Page 100 - Mechanics Analysis Composite Materials

Chapter 3. Mechanics of a unidirecrional ply 85

Fig. 3.34. A first-order model of a unidirectional ply.

Introducing transverse strains

we can write Eq. (3.67) in the following form

The same assumptions can be made for shear stresses and strains, so that

(3.69)
(3.70)

With due regard to Eqs. (3.65), (3.66), and (3.69) constitutive equations, Eqs. (3.63)
can be reduced to

1 , 1
&I = -(e, - VfUZ), &I =-(e$ - vmcJz) , (3.71)
Ef Em

(3.73)

The first two equations, Eqs. (3.71), allow us to find longitudinal stresses, Le.,

0: EfSl + Vf62, e? =EmEl + V,~JZ . (3.74)

Equilibrium equation, Eq. (3.64) can be rearranged with the aid of Eqs. (3.62) to the
form

01 = OfUf + b;lVn, . (3.75)