## 6.4. Calculating Laminate Properties from Uni-Directional Data

Laminates made from composite materials often consist of a number of repeating sublaminates or individual lamina. Typically material data may be available for a uni-directional lamina and it is therefore desirable to be able to be able to calculate the effective material properties for the laminate from the constituent lamina properties.

This is also useful since within Autodyn each layer of the laminate is not explicitly modelled, rather continuum elements representing equivalent homogeneous anisotropic solids are used to represent thick laminates consisting of a number of repeating lamina.

The approach of Sun and Li [4] has successfully been used to calculate laminate properties for use in Autodyn and is now described.

Consider a laminate consisting of N orthotropic fiber composite lamina of arbitrary fiber orientations. In the following description the x and y co-ordinates are in the plane of the composite and z is through the thickness. The effective macro-stress and macro-strains are defined to give,

| (6–15)

| (6–16)

where and are the stresses and strains in the kth lamina and, if t k is the lamina thickness and h the total thickness

| (6–17)

The effective elastic properties for the laminate are given by,

| (6–18)

The x-y plane for a lamina is a plane of symmetry and is also a symmetry plane for the effective solid. Therefore the effective stiffness matrix reduces to the following form,

| (6–19)

and effective compliance matrix is calculated as,

| (6–20)

where the effective elastic properties are then,

| (6–21)

After lengthy algebraic manipulations the following expressions are recovered for the effective stiffness matrix coefficients [4],

| (6–22)

where,

The principal material directions of all the lamina in the laminate will not necessarily be aligned with the global axes. Therefore, before the above summations can be performed it will be necessary to transform the stiffness matrix for each lamina as follows,

| (6–23)

where the transformation matrix T is defined as,

| (6–24)

and the angle θ is the angle of the material directions with regards to the global axes.

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