Local Orientations
Many stress and strain tensor components are available both in local and global directions. Some examples are:
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solid.sxy — Cauchy stress with respect to the global spatial coordinate system
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solid.sl12 — Cauchy stress with respect to the local coordinate system of the material.
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solid.SXY — Second Piola–Kirchhoff stress with respect to the global material coordinate system
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solid.Sl12 — Second Piola–Kirchhoff stress with respect to the local coordinate system of the material
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solid.eXY — Strain with respect to the global material coordinate system
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solid.el12 — the local coordinate system of the material
As can be seen, tensor component indices containing the names of a coordinate directions has orientations along those axes. Components in local directions contain the letter ‘l’ and numerical indices.
The local directions are defined by the coordinate system attached to a material model. For most material models, you can select a local coordinate system in the Coordinate System Selection section of its settings. The purpose of this selection is twofold:
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It provides the orientations along which orthotropic and anisotropic material data are interpreted.
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It acts as the coordinate system in which the local stress and strain tensor components are presented.
When the material is isotropic, you can utilize the local coordinate system just for the second purpose. In this case, the results of the analysis itself are independent of the selected coordinate system. It just provides a transformation to be utilized during result evaluation. If you want to change the orientations for the local components of the tensors, you do not have to solve the study again. Instead, you select the new coordinate system in the material model node, and then run Update Solution () for the study or studies where you want the new definition to be applied.
Updating a Solution in the COMSOL Multiphysics Reference Manual.
Adding Your Own Transformations
If there are no suitable local coordinate system variables defined from the physics interface itself, you can create your own transformations.
The easiest way of doing that is to use the Local System Results node, available in some of the structural mechanics interfaces. Here, the input is just a local coordinate system.
A more general approach is to add a Vector Transform or Matrix Transform under Definitions>Variable Utilities, depending on the type of object you are going to transform.
These nodes provide a large degree of flexibility in defining various types of transforms, but for a pure rotation into a new coordinate system, the settings are straightforward. Do the following:
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Add the local coordinate system in which the results are to be presented under Definitions.
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In the Input section, enter the components of the vector or tensor to be transformed. In most cases, you can pick it using Replace Expression ().
Some tensors within the structural mechanics interfaces do not contain an intrinsic information about the associated coordinate system. This is in particular true for those tensors labeled as ‘local’. When using them in the Matrix Transform node, you must then manually select the coordinate system for the input tensor.
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In the Vector Transform or Matrix Transform node, select the local coordinate system in the Output section. In the latter node, select it twice.
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Select the domain where you want this transformation to be valid.
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Often, you want to enter your own name for the transformed object in the Name text field.
Figure 2-39: Example of settings for transforming the displacement vector to a cylindrical coordinate system.
If you define the transformation after the study was solved, you will need to run Update Solution () for the study or studies where you want to access the transformed variables.
You can now access the new transformed quantities for various type of result presentation. They are accessible under Definitions in the Replace Expression dialog.
Figure 2-40: Picking a transformed result in the Replace Expression dialog.
Vector Transform and Matrix Transform in the COMSOL Multiphysics Reference Manual.