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 27834, North Carolina, USA
Received 14 April 1981
Copyright © 1982 S. K. Bose and L. Debnath. 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 where and are the shear modulus of the matrix and fibers respectively and is the concentration of the fibers less that . For , the fiber and matrix moduli are to be interchanged and is to be replaced by . 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.