Stress-strain Relationship in a Laminate

In order to extend the relationship for the complete laminate. You will need first transformation of the previous relationship with respect to the ply-angle - since every ply need not be oriented towards the fibre direction. Applying a transformation coordinate, the stress-strain relationship is redefined as:

Where, the new elastic constants are obtained by using the transformation matrix given by:

Where, m= Cos ? , n=Sin ?