Modelling hyperbolic and elliptic elasticity with discontinuous coefficients using an error driven adaptive isogeometric basis

使用误差驱动的自适应等几何基础对具有不连续系数的双曲和椭圆弹性进行建模

• 批准号: EP/W023202/1
• 负责人: Adriana Paluszny Rodriguez
• 金额: $ 9.75万
• 依托单位: Imperial College London
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2022
• 资助国家: 英国
• 起止时间: 2022 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FW023202%2F1
• 关键词: Modelling; hyperbolic; elliptic; elasticity; discontinuous

The UK has pledged to achieve net zero emissions by 2050, aiming to develop green transition technologies such as geothermal energy, geological storage of CO2 from industrial and direct air capture sources, hydrogen fuel cells, batteries, and compressed-air energy, as well as advancing nuclear as a clean energy source through clean storage and disposal. The success of these technologies is highly dependent on understanding the behaviour of Earth materials at a range of scales, in the context of deformation, fluid flow, and temperature changes, which can affect how rocks break and how fluids and heat migrate in the subsurface through these rocks. Understanding how fractures and other smaller-scale heterogeneities affect rock properties also furthers the capabilities of numerical models dedicated to predicting fractures in ceramics, composites, bioengineered materials, human bones, and ion lithium batteries, as additional examples.Processes governing fracturing in complex media, and the interaction of fractures with smaller and larger scale discontinuities and material variations, is often investigated using numerical models. The main drawback of these models is that their performance usually depends on the amount of detail included, such as the geometric details of the ensuing fractures, and distributions of differently shaped embedded inclusions that tend to change the material's behaviour. However, having the ability to effectively and accurately model real full-scale heterogeneous multi-scale problems is necessary to the development of robust, low-carbon and cost-effective strategies that underpin the energy transition. This project proposes to develop a key mathematical strategy to enhance the performance of computational solid mechanics methods, while incorporating additional levels of detail in the description of the material. We propose to develop, implement, and validate an efficient three-dimensional multi-scale numerical method, that combines 3D volumetric isogeometry in bodies containing fractures, with numerical error estimators to more efficiently represent mm- and cm-scale heterogeneities when computing the deformation of a meter- to km-scale body containing multiple fractures. Error estimators enable regions critical to overall solution accuracy to be targeted with higher levels of computational power, dynamically adjusting detail and load during the simulation. As opposed to other methods, the specific method to be developed during this project supports both small and large variations in the material properties, without compromising the quality of the solution, and without inflating the computational cost of the method. Computational efficiency and accuracy enable the method to be applied effectively to large real-world problems, enabling the consideration of larger and more realistic problems without significantly increasing computational effort. Developing the ability to model such problems, and sharing the development through open-source code with the wider scientific community, is of national importance. Quantifying the relationship between scales in the context of solid body fracturing, in complex scenarios, directly supports responsible innovation in the UK, and supports the development of low-carbon and effective energy generation schemes, safe and clean deposition of waste materials, and elongating the life and increasing the efficacy of electrical storage devices.

英国承诺到2050年实现净零排放，旨在开发绿色转型技术，例如地热能、工业二氧化碳地质储存和直接空气捕获源、氢燃料电池、电池和压缩空气能源，以及通过清洁储存和处置，推动核能成为清洁能源。这些技术的成功在很大程度上取决于对地球材料在变形、流体流动和温度变化的背景下在一定范围内的行为的理解，这可能会影响岩石的破裂以及流体和热量如何在地下通过这些岩石。了解裂缝和其他较小尺度的非均质性如何影响岩石特性还可以进一步增强致力于预测陶瓷、复合材料、生物工程材料、人体骨骼和离子锂电池等裂缝的数值模型的能力。控制复杂介质中破裂的过程，以及裂缝与更小和更大尺度的不连续性和材料变化的相互作用，通常使用数值模型进行研究。这些模型的主要缺点是它们的性能通常取决于所包含的细节数量，例如随后断裂的几何细节，以及往往会改变材料行为的不同形状嵌入夹杂物的分布。然而，拥有有效、准确地模拟真实的全面异构多尺度问题的能力对于制定支持能源转型的稳健、低碳和具有成本效益的战略是必要的。该项目建议开发一种关键的数学策略来增强计算固体力学方法的性能，同时在材料的描述中纳入额外的细节级别。我们建议开发、实施和验证一种高效的三维多尺度数值方法，该方法将包含裂缝的物体中的 3D 体积等几何测量与数值误差估计器相结合，以便在计算变形时更有效地表示毫米和厘米尺度的异质性。一个米到公里大小的物体，含有多个裂缝。误差估计器使对整体解决方案精度至关重要的区域能够以更高水平的计算能力为目标，在仿真过程中动态调整细节和负载。与其他方法不同，该项目期间开发的特定方法支持材料属性的小变化和大变化，而不会影响解决方案的质量，也不会增加该方法的计算成本。计算效率和准确性使该方法能够有效地应用于大型现实问题，从而能够在不显着增加计算量的情况下考虑更大、更现实的问题。培养对此类问题进行建模的能力，并通过开源代码与更广泛的科学界分享开发成果，具有国家重要性。量化固体压裂背景下、复杂场景下的尺度关系，直接支持英国负责任的创新，支持制定低碳有效的能源发电方案，安全清洁地沉积废弃物，延长英国的生命周期。寿命并提高蓄电装置的功效。