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

就像植物通过细胞的扩张和繁殖生长一样，3D打印组件是通过自下而上逐点粘合材料形成的。利用这种类比，这项工作采用了三维植物生长的数学模型，以进一步理解和帮助实施增材制造（AM）技术（也称为3D打印）。这些打印结构的分辨率在模拟组织的机械性质的组织支架或构造的制造中是最重要的。因此，首要目标是通过操纵系统的底层物理来推导出一个通用的数学模型来模拟基于挤出的生物打印过程。这样的模型有可能在理论上确定打印工艺参数的哪些组合产生成功的分辨率：生物墨水的“可打印性窗口”。水凝胶通常呈现剪切稀化行为。在这篇论文中，我们开始考虑最简单的情况：远离任何边缘效应的牛顿流体流动。我们实现这一点，通过推导出一个稳态模型的粘性螺纹挤压下使用弧长为基础的坐标系。这个初始模型仍然是我们朝着非牛顿模型方向努力的一个重要里程碑，为我们提供了一个强有力的框架，在此基础上可以建立非牛顿扩展。有了这一点，我们打算迭代放松假设的粘度和表面张力，使模型逐渐收敛到真实的系统，以及提供任何理由的影响假设在建模过程中可以忽略不计。我们计划采用实验技术在每个里程碑进行验证。这种独特的跨学科方法旨在优化材料和实验室之间结果的可比性和可移植性，最重要的是，通过为工程师设计一个用户友好的可持续工具，将AM可视化为一个增长过程，从而扩展AM设计的创造力和效率。

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.