Cell Periodicity
Use the Cell Periodicity node to model a repeating unit cell (RUC) or representative volume element (RVE) of a larger repetitive structure. Periodic or uniform temperature boundary conditions are then used on the cell outer boundaries.
From the Cell Periodicity node, it is possible to compute the thermal conductivity tensor, the heat capacity at constant pressure and the density for the equivalent homogenized material.
This node is available for 3D and 2D components. Since the homogenization is only for heat transfer by conduction, the Cell Periodicity node is only applicable on Solid domain feature.
Cell Properties
Select the Boundary condition type among Periodic temperature (default) and Uniform temperature gradient.
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When Periodic temperature is selected, the temperature is periodic over the cell outer boundaries. Boundary Pair subfeature must then be applied to all the cell outer boundaries.
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When Uniform temperature gradient is selected, the temperature gradient is uniform over the cell outer boundaries. This option can be used to prescribe boundaries when the cell geometry does not represent a periodic microstructure.
The Temperature scale factor (dimensionless, default value 1) multiplied by 1 kelvin defines the amplitude of temperature used for the calculation of equivalent homogenized material properties. Changing this value only affects results if the material properties used in the unit cell depend on the temperature.
The temperature over the cell outer boundaries is set to the Reference temperature defined in the Physical Model section of the physics interface, plus the amplitude of temperature defined by the Temperature scale factor.
Load Group, Material and Study Generation
The equivalent material properties for a homogenized material can be created, and made accessible as a material to be used in other components. In order to do this, a number of fundamental load cases must be analyzed. The necessary definitions and steps required for such an analysis can be automated as described below.
On the Cell Properties section toolbar, the Automated Model Setup () menu has the following entries:
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Create Load Groups and Study (). This option can be selected when the Domain Selection of the Cell Periodicity feature is not empty. When selected, 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 Heat Transfer Cell Periodicity. The load groups correspond to unit loads along different axes.
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A new study, named Cell Periodicity Study htcp1, with ht and cp1 referring respectively to the tags of the parent physics interface and the corresponding Cell Periodicity feature, will be created. This study contains a stationary study step that solves for the parent physics interface only. 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 Domain Selection of the Cell Periodicity feature is not empty. When you select it, a new material will be created under Global > Materials. It contains the thermal conductivity tensor, the heat capacity at constant pressure, and the density of the equivalent homogenized material. The name of this material is Homogeneous Material (htcp1mat), with ht and cp1 referring respectively to the tags of the parent physics interface and the corresponding Cell Periodicity feature.
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Create Material by Value (). This option can be selected when results from the study generated by Create Load Groups and Study are available. 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 homogenized material generated from it can still be used in subsequent computations.
For this type of analysis to work correctly, it is important not to manually edit the generated nodes. By clicking the Create Load Groups and Study () button again, all settings in the generated nodes are reset to their default values.
Constraint Settings
To display this section, click the Show More Options button () and select Advanced Physics Options in the Show More Options dialog.
The Constraint settings can be set to Pointwise constraints (default), Weak constraints or Nitsche constraints.
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Constraint Reaction Terms
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Weak Constraints
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Constraint Settings
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Theory for Cell Periodicity
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Using Load Cases and Materials in the COMSOL Multiphysics Reference Manual.
Equivalent Properties of Periodic Microstructures: Application Library path Heat_Transfer_Module/Applications/equivalent_properties_of_periodic_microstructures
Location in User Interface
Context Menus
Heat Transfer in Solids and Fluids > Specific Media > Cell Periodicity
Heat Transfer in Solids > Specific Media > Cell Periodicity
Heat Transfer in Fluids > Specific Media > Cell Periodicity
Heat Transfer in Porous Media > Specific Media > Cell Periodicity
Heat Transfer in Building Materials > Specific Media > Cell Periodicity
Bioheat Transfer > Specific Media > Cell Periodicity
Ribbon
Physics tab with interface as Heat Transfer in Solids, or any version of the Heat Transfer interface selected:
Domains > interface > Specific Media > Cell Periodicity