Regularisation in Direct FE2 multiscale modelling of fused-filament fabricated parts

Abstract

This study investigated regularisation methods in Direct FE${}^2$ failure analysis of fused-filament fabricated (FFF) parts modelled as fibre-reinforced composites. Direct FE${}^2$ technique offers simplicity with moderate computational cost by incorporating microstructural variations of FFF parts into macroscopic constitutive behaviour. However, similar to conventional FE${}^2$ methods, loss of positive-definiteness in tangent stiffness matrix occurs at structural level because of the material-level strain localisation and softening behaviour. Further numerical complexity is added when element deletion technique (EDT) is employed; an aspect which remains unexplored for Direct FE${}^2$. To address these issues, three regularisation methods (fracture energy, viscous, and combined schemes) were implemented in Direct FE${}^2$ analyses with EDT and their performance was evaluated in predicting the stiffness, strength, and deformation modes of poly(lactic) acid FFF parts with varying ductility. The results of Direct FE${}^2$ numerical analyses were compared to regular FE predictions and experimental tensile samples manufactured with different raster angles. It was found that unregularised Direct FE${}^2$ simulations suffered from convergence issues and the effectiveness of the regularisation method depended on material ductility, i.e., while some regularisation schemes could alleviate instabilities, others made an unrealistic prediction of failure mechanism. The combined regularisation approach was most effective in predicting ductile (0°) and moderately-ductile (mixed-mode, 45°) behaviour whereas fracture energy approach was best-suited for brittle failures (90°). The viscous regularisation tended to initiate EDT prematurely while combined regularisation provided more realistic depiction of microstructural deterioration.