# 2.1. RVE Processing

The use of the RVE capability requires two regions, each with its own mesh file. One region processes the reference mesh and the other processes all the RVEs. The commands used in the input file for the reference mesh region are the same as any other Sierra/SM region with the exception that a special RVE material model is used for every element block that uses an RVE. The RVE region is similar to an ordinary region. The only differences are that an RVE region has a line command for defining the RVEs’ relationship to parent elements in the reference region and has restrictions on the use of boundary conditions.

The processing of an RVE essentially replaces the constitutive model of the parent element in the reference mesh. The steps followed at each iteration/time step of the reference mesh during an analysis using RVEs are as follows:

- Internal force algorithm is called in the reference region to compute rate of deformation.

- Each RVE gets the rate of deformation from its integration point on its parent element in the reference region.

- The rate of deformation is applied to each RVE as a periodic boundary condition using prescribed velocity.

- The RVE region is solved to obtain the stress in each element of each RVE.

- The stresses in the elements of an RVE are volume-averaged over the RVE.

- Each RVE passes its homogenized or volume-averaged stress tensor back to its integration point of its parent element in the reference mesh.

- The reference region computes internal force again. Element blocks whose elements have associated RVEs do not compute a stress; they use the stress passed to them from their RVE.