Implementation of periodic boundary conditions for loading of mechanical metamaterials and other complex geometric microstructures using finite element analysis

The implementation of periodic boundary conditions (PBCs) is one of the most important and difficult steps in the computational analysis of structures and materials. This is especially true in cases such as mechanical metamaterials which typically possess intricate geometries and designs which makes finding and implementing the correct PBCs a difficult challenge. In this work, we analyze one of the most common PBCs implementation technique, as well as implement and validate an alternative generic method which is suitable to simulate any possible 2D microstructural geometry with a quadrilateral unit cell regardless of symmetry and mode of deformation. A detailed schematic of how both these methods can be employed to study 3D systems is also presented.

Automated summary

The implementation of PBCs is crucial and challenging in computational analysis of structures and materials, especially for complex geometries like mechanical metamaterials. This work analyzes a common PBCs implementation technique and introduces an alternative method for simulating 2D microstructural geometries with quadrilateral unit cells. It also provides a detailed schematic for studying 3D systems using both methods.