The European Ceramic Society


Dec 18, 2023

YCN Newsletter 19 - Near-universal slicing for continuous-extrusion Direct Ink Writing through Differential Growth algorithms by Marco D’Agostini

Additive Manufacturing (AM) processes have unlocked groundbreaking potential for the production of ceramic components.

Direct Ink Writing (DIW) is a versatile AM technique which involves shaping the desired object by layerwise extrusion of the feedstock material through a fine nozzle, similarly to the Fused Deposition Modelling (FDM) process applied to thermoplastic polymers. FDM features a large collection of user-friendly, commercial slicing software which automatically generates printing toolpaths from a 3D CAD model of the object, but in DIW the challenging implementation of discontinuous extrusion limits their applicability and renders toolpath design an often manual and tedious process.

In order to achieve continuous extrusion, the toolpaths describing the movement of the nozzle during the 3D-printing process must form a single, continuous and non-intersecting curve perfectly tracing the desired object; thus, automated generation of the curve for any object of arbitrary shape is a complex mathematical problem with few analytical solutions outside of simple geometries. The approach followed in our research is inspired by Differential Growth, a common phenomenon in the natural world involving the growth of biological systems in confined spaces: this results in the formation of space-filling, heavily folded 2D or 3D patterns commonly seen, for example, in the shape of corals and mammalian brains. These types of patterns often comply with the geometrical requirements discussed above, making them ideal continuous-extrusion toolpaths.

A custom Differential Growth algorithm was developed in Grasshopper3D. After sectioning the 3D CAD model of the object into horizontal layers, the algorithm attempts to maximise the length of a curve inside each section through an iterative approach, where “growth” of the curve is prompted locally by the presence of empty space. The curve progressively fills the entire section, with self-avoidance and homogeneity ensured by treating the vertices of the curve as solid, colliding spheres. The final curve approximates the desired section and respects continuity requirements even in the case of complex geometries, providing a reliable and fully automated way to generate continuous toolpaths for DIW from the initial CAD model and user-defined settings similarly to commercial FDM slicers. In addition to DIW, the same approach can be extended to FDM processes in cases where the use of discontinuous extrusion may be problematic, such as for pellet-based FDM or when working with fibre-reinforced filaments.


Example of a Differential Growth pattern generated through Grasshopper3D (left); automated generation of continuous toolpaths from a geometrically complex CAD model and PLA prototype printed by entirely continuous extrusion (right) 


Marco D’Agostini

CerAMglass Research Group – Advanced Ceramics and Glasses 

Department of Industrial Engineering, University of Padova (Italy) 


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