Cell Periodicity

Use the node to model a unit cell (representative volume element; RVE) representing a large repetitive structure. Periodic boundary conditions will be used on the outer boundaries of this unit cell.

From the node, is possible to generate the elasticity matrix for the equivalent homogenized material.

If more than one node are used, they must have disjoint selections. It is thus possible to evaluate more than one RVE in the same study.

Periodicity Type

Select a — , , , or .

With the periodicity type, the unit cell is allowed to expand freely in a periodic manner. This option is useful to determine the thermal expansion or hygroscopic swelling coefficients of a heterogeneous unit cell. Select — , , or .


	In 2D, use either a Plane stress or a Generalized plane strain approximation to calculate averaged properties with the Free expansion periodicity type.

The periodicity type makes it possible to derive homogenized elastic properties of media with periodic structures, such as a perforated plates, porous media or composites structures. In this case, you have to examine six load cases in 3D. Enter values or expressions for the components of the tensor εavg. In a geometrically nonlinear analysis, the average strains are interpreted as Green–Lagrange strains.

Select — , , or .

The periodicity type makes it possible to derive the homogenized compliance matrix of media with periodic structures. Enter values or expressions for the components of the tensor σavg. In a geometrically nonlinear analysis, the stresses are interpreted as Second Piola–Kirchhoff stresses.

Select — , , or .


	In 2D, use a Generalized plane strain approximation to calculate averaged properties with the Average strain or Average stress periodicity types.

With the periodicity type, enter either the average strain or average stress tensor components.


	When using a Plane stress or a Plane strain 2D approximation with the Mixed periodicity type, 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.

For all values of , select the — , , or .

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When is selected, the volume of the RVE is computed from the domains selected in the node.

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The option can be used to scale the RVE volume when there are voids inside the RVE that are not selected as domains. Enter the void volume fraction, f. This is the fraction of the total RVE that is occupied by voids. The volume of the RVE is computed as

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By using the option, you can enter the volume of the RVE, V, explicitly.

The variable <item>.vol contains the volume of the RVE used when computing average strains and stresses.

Load Group, Material and Study Generation

You can create the elasticity matrix for a homogenized material, and make it 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 section toolbar, there is an icon (

). It has a list with two entries:

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. This option can be selected when is or . When you select it, the following changes will be made to the model:

A number of load groups will be created under . They are collected in a group named . The load groups correspond to unit loads along different axes.

The or tensor in the section will be populated using the load group variables.

A new study, named , will be created. This study contains a stationary study step. In the section of the new , one load case is added for each load group.

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(

). This option can be selected when is and not set to . When you select it, a new material will be created under . It contains the, in general anisotropic, elasticity matrix. The name of this material is .


	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.