International Journal of Mathematics and Mathematical Sciences
Volume 5 (1982), Issue 2, Pages 393-401
doi:10.1155/S0161171282000386
Axial shear modulus of a fiber-reinforced composite with random fiber cross-sections
S.K. Bose1
and L. Debnath2
1Department of Mathematics, Regional Engineering College, Durgapur 713209, India
2Mathematics and Physics Departments, East Carolina University, Greenville 27834, North Carolina, USA
Abstract
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/{1−2c(μ2−μ1)/(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 1−c. 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.