4.1.1 Modulus, Moduli

Modulus is Latin for stiffness, like in Young’s modulus. The plural is Moduli. A lamina can be approximated very well by a transversely isotropic material, which requires 5 properties to be completely described. Sometimes it is convenient to use 6 properties, although one of the 6 can be computed from the other. The 5 useful properties are:

$E_1$. Longitudinal modulus. Longitudinal means fiber direction, i.e., 1-direction.

$E_2$. Transverse modulus. Transverse means perpendicular to the 1-direction but still in the plane (surface) of the lamina.

$G_{12}$. In-plane Shear modulus.

$\nu _{12}$. In-plane Poisson’s ratio.

$\nu _{23}$. Intralaminar Poisson’s ratio.

The following derived properties are necessary if the lamina needs to be modeled as orthotropic [3, Eq. (1.91)], [4, Eq. (1.91)], for example to generate input data for certain finite element analysis software:

$E_3=E_2$. Through-the-thickness modulus.

$G_{23}=E_2/[2(1+\nu _{23})]$. Intralaminar Shear modulus, also called out-of-plane shear modulus.


$\nu _{13}=\nu _{12}$.

I prefer to report (or seek) $\nu _{23}$ rather than $G_{23}$ because the former is always a value approximately in the range 0.3–0.5, while the later can be anything. So, I can immediately tell if the data I am given is reasonable or not. Since always $E_2$ must be available, you can can easily calculate one from the other using the formula above, which is nothing but Equation 4.2.