In 2D, use either a Plane stress or a Generalized plane strain approximation to calculate averaged properties with the Free expansion boundary condition.
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When Periodic is selected, the average stresses or strains are periodic over the cell boundaries.
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The Homogeneous option can be used to prescribe boundaries when the cell geometry does not represent a periodic microstructure.
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When Free expansion is selected from the Boundary conditions list, the cell is allowed to expand freely. This option is useful to determine the thermal expansion or hygroscopic swelling coefficients in heterogeneous media.
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In 2D, use either a Plane stress or a Generalized plane strain approximation to calculate averaged properties with the Free expansion boundary condition.
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When Average strain is selected from the Boundary conditions list, it possible to derive homogenized elastic properties of media, such as a perforated plates, porous media or composites structures. In this case, six load cases need to be examined in 3D.
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When Average stress is selected from the Boundary conditions list, it is possible to derive the homogenized compliance matrix. Enter values or expressions for the components of the Average stress tensor σavg. In a geometrically nonlinear analysis, the stresses are interpreted as second Piola–Kirchhoff stresses.
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In 2D, use a Generalized plane strain approximation to calculate averaged properties with the Average strain or Average stress boundary conditions.
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When Mixed is selected from the Boundary conditions list, enter either the Average strain or Average stress for each tensor component.
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When using a Plane stress or a Plane strain 2D approximation with the Mixed boundary condition, you only need to enter three components (XX, YY, XY) of the average strain or average stress tensors. For the Generalized plane strain approximation, you also need to enter the ZZ component.
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When Automatic is selected, the cell volume is computed from the domain or domains selected in the Domain Selection section.
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The Void volume fraction option can be used to scale the cell volume when there are voids that are not selected as domains. Enter the void volume fraction, f. This is the fraction of the cell that is occupied by voids. The volume of the cell is computed as
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). It has a list with three entries:|
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Create Load Groups and Study
 . This option can be selected when the Boundary conditions are Average strain or Average stress. When you select it, the following changes will be made to the model: |
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A number of load groups will be created under Global Definitions. They are collected in a group named Load Groups for Cell Periodicity. The load groups correspond to unit loads along different axes.
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The Average strain or Average stress tensor in the Cell Properties section will be populated using the load group variables.
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A new study, named Cell Periodicity Study, will be created. This study contains a stationary study step. In the Study Extensions section of the new Cell Periodicity Study, one load case is added for each load group.
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Create Material by Reference (
 ). This option can be selected when the Boundary conditions are Average strain or Average stress, and Calculate average properties is not set to None. When you select it, a new material will be created under Global>Materials. It contains the elasticity matrix or the compliance matrix. The name of this material is Homogeneous Material. |
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Create Material by Value (
 ). This option is similar to Create Material by Reference, with the difference that the material properties are numerical values, and not references to variables in the node. The benefits of this option is faster computation when the material is used by other physics interfaces. Also, if the Cell Periodicity node is deleted, the material created from it can still be used in sequential computations. |
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For this type of analysis to work correctly, it is important that you do not edit the generated nodes manually. By clicking the Create button again, you can reset all settings in the generated nodes to their default values.
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) and select Advanced Physics Options in the Show More Options dialog box. Furthermore, this section is shown only if elasticity or compliance matrices are requested through Calculate average properties.
) and select Advanced Physics Options in the Show More Options dialog box.
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In the COMSOL Multiphysics Reference Manual:
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