Comparison of the implicit and explicit finite element methods using crystal plasticity

Abstract

The implicit finite element (FE) method can encounter numerical difficulties when solving non-linear quasi-static problems. The iterative approach employed may have trouble achieving convergence in analyses with a highly non-linear material behaviour, such as a crystal plasticity constitutive model. In the case of the explicit FE method the solver equations can be solved directly to determine the solution without iteration, thus providing an alternative, more robust method. In this study, a rate-dependent crystal plasticity algorithm was developed for use with the explicit FE package, ABAQUS/explicit. The subroutine and an equivalent implicit version were used in a series of comparative boundary value problem analyses. The suitability of the implicit and explicit solvers to various loading conditions was assessed and multiple processor speedup rates were also investigated. The results of the study showed that, for simpler loading conditions, the implicit method had a shorter solution time. In the case of loading conditions involving contact, the explicit method proved to be the preferable choice. The explicit method displayed constantly high levels of parallelisation efficiency compared to the implicit method for analyses solved using multiple processors. In conclusion, although the implicit FE method is traditionally favoured when solving quasi-static problems, it is important to recognise the advantages that the explicit method has in solving certain loading conditions.