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Hooke's Law of a Composite Lamina

The constitutive equations describe how the stresses and straines relate within each lamina (Hooke's law). Detailed discussion can be found in the following sections: stress-strain relations of materials, stress-strain relations of lamina for principal directions, coordinate transformation of lamina for arbitrary orientation, and stress-strain relations of lamina for arbitrary orientation.

For a single lamina of any orientation,


and [C] is the principal stiffness matrix.



and [S] is the principal compliance matrix.

The coordinate transformation matrix is

and the angle is illustrated below

Hooke's Law of a Lamina within Laminated Composites

For a single lamina of any orientation within a laminated composite plate, the same relations apply. Let the subscript k indicate the kth layer of the laminate, counting from the top, we can write