Modelling of 3D concrete printing based on SPH method with the Herschel–Bulkley-Papanastasiou rheology model

A smooth particle hydrodynamic (SPH) method combined with the Herschel–Bulkley-Papanastasiou (HBP) model is proposed to simulate 3D concrete printing (3DCP). HBP model can better resolve the divergence of equivalent viscosity coefficient under small deformation and extend the compatibility of simulation to dilatant and pseudoplastic fluids, so it possesses natural superiority in modelling the 3D printing of cement-based material with visco-plastic rheology behaviour. The HBP-based SPH method considers the influence of the printing parameters including nozzle characteristics and printing-to-extrusion velocity ratio on the cross-sectional geometry of the deposited filament, and its outcomes agree qualitatively well with the experiment results. Furthermore, by utilising process parameters furnished by simulation cases, it is possible to determine the critical conditions under which filaments printed by different nozzle shapes are vulnerable to tearing, and the corresponding critical intervals when tearing occurs are also defined. 3DPC experiments verify these findings and confirm that SPH simulation provides additional information on the geometric characteristics of single-layer structures, as well as physical quantities that cannot be straightforwardly measured.