DIscontinuous Noisy Active Meta I Composite MATERIALS

精心设计的结构可以形成一种有效的材料，其性质和功能在固体中是不寻常的；这种材料被称为超材料。机械超材料利用其构建块的弹性响应。传统上，超材料的性质是连续变化的，但最近出现了一类新的不连续的机械超材料。到目前为止，大多数设计不连续的机械超材料的尝试都集中在不同空间维度上的不同行为上，而完全忽略了第四个维度-时间-。然而，我们也知道弹性弹跳显示出错综复杂的动态行为。这项建议涉及如何利用弹性不稳定的时间尺度来设计和驱动机械超材料。我们将寻求对从单个元件到耦合单胞的集合，以及其动力学如何受热涨落影响的更好的定量理解；我们期望这种理解可能为设计新材料提供更有效的策略。这些数学模型将专注于细长的固体，但也将是迈向更一般、更抽象的超材料行为理论的第一步，这些超材料具有相同的弹性不稳定的基本成分。为了达到预定的目标，我们将利用该研究员在弹性不稳定和统计力学方面的经验，以及该研究员在细长结构弹性变形的数学建模方面的经验。在Dominic Vella教授的指导下，该奖学金将广泛地拓宽该研究员对动态细长结构和超材料的数学模型的知识，以及其他补充的科学技能。这一行动将对该研究员的中长期职业发展做出重大贡献。

Carefully architected structures can form an effective material whose properties and functionalities are unusual in solids; such materials are called metamaterials. Mechanical metamaterials harness the elastic response of their building blocks. Conventionally, a metamaterial's properties change continuously, but a new class of 'discontinuous mechanical metamaterials' have emerged recently. Thus far, most attempts to design discontinuous mechanical metamaterials have focussed on varying behaviour in different spatial dimensions but neglect the fourth dimension - time - altogether. However, it is also known that elastic snap-through shows intricate dynamic behaviour. This proposal is concerned with how the time scales of elastic instability can be harnessed for designing and actuating mechanical metamaterials.We will seek a better quantitative understanding of snap-through, from a single element to an ensemble of coupled unit cells, and how its dynamics is affected by thermal fluctuations; we expect that this understanding may give more effective strategies for designing new materials. These mathematical models will focus on slender solids but would also be a first step towards a more general, abstract theory of the behaviour of discontinuous metamaterials with the same basic ingredients of elastic instabilities. To meet the intended objectives, we will build on the fellow's experience in elastic instabilities and in statistical mechanics, and the supervisor's experience in the mathematical modelling of elastic deformation of slender structures.The fellow will be based in the Mathematical Institute of the University of Oxford. Under the supervision of Prof. Dominic Vella, the fellowship will extensively broaden the fellow's knowledge of the mathematical models of dynamic slender structures and metamaterials, together with other complementary scientific skills. This action will significantly contribute to the fellow's medium and long-term career development.