TMM4175 Polymer Composites

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Assumptions for the laminate theory¶

The following assumptions are made for the classical laminate theory:

The layers are perfectly bonded
Each layer is homogeneous
Individual layer properties can be isotropic, transverse isotropic or orthotropic
Each layer is in a state of plane stress
The laminate deforms according to the Kirchoff assumptions:
1. Normals to the midplane remain straight and normal to the deformed midplane after deformation
2. Normals to the midplane do not change length

These assumptions simplify the analysis of laminates considerably, and is considered valid, or sufficiently accurate, when analysing thin plates and shells. A brief discussion on the assumptions follows.

Perfectly bonded layers

Separation between layers may exist due to lack of adhesion in the first place, or loading induced failure and damage (delamination). In such cases, the classical laminate theory will be unable to provide realistic results.

Homogeneous layers

A homogeneous layer has a set of properties that does not vary across the plane or through the thickness. For example, a honeycombe core is not homogeneous (although it is frequently treated as homogeneous), while fiber composite materials are considered homogeneous on the layer scale.

Plane stress

The assumption of plane stress is usually very reasonable over a larger region of thin laminates. However, 3-dimensional states of stress do generally exist at joints, transitions and boundaries of the shell structure. For example, the elastic mismatch between layers of different fiber orientation will cause both transverse shear stresses and normal stress through the thickness of the laminate at the free edges as shown in Figure-1 and Figure-2.

Figure-1: Through the thickness stress $\sigma_z$ at the free edges of a laminate [0/90/90/0] subjected to a tensile loading in the $x$-direction.

Figure-2: Through the thickness stress $\tau_{yz}$ at the free edges of a laminate [0/90/90/0] subjected to a tensile loading in the $x$-direction.

More on this topic in the case study Free edge effects of laminates

Kirchoff assumptions

As the thickness becomes large relatively to the other characteristic dimensions of the laminate, the Kirchoff assumptions become less realistic.

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