a$)$ Explain the difference$($s$)$ between orthotropic and anisotropic materials.

b$)$ See the sketch of a ply consisting of aligned unidirectional

fibers embedded in a matrix. The $x$ axis is aligned along

the fiber orientation $($longitudinal$).$ The $y$ and $z$ axes are

perpendicular to the fiber orientation $($transverse$).$

Materials properties about this ply are defined as below.

Provide the compliance matrix of this ply$.$

$E_L$ : elongation modulus along the longitudinal direction

$E_T$ : elongation modulus along the transvers direction

$v_{TL}$ : Poisson's ratio to calculate longitudinal strain caused by

transverse strain$/$stress

$v_{LT}$ : Poisson's ratio to calculate transverse strain caused by longitudinal strain$/$stress

$v_T$ : Poisson's ratio to calculate transverse strain in one direction caused by transverse strain in

the other direction

$G_{LT}$ : shear modulus for the shear strains within the plane defined by the transverse direction

$G_T$ : shear modulus for the shear strains within the plane defined by the longitudinal direction

c$)$ About the above material properties of a ply$,$ provide and justify a relationship between $v_{TL}$ and

$v_{LT}.$