Concurrent finite element analysis of periodic boundary value problems Original Research Article

A parallel finite element approach for analyzing micromechanical problems with periodic unit cells is discussed. The method uses a direct solution strategy so that general periodic boundary conditions can be treated using a two-step domain decomposition strategy. The speedup results show a good performance of the method on coarse-grained problems, i.e. for cases where the computational work done on the substructures that are treated in parallel is relatively large compared to the total amount of computational work. Application examples using crystal-plasticity on an array of planar crystals and a metal matrix composite are used to show that the overall response of these materials is rather strongly dependent on the constraint imposed on the unit cell so that a correct treatment of the periodic boundary conditions is required to accurately predict the macroscopic response of a periodic material even though a unit cell with a large number of grains or fibers is used.