Hi Samson07,
I think this needs to be tackled from a strain perspective as well as a stress perspective as the material is a laminate. For composites, you need to perform both on-axis properties and off-axis properties in order to fully analyse the laminate.
Try looking under 'Stress and Strain Transformations in Composites'. This should tell you a bit more about it and it will also explain the stiffness matrix that you have presented in your attachment.
Good luck...
Kind Regards,
Jus