Comparison between periodic and non-periodic boundary conditions in the multi-particle finite element modelling of ductile powders

Abstract

In recent years, the multi-particle finite element method (MPFEM) has demonstrated its suitability for the micromechanical modelling of granular systems made up of highly deformable particles. This method combines the advantages of the finite element method to compute particles’ deformations and of the discrete element method to simulate particles’ interactions. Being computationally expensive, its main drawback is the limitation of the number of particles which can be included in a simulation. However, using a multi-scale approach, it is possible to deduce mesoscopic material properties from the simulation of a relatively small number of particles within an elementary volume, through appropriate averaging techniques. Such simulations are significantly influenced by the boundary conditions (BCs) applied. Periodic BCs are commonly admitted to be the most accurate. However, they are technically rather difficult to implement in the MPFEM because of the multiple contacts which need to be handled in the model. As a result, simplified BCs involving for example, rigid walls, remain used. This study analyses the effect of different types of BCs on the simulated mechanical response of a numerical granular sample, under quasi-static loading. Two different techniques for implementing full or simplified periodic BCs, introduced by Schmidt et al. [1] and Loidolt et al. [2], respectively, were compared with simpler, non-periodic BCs. In the comparison, the same initial microstructure was used; it consisted of an assembly of 50 spherical particles with a periodic topology. The results suggest that considering the additional computational cost induced by the implementation of multi-point constraints, the advantage brought by periodic BCs is relatively limited. The study also highlights the differences between BC types and provides interpretations relative to the particularities of the numerical method used.