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International Journal of Mathematics and Mathematical Sciences
Volume 5 (1982), Issue 2, Pages 393-401

Axial shear modulus of a fiber-reinforced composite with random fiber cross-sections

1Department of Mathematics, Regional Engineering College, Durgapur 713209, India
2Mathematics and Physics Departments, East Carolina University, Greenville, North Carolina 27834, USA

Received 14 April 1981

Copyright © 1982 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


A study is made of the effective axial shear modulus of a fiber reinforced material with random fiber cross-sections so that the micromechanics is governed by stochastic differential equations. A coarse-graining procedure is adopted to investigate the macroscopic behavior of the material. This analysis leads to the formula for the effective axial shear modulus μ=μ1/{12c(μ2μ1)/(μ2+μ1)},where μ1 and μ2 are the shear modulus of the matrix and fibers respectively and c is the concentration of the fibers less that 0.5. For c>0.5, the fiber and matrix moduli are to be interchanged and c is to be replaced by 1c. The results of this study are compared with those of the theory of fibre reinforced materials. Finally, a numerical example is presented with graphical representation.