Table 1 Solution scheme of FEPOD

Offline

Set up RVE

Apply predefined idenpendent deformation states

Run and save solutions for each case

Calculate subspace for each RVE separately

Online

1. Set up macroscopic model

   Geometry, boundary conditions

Initialize RVEs

   FE discretization

Load subspace

   Set RVEs for each material

2. Run simulation

   Loop time or load step

      Apply load increment

   Loop Newton iteration

   Loop elements

   Loop material points

      Calculate \({\mathbf F}_M\)

      Load history variables

\(\Rightarrow \)

Calculate boundary conditions for RVE

Solve RVE with POD reduction

If convergence is reached:

   Calculate \({\mathbf P}_M\)

   Calculate \({\mathbf C}_M\)

    Save local history variables globally

      Store \({\mathbf P}_M\), \({\mathbf C}_M\) and history

\(\Leftarrow \)

   End (material points)

   End (elements)

      Global assembling

      Check convergence

      If converged: BREAK

   End (Newton iteration)

   Update displacements

   End (time/load step)