Layerwise (LW) Theory
A layerwise (LW) theory for modeling composite laminates is very similar to a traditional 3D elasticity theory, where the degrees of freedom are the displacements defined in the product geometry created by the reference surface, and an extra dimension in the thickness direction.
There are two approaches depending on the way degrees of freedom are defined:
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Partial displacement field approach
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Full displacement field approach
In the partial displacement field approach, the laminate thickness remains constant, whereas the full displacement field approach allows a change in thickness of the laminate. In COMSOL Multiphysics, a full displacement field based layerwise theory is implemented in the Layered Shell interface.
The layerwise theory is more accurate than the equivalent single layer theory, but it comes at the cost of more degrees of freedom. It is significantly more expensive in terms of computer resources.
From accuracy point of view, the layerwise theory is as accurate as traditional 3D elasticity theory, but it has several benefits:
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No need to build a 3D geometry with many thin layers.
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Easy to handle layerwise and interfacial data.
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In-plane finite element meshing is independent of the out-of-plane (thickness direction) meshing.
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A separate, either lower or higher, shape function order can be chosen in the thickness direction in order to avoid shear locking or to gain accuracy advantages.
Key Features
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Degrees of freedom (3 displacements) are defined in the product geometry created by the reference surface, with an extra dimension in the thickness direction.
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Predicts correct through-thickness or transverse shear stress variation, thus making it suitable for modeling thick shells.
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Predicts correct interlaminar stresses, and has degrees of freedom in the thickness direction making it suitable for delamination and detailed damage analysis.
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Supports nonlinear material models for advanced composite modeling.
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Supports different material models in different layers of a laminate. It is for example possible to combine linear elastic and hyperelastic materials in a single laminate.