Composite Materials Research Progress

150
Governing Equation
For the fiber element
where,
For the matrix
Yuanxin Zhou, Hassan Mahfuz, Vijaya Rangari et al.
Figure 21. Interface shear stress between fiber element and matrix element.
d u
dfE τ τ
(8a)
f
2
i,
j
+ 2
dx
i / i+
1,
j i−1
/ i,
j
( − ) = 0
d u
dmE τ τ
(8b)
m
2
i,
j
+ 2
dx
i / i+
1,
j i / i−1,
j
( − ) = 0
d u
dmE τ (8c)
m
2
1,
j
+ 2
dx
1/
2,
j
( − 0)
= 0
2
d u2n
+ 1,
j
dmEm + ( 0 −τ
2 / 2 1,
) = 0
2
n n+
j
(8d)
dx
Equation 8A-D can be expressed by the governing equation as follow
A i
A dfE
i
f
d
u
2G
G
2
i,
j
2 +
dfGm
m f
+ dmG f
i+
1,
j i,
j i−1,
j
dx
⎛1
+ μ ⎞ ⎛1
+ μ ⎞
= ⎜ ⎟ + ⎜ ⎟( −1)
⎝ 2 ⎠ ⎝ 2 ⎠
i
( u − 2u
+ u ) = 0
( 1
− )
E dm E V
m
μ = =
E df E V
f
m f
f f
(9)