Composite Materials Research Progress

148
Yuanxin Zhou, Hassan Mahfuz, Vijaya Rangari et al.
H = πD
/ 2 df = D / 2
dm =
V
1
( −V
f )
df
where H, df and dm are the thickness of composite, the width of fiber and the width of matrix,
respectively (as shown in Figure 20). D and Vf are the diameter and the volume fraction of
fiber. The displacement component at node (i,j) is expressed as u i,
j .
Figure 20. Model of Unidirectional carbon fiber reinforced matrix resin.
The composite is pulled at one end and fixed at the other end. In figure 20, the left
boundary is fixed, and the right moves with a constant speed V, namely
The initial condition is
⎪⎧
u
⎨
⎪⎩ u
k
i,
0
k
i,
m
= 0
= VkΔt
0
u 0 ( 1 ≤ ≤ 2n
+ 1)
, = i j
Constitutive Assumptions
( 1 ≤ i ≤ 2n
+ 1)
( 1 ≤ i
≤ 2n
+
i and ( ≤ j ≤ m)
f
(1)
(2)
0 (3)
It is assumed that the fibers are homogeneous and linear elastic, the fiber strength is described
statically by single Weibull distribution [34]: