Formulation of a unit cell of a reduced size for plain weave textile composites

A unit cell of a much reduced size for plain weave textile composites has been formulated in this paper. Use has been made all available and independent types of geometric symmetries, including translations, reflections and rotations. These geometric symmetries have been interpreted into appropriate mechanical terms based on the concept of relative displacements, from which boundary conditions for the unit cell have been derived systematically. All loading conditions in terms of macroscopic stresses/strains have been considered for full characterisation of such composites. As loading conditions associate with shear have to be derived individually and separately from the direct stress loading conditions due to the use of reflectional and rotational symmetries, the boundary conditions obtained may therefore appear to be tedious but comprehensive and systematic. The unit cell formulated has been validated and an example of application has been illustrated.