Geometric Mechanics of Solids: new analysis of modern engineering materials, EPSRC

Abstract

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 service 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 existing 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. We need a change of perspective in order to overcome the constraint of the lab-based phenomenology and bring scientific advances into engineering. In contrast to existing methods, our perspective is that materials are collections of finite entities at any experimentally observable length scale as the atoms organise in regular lattices, so such lattices organise in larger-scale irregular collections, e.g. crystals, and so on to the engineering structure. This discrete, geometric, view allows for mathematically exact, algebraic, description and analysis using modern mathematical techniques, such as algebraic topology and discrete exterior calculus. Taking this opportunity, we are developing a geometric mechanics of solids, which solves the problem of localisation and finite size of degradation by linking energy and entropy to the geometric elements of the discrete space. This theory is being 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. Ultimately, we will be able to make predictions for structural behaviour with higher confidence, reducing the cost of construction and maintenance of engineering assets.