Geometric Mechanics of Solids: new analysis of modern engineering materials

我们生活中重要元素的成本和安全——能源、运输、制造——取决于我们用来制造部件和结构的工程材料。工程师们需要回答这样一个问题：一个特定的部件或系统是否适合使用：核反应堆中的压力容器；机翼:飞机的机翼;一座桥;燃气轮机；无论是在设计阶段还是在他们的整个工作寿命中。目前意外结构故障造成的损失占GDP的4%，这说明用现有的工程方法给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，即依赖于实验室长度和时间尺度的实验来捕捉整体的材料行为。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。当前方法的一个大问题是，通过将材料视为连续体，即均匀分布的质量，它们不能固有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基于实验室现象学的约束，我们将能够以更高的信心对结构行为做出预测，从而降低工程资产的建设和维护成本，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，每小时产生的电力将比新建核反应堆或传统发电厂的成本低1万至1.5万英镑。这个项目是关于创造一种全新的高保真设计和评估工程结构的技术。我将探索一种原始的固体几何理论，以克服现象学的限制，为结构分析提供一个开创性的软件平台，在几个长度尺度上验证理论，并向工程师展示新技术如何解决目前方法不足的实际问题。与经典方法相反，工程材料将被视为有限实体或细胞的离散集合；重要的是，这不是一个连续体的离散化，例如在当前的数值方法中使用的那些，而是反映了材料如何在任何长度的观察尺度上组织-从原子到形成工程组件的多晶聚集体。细胞结构的特征是由不同的元素组成——细胞、面、边和节点——该理论提出了一种创造性的方法，通过将能量和熵与这些元素的几何属性——体积、面积、长度、位置——联系起来，来描述这种结构的行为。这一理论将在一个高效的软件平台上实现，通过采用和现代化现有算法，并为大规模并行计算开发新的算法，这将使工程师和科学家能够利用即将到来的硬件加速能力。随着未来五年计算能力的飞跃（到2020年每秒1018次运算），新技术将允许计算工程部件和结构的行为，从原子到结构的长度尺度放大和缩小。由于非常强大的实验技术，如基于实验室或同步加速器的断层扫描，结合图像分析技术，如数字体积相关，现在可以在多个长度尺度上对理论进行验证和验证。一旦得到验证，该技术将应用于一系列与工业直接相关的工程问题，如解理、韧性断裂和疲劳裂纹扩展，为工程界提供令人信服的示范。该产品的工作将使结构的建模和仿真有一个台阶的变化，适用于分析高价值、高风险、高回报的工程案例。

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.