RVE. In a hexagonal RVE there is symmetry about the y-axis and also about the +30

degree directions. The hexagonal unit cell is modeled using 2,400 quadratic solid

elements with periodic boundary conditions [10].






 Matrix









Figure 2-2. A hexagonal RVE and corresponding FE mesh.

 C1
 Y1
 y, 3, v
 I bo a,

 x, 2, u "


 z,I1,w xo X1 )


 Yo


Figure 2-3. Geometry of square and hexagonal unit cells.

 The unit cells are subjected to axial and shear displacements combined with

thermal effects using periodic boundary conditions. The boundary condition on a RVE

element is established by symmetry consideration so that the micromechanics analysis

can be confined to a single repeating element. The periodic boundary conditions maintain

equal boundary displacements with the adjacent unit cells to satisfy the compatibility of

displacements on opposite faces of the unit cell and enforce the continuity of stresses.