The unit-cell is subjected to different strain components individually using the periodic
boundary conditions shown in Table 2-1 [7-9]. For the hexagonal unit cell, the periodic
boundary conditions corresponding to unit value of each strain component are shown in
Table 2-2 [10]. The equations of periodic boundary conditions corresponding individual
unit strains were embedded in the ABAQUS input code to perform the finite element
(FE) analysis.
Table 2-1. Periodic boundary conditions for the square unit cell for unit values of
different strain components.
Ex=l y=ll z=l Yxy=l xz=l yz=l
uxl-Ux0= L uxl-Mxo= 0 Uxl-UxO= 0 Vxl-Vxo= 1/2L Wxl-wx0= L Wyl-Wyo= L
Vyl-Vyo= 0 Vyl-VyO= L Vyl-VyO= 0 uyl-Uyo= 1/2L uzl-uz= 0 Vzl-Vzo= 0
Wzl-Wzo= 0 Wzi-Wzo= 0 Wzi-Wzo= t Wzi-Wzo= 0
Table 2-2. Periodic boundary conditions for the hexagonal unit cell for unit values of
different strain components.
Ex=l EY=1 Ez=l /xy=l /xz=l yz=l
Ual-Ua0= Ual-Ua0= 0 Ual-UaO= 0 Ual-UaO= 0 Uzi-Uzo=0 Vzl-Vzo=0
43/2L Ubl-Ub0= 0 Ubl-Ub0= 0 Ubl-Ub0= 0 Uc= 0 Wcl= 12L
Ubl-UbO= Val-VaO= 12L Val-VaO=0 Uc 0= 0 U,= 0 WO= -1/2L
/3/2L Vbl-VbO= 12L Vbl-VbO= 0 Uc= 0 Vcl= 0 Wal-WaO=
Val-Va= 0 Vc' 1/21 V1c= 0 Val-Vao=I3/2L Vc0= 0 12L
Vbl- Vb= 0 Vc0= -1/2L V0= 0 Vbl-VbO= Wal-Wa0= WbO-Wbl=
V,1= 0 Wzi-Wzo= 0 Wzi-Wzo= t -I3/2L I3/2L V2L
VcO= 0 Wzi-WzO= 0 Wbl-WbO=
WZi-Wzo= 0 _3/2L
Thermo-Elastic Properties of the Composite Constituents
For accurate prediction of stresses at cryogenic conditions, one requires
temperature dependent thermo-elastic properties of the constituent materials. In the
present study the matrix properties are considered as temperature-dependent and the fiber
properties temperature independent. Most of the advanced composite systems such as
aerospace graphite/epoxy are cured at about 455 K. When the temperature rises above the