Developing mathematical models to incorporate microstructural heterogeneities into viscous flow

开发数学模型将微观结构不均匀性纳入粘性流

• 批准号: 2745507
• 金额: --
• 依托单位: University of Leeds
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2022
• 资助国家: 英国
• 起止时间: 2022 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2745507
• 关键词: Developing; mathematical; models; incorporate; microstructural

Ice and rocks flow viscously as complex non-Newtonian fluids. Current models commonly neglect several key rheological effects introduced by the heterogeneity of the materials' (micro)structure. The incorporation of these complex features into viscous fluid dynamics presents exciting research opportunities, to be addressed in this PhD project. An example concerns our ability to predict the rate of collapse of the Earth's ice sheets, which depends centrally on the dependence of ice rheology on the heterogeneities of its microstructure. Another is the movement of tectonic plates, which controls the occurrence and severity of earthquakes. Simulations in solid-Earth viscous flows typically apply isotropic models that are insufficient to describe leading-order characteristics of ice and rock flow dynamics because of the presence of microstructural heterogeneities: complexities at a small scale due to the presentence of differing material types (e.g. layering) and polycrystal arrangement (crystal grains, each oriented/slipping in different directions). This project presents an opportunity to address key open questions needed to close this gap in fluid-mechanical modelling of environmental systems. The effects of polycrystalline arrangement involves coupling a statistical representation of the material's microstructure with viscous anisotropy. The evolution of layers involves the analysis of the folding and necking instabilities associated with elastic and viscous beams separated by interstitial fluid of different material properties. The project thus presents a variety of directions, and the specific focus will be primarily mathematical, but otherwise tailored to the interests of the student.

冰和岩石作为复杂的非牛顿流体粘性流动。目前的模型通常忽略了几个关键的流变效应所引入的材料的（微观）结构的不均匀性。将这些复杂的功能纳入粘性流体动力学提出了令人兴奋的研究机会，将在这个博士项目中解决。一个例子涉及到我们预测地球冰盖崩溃速度的能力，这主要取决于冰的流变学对其微观结构的非均匀性的依赖。另一个是构造板块的运动，它控制着地震的发生和严重程度。固体-地球粘性流的模拟通常采用各向同性模型，这些模型不足以描述冰和岩石流动动力学的主导阶特征，因为存在微观结构的不均匀性：由于存在不同的材料类型（例如分层）和多晶排列（晶粒，每个晶粒在不同方向上取向/滑动），小尺度上的复杂性。该项目提供了一个机会，以解决关键的开放性问题，需要关闭这一差距，在流体力学建模的环境系统。多晶排列的影响涉及耦合材料的微观结构的统计表示与粘性各向异性。层的演变涉及的折叠和颈缩不稳定性的分析与弹性和粘性梁分离的间隙流体不同的材料特性。因此，该项目提出了各种方向，具体重点将主要是数学，但在其他方面适合学生的兴趣。