Translating the Three-Dimensional Mathematical Modelling of Plant Growth to Additive Manufacturing

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Much like how plants grow via the expansion and multiplication of cells, a 3D printed component is formed via the bonding of material point-by-point from the bottom-up. Exploiting this analogy, this work employs mathematical models of three-dimensional plant growth to further understand and aid implementation of additive manufacturing (AM) technologies (otherwise known as 3D printing). The resolution of these printed structures is of the upmost importance in the fabrication of tissue scaffolds or constructs that mimic the mechanical properties of tissues. As such, the overarching aim is to derive a generalised mathematical model to simulate the extrusion-based bioprinting process via manipulation of the underlying physics of the system. Such a model has the potential to theoretically identify which combinations of printing process parameters generate a successful resolution: the 'window of printability' of a bioink.A hydrogel typically presents a shear-thinning behaviour. In this thesis we begin by considering the simplest case: a Newtonian fluid flow far from any edge effects. We achieve this via derivation of a steady-state model for a viscous thread under extrusion using an arc-length-based coordinate system. This initial model remains an important milestone in our work towards the non-Newtonian model; providing us with a strong framework upon which non-Newtonian extensions can build. With this in place, we intend to iteratively relax assumptions on the viscosity and surface tension, enabling the model to gradually converge towards the real system as well as provide any justification for effects assumed negligible in the modelling process. We plan to employ experimental techniques to provide validation at each milestone.This uniquely transdisciplinary methodology seeks to optimise the comparability and transferability of results across materials and laboratories and, above all, extend the creativity and efficiency of Design for AM by devising a user-friendly, sustainable tool for engineers to visualise AM as a process of growth.