Geometric Mechanics of Solids: new analysis of modern engineering materials

我们生活中的重要元素--能源、运输、制造--的成本和安全取决于我们用来制造部件和结构的工程材料。工程师需要回答的问题是，一个特定的部件或系统在多大程度上适合于特定的用途：核反应堆中的压力容器；飞机机翼；桥梁；燃气轮机；无论是在设计阶段还是在其整个工作寿命内。目前意外结构失效造成的损失占GDP的4%，这说明用现有的工程方法得出的答案并不总是可靠的。这些方法在很大程度上是现象学的，即依靠实验室的长度和时间尺度的实验来捕捉整个材料的行为。将这种行为外推到实际使用条件下的实际部件会带来不确定性。现有方法的主要问题是，通过将材料视为连续介质，即均匀分布的质量，它们不能本质地描述导致失效的材料老化机制的有限性质。如果我们学会如何克服以实验室为基础的现象学的限制，我们将能够以更高的信心预测结构行为，从而降低工程资产的建造和维护成本，从而降低所有个人和社会的商品和服务成本。例如，通过延长一个民用核反应堆的寿命，每小时产生的电力比新建核反应堆或传统发电厂的电力成本低10K-15K GB。这个项目是关于创造一种全新的技术，用于工程结构的高保真设计和评估。我将探索一种原创的固体几何理论，以克服唯象约束，开发一个开创性的结构分析软件平台，在几个长度尺度上验证该理论，并向工程师演示新技术如何解决现有方法不足以解决的实际问题。与经典方法不同，工程材料将被视为有限实体或单元的离散集合；重要的是，这不是像当前数值方法中使用的那样的连续统的离散化，而是材料如何在任何长度的观察尺度上组织的反映-从原子到形成工程组件的多晶聚集体。细胞结构的特征是不同的元素--细胞、面、边和节点--该理论提出了一种创造性的方法来描述这种结构的行为，将能量和熵与这些元素的几何属性--体积、面积、长度和位置--联系起来。这一理论将通过采用和更新现有算法并开发用于大规模并行计算的新算法，在一个高效的软件平台上实施，这将使工程师和科学家能够利用即将到来的硬件能力加速。随着未来五年计算能力的预期飞跃(到2020年，每秒1018次运算)，这项新技术将允许计算从原子到结构的整个长度尺度上的工程组件和结构的行为。由于非常强大的实验技术，例如基于实验室或同步加速器的层析成像，与图像分析技术相结合，如数字体积相关，现在可以在多个长度尺度上验证和确认该理论。一旦得到验证，该技术将被应用于一系列与工业直接相关的工程问题，如解理和延性断裂以及疲劳裂纹扩展，为工程界提供令人信服的演示。该工作的成果将使结构的建模和仿真有一个新的进步，适用于高价值、高风险、高回报的工程案例分析。

The cost and safety of the important elements of our life - energy, transport, manufacturing - depend on the engineering materials we use to fabricate components and structures. Engineers need to answer the question of how fit for purpose is a particular component or a system: a pressure vessel in a nuclear reactor; an airplane wing; a bridge; a gas turbine; at both the design stage and throughout their working life. The current cost of unexpected structural failures, 4% of GDP, illustrates that the answers given with the existing engineering methods are not always reliable. These methods are largely phenomenological, i.e. rely on laboratory length- and time-scale experiments to capture the overall material behaviour. Extrapolating such behaviour to real components in real service conditions carries uncertainties. The grand problem of current methods is that by treating materials as continua, i.e. of uniformly distributed mass, they cannot inherently describe the finite nature of the materials aging mechanisms leading to failure. If we learn how to overcome the constraint of the lab-based phenomenology, we will be able to make predictions for structural behaviour with higher confidence, reducing the cost of construction and maintenance of engineering assets and thus the cost of goods and services to all individuals and society. For example, by extending the life of one civil nuclear reactor the produced electricity each hour will cost £10k-15k less than from a new built nuclear reactor, or from a conventional power plant.This project is about the creation of a whole new technology for high-fidelity design and assessment of engineering structures. I will explore an original geometric theory of solids to overcome the phenomenological constraint, produce a pioneering software platform for structural analysis, validate the theory at several length scales, and demonstrate to the engineers how the new technology solves practical problems for which the present methods are inadequate. In contrast to the classical methods, the engineering materials will be seen as discrete collections of finite entities, or cells; importantly this is not a discretization of a continuum, such as those used in the current numerical methods, but a reflection of how materials organise at any length scale of observation - from atomic through to the polycrystalline aggregates forming engineering components. The cellular structure is characterised by distinct elements - cells, faces, edges and nodes - and the theory proposes an inventive way to describe how such a structure behaves by linking energy and entropy to the geometric properties of these elements - volumes, areas, lengths, positions. This theory will be implemented in a highly efficient software platform by adopting and modernising existing algorithms and developing new ones for massively parallel computations, which will enable engineers and scientists to exploit the impending acceleration in hardware power. With the expected leaps of computing power over the next five years (1018 operations per second by 2020) the new technology will allow for calculating the behaviour of engineering components and structures zooming in and out across length-scales from the atomic up to the structural. The verification and validation of the theory at multiple length-scales are now possible due to exceptionally powerful experimental techniques, such as lab- or synchrotron-based tomography, combined by image analysis techniques, such as digital volume correlation. Once verified, the technology will be applied to a series of engineering problems of direct industrial relevance, such as cleavage and ductile fracture and fatigue crack growth, providing convincing demonstrations to the engineering community. The product of the work will make a step change in the modelling and simulation of structures, suitable for the analysis of high value, high risk high reward engineering cases.