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

将植物生长的三维数学模型转化为增材制造

• 批准号: 2449766
• 金额: --
• 依托单位: University of Birmingham
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2020
• 资助国家: 英国
• 起止时间: 2020 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2449766
• 关键词: Translating; Three; Dimensional; Mathematical; Modelling

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.

就像植物通过细胞的扩张和增殖来生长一样，3D 打印组件是通过材料自下而上逐点粘合而形成的。利用这个类比，这项工作采用了三维植物生长的数学模型来进一步理解和帮助实施增材制造 (AM) 技术（也称为 3D 打印）。这些印刷结构的分辨率对于制造组织支架或模仿组织机械性能的结构至关重要。因此，总体目标是推导出一个通用数学模型，通过操纵系统的基础物理来模拟基于挤出的生物打印过程。这样的模型有可能从理论上确定哪些印刷工艺参数组合可以产生成功的分辨率：生物墨水的“可印刷性窗口”。水凝胶通常呈现剪切稀化行为。在本文中，我们首先考虑最简单的情况：远离任何边缘效应的牛顿流体流动。我们通过使用基于弧长的坐标系推导挤出下的粘性螺纹的稳态模型来实现这一点。这个初始模型仍然是我们研究非牛顿模型的一个重要里程碑；为我们提供了一个可以构建非牛顿扩展的强大框架。有了这个，我们打算迭代地放宽对粘度和表面张力的假设，使模型能够逐渐向真实系统收敛，并为建模过程中假设的可忽略不计的影响提供任何理由。我们计划采用实验技术来验证每个里程碑。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转移性，最重要的是，通过设计用户友好的模型来扩展增材制造设计的创造力和效率是工程师将增材制造可视化为增长过程的可持续工具。