserved.
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