To model a periodic unit cell or a RVE (representative volume element), you add the domain feature Cell Periodicity, and select the domains representing the cell. For each pair of matching boundaries, add a Boundary Pair subnode, and select the corresponding boundaries, typically on the opposite sides of the cell.

In principle, there is no limitation on the physics features you can use for modeling the cell, as long as the basic assumptions about periodicity and homogeneity are valid. You should, however, not add any displacement constraints since the possible rigid-body motions are automatically constrained by the Cell Periodicity node.

Two different types of material properties can be automatically evaluated using the Cell Periodicity node. With the Free Expansion periodic condition, you can calculate the homogenized material properties related to the free expansion of the RVE when exposed to a variation in temperature or moisture concentration — that is, the averaged coefficient of thermal expansion and the averaged coefficient of hygroscopic swelling. To set up an analysis for the evaluation of thermal properties, add a Thermal Expansion subnode to each material model used in the RVE, and apply a one degree increment in temperature. Similarly, for hygroscopic properties, add Hygroscopic Swelling subnodes and apply a unit increment in concentration. Without adding these subnodes to the material models of the RVE, no expansion is applied to the unit cell, and consequently the results will be zero. The results will also be zero if no variation in temperature or concentration is applied. If requested, the computed material properties are by default presented in a separate evaluation group under Results.

With the Average strain or Average stress periodic conditions, you can calculate the homogenized elastic properties of the RVE. Use Average strain to compute the elasticity matrix, or Average stress to compute the compliance matrix. In order to compute these properties, the deformation of the RVE needs to be evaluated for a number of fundamental load cases. These correspond to the perturbations of the unit cell with each component of the average strain or stress tensor, while keeping the other components equal to zero. Setting up this analysis can be automated with the Create Load Groups and Study option under the Study and Material Generation button. It creates a load group for each tensor component, populates the average strain or stress tensor, and creates a study with a load case for each load group. When the calculation of an average material property is requested, the computed values are by default presented in a separate evaluation group under Results. If no material property evaluation is requested, or if it is not available, the results can be used to study the response of the RVE to the applied load cases.

You can also create a global material using the Create Material option under the Study and Material Generation button. This is available for the Average strain or Average stress periodic conditions. This option creates a material that contains the homogenized elasticity or compliance matrix, which can be accessed by other components in the model. Note that if you want to use the computed material properties in another model or store them in a user-defined material library, use the Create Material by Value option. For the Create Material by Reference option, the automatically generated global material contains variables linked to the Cell Periodicity node in the current model.