Development of a finite element based strain periodicity implementation method

The current work proposes a novel approach for the implementation of periodic representative volume element (RVE) based multiscale modeling using the finite element method. The approach is based on a rigorous mechanics foundation that implements appropriate boundary conditions for the RVE analysis and simplifies the homogenization technique. Stress components are relaxed in the chosen periodic directions and associated strains are calculated while maintaining periodicity. Our concept ensures that for a displacement-based mechanics approach, the stresses and strains in the domain are periodic, rather than the displacements. This approach allows for computing homogenized effective mechanical properties of heterogeneous materials and capturing appropriate volume change and shape distortion of the RVE at lower length scales. We use the finite element based Multi-physics Object Oriented Simulation Environment (MOOSE, https://mooseframework.org) for implementing the proposed periodic RVE scheme. Our model has been verified with analytical calculations and effective property estimation from various micromechanical approaches. The effective stiffness of a composite material calculated from this approach is in good agreement with other computational and experimental findings. The proposed model has also been applied to different multiscale and multiphysics engineering applications.