NEMESIS: NEw Mathematics for Materials Modelling in the Engineering Sciences and Industrial Sectors

几千年来，人类已经认识到非均匀介质的重要性：两种或两种以上单独材料的组合。这些材料远远优于其部件的总和，例如导致刚度或强度的巨大增加。今天，存在大量所谓的复合材料或智能材料，使许多领域的科学和工程取得了惊人的进步，包括航空航天，汽车，结构，通信和声学工程，生物技术和健康，休闲和核部门仅举几例。非均匀材料也会在许多情况下自然产生，例如生物组织中通常存在多个尺度的非均匀性。一个自然的、通常困难的研究挑战是根据组成相的性质及其分布来预测非均匀材料的有效行为。这些材料通常具有相当令人惊讶和违反直觉的特性，例如，气泡水中的声速比水或空气中的声速快！非均匀介质的模型对于复合材料的优化设计策略、取代工程应用中昂贵的实验以及理解生物力学中的结构-功能关系都是非常重要的，除了它们的有效行为之外，波在这种材料中的传播方式也非常重要。近年来，人们设计出了超材料，它具有令人难以置信的非直观特性，如强吸收和过滤特性，波导和定位能力以及负折射，聚焦行为甚至隐形的令人兴奋的概念！该项目的重点是开发和应用新的数学方法和模型与复杂的非均匀，一般非线性，材料。三个主题集中在（A）工业复合材料，（B）超材料和声子，（C）软生物材料。尽管有三个不同的主题，但这些主题之间存在大量重叠，这意味着在一个领域开发的方法也可以应用于其他显然无关的主题。这就是应用数学的美！在主题（A）中，该团队将与项目合作伙伴Thales Underwater Systems Ltd合作，以了解声音在高压下通过复杂复合材料传播的方式。载荷显著改变了材料的微观结构和随后对传播波的响应，因此预测这些材料的反射和透射声场是一项重要的任务。主题（B）将进一步研究超弹性隐身理论，这是PI最近开发的一种技术，它使用预应力材料来引导空间特定区域的波。他们还将进一步了解具有周期性微观结构的特殊材料可以通过允许或限制波在给定频率下的传播来充当波滤波器的方式。特别感兴趣的是可调材料，以便我们可以修改材料的响应，例如施加预应力或磁场。在主题（C）中，该团队将开发软组织行为的模型：肌腱和皮肤，使用来自微观结构的信息，以便“升级”到宏观模型。软组织是高度可变形的，并且特别是粘弹性的，这意味着在变形期间损失能量。预测这些材料的装载和卸载是一项非常困难的任务，由于其复杂的结构组织，皮肤变得更加困难。充分了解这些材料的行为方式在医学和制药行业有着广泛的应用。开发的模型不断得到实验合作者的输入和迭代，他们的工作对这个项目非常重要。

For millennia, mankind has recognized the importance of inhomogeneous media: a combination of two or more individual materials. Such materials are far better than the sum of their parts, e.g. leading to a huge increase in stiffness or strength. Today a plethora of so-called composite or smart materials exist enabling wondrous scientific and engineering advances in a many sectors including aerospace, automobile, structural, communications and acoustic engineering, biotechnology and health, leisure and the nuclear sector to name but a few. Inhomogeneous materials also arise naturally in a number of contexts, e.g. biological tissues where there are often several scales of inhomogeneity.A natural, often difficult research challenge is to predict the effective behaviour of inhomogeneous materials from knowledge of the properties of the constituent phases and their distribution. Such materials often possess rather surprising and counter-intuitive properties, for example the speed of sound in bubbly water is faster than that in either water or air! Amongst other benefits, models of inhomogeneous media are important for design optimization strategies for composites, for the replacement of prohibitively costly experiments in engineering applications and for understanding structure-function relationships in biomechanics.In addition to their effective behaviour, the way that waves propagate through such materials is of great importance. In recent times metamaterials have been devised which allow incredible non-intuitive properties such as strong absorption and filtering properties, waveguiding and localization capabilities and the exciting notions of negative refraction, focussing behaviour and even cloaking!This project focuses on the development and application of new mathematical methods and models associated with complex inhomogeneous, generally nonlinear, materials. Three themes focus on (A) Industrial composites, (B) metamaterials and phononics, (C) Soft biomaterials. Despite there being three distinct themes, there exists a great deal of overlap between these topics meaning that methods developed in one area can also apply to other, apparently unconnected topics. This is the beauty of applied mathematics!In theme (A) the team will work with project partner Thales Underwater Systems Ltd in order to understand the way that sound propagates through complex composite materials when they are subject to high pressures. The load significantly modifies the microstructure of the material and subsequent response to propagating waves and as such the prediction of the reflected and transmitted sound field from such materials is a non-trivial task.Theme (B) will further research into hyperelastic cloaking theory, a technique recently developed by the PI, which uses pre-stressed materials in order to guide waves around specific regions of space. They will also understand further the way that special materials with periodic microstructure can act as wave filters by permitting or restricting wave propagation at given frequencies. In particular the interest is tunable materials so that we can modify the material response at will be applying a pre-stress, or magnetic field for example. In theme (C) the team will develop models for the behaviour of soft tissues: tendon and skin, using information from the microstructure in order to ``upscale'' to macroscopic models. Soft tissues are highly deformable and in particular are viscoelastic meaning that energy is lost during deformation. The prediction of the loading and unloading of such materials is a notoriously difficult task, made even harder in skin due to its complex structural organization. A full understanding of the way that such materials behave has a multitude of applications in medicine and pharmaceutical industries.Models developed are continuously informed and iterated by input from experimental collaborators, whose work is of great importance to this project.