$($Maximum $10$ points$)$

$($a$)(5$ points$)$ A material following Hook's law will have $81$ constants. Show that for a general anisotropic material will have only $21$ independent constants, known as triclinic material.

$($b$)(5$ points$)$ Show that for an isotropic material principal stress and strain directions are same.

$($Maximum $10$ points$)$

$($a$)(8$ points$)$ Derive the expression for constitutive matrix for an angle ply lamina using generalized Hooke's law. Consider $E_1,E_2$ are Young's moduli,

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