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

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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.