Rigidity

Modulus of elasticity (Young's modulus) is a measure of rigidity. Modulus of elasticity has units of stress - [GPa] or [MPa].

The modulus of elasticity of a composite material depends on the component's parameters, fiber content and structure of the composite.

Boron, aramid, carbon fibers are more rigid than an aluminum or epoxy matrix:

E_f >> E_m

Both the matrix and fibers have the same strain under tension.
Stress is higher in the more rigid component.

The stress pattern in a composite beam demonstrates higher stress in rigid components and in external layers. Local delaminations and voids have a small effect on the flexural stiffness of the composite beam.

Poisson's ratio is a measure of transverse deformation under tension (compression).
An ordinary value of Poisson's ratio is 0.3 for steels.
There is lay-up scheme for which transverse deformation in a composite is higher in the longitudinal direction. Heres, Poisson's ratio is higher than 1.