study, the micromechanics method is performed to estimate the laminate properties of
various laminate systems and compared with theoretical and semi-empirical solutions to
verify the transverse isotropy.
The unit cell model is used to estimate the elastic constants and the coefficient of
thermal expansion using the FE based micromechanics method. The fiber volume
fraction was assumed to be 60%. The thermo-elastic stress-strain relations of the
composite material at macro-scale can be written as
0o Cl C12 C13 0 0 0 E a1
SC22 C23 0 0 0 2 a2
03 C33 0 0 0 e3 AT a3 (2.2)
=< -A
23 C44 0 0 23 a23
r31 SYM C 0 731 a31
r12 C66 \712 a12
The elastic constants and the CTE's in Equation 2.2 were obtained by performing
7 sets of micromechanical analyses. In the first 6 cases the temperature difference ATwas
set to zero and the unit-cell was subjected to periodic boundary conditions corresponding
to one of the macro-strains as given in Tables 1 and 2. The macro-stresses in the unit cell
were calculated as the volume average of the corresponding micro-stress components:
1 NELM
c =- cr) V(), i = 1,6 (2.3)
V k=l
In Equation 2.3, k denotes the element number, NELM is the total number of
elements in the FE model, V(k) is the volume of the kth element and Vis the volume of the
unit-cell. The average or macro-stresses are used to calculate the stiffness coefficients in
a column corresponding to the nonzero strain. In order to calculate the CTE's, the unit-
cell is subjected to periodic boundary conditions such that the macro-strains are