Nov 14 2006
The University of Oxford has initiated a new five-year project which could enhance tumour research, nanotechnology and the use of alloys by advancing the mathematics and computation of solid mechanics.
New Frontiers in the Mathematics of Solids (OxMOS), which is funded by the Engineering and Physical Sciences Research Council as a Critical Mass Project, is holding its Launch Workshop at Oxford today. The project co-coordinators are Professor Sir John Ball and Professor Jon Chapman of the Oxford Mathematical Institute and Professor Endre Süli of the Oxford University Computing Laboratory.
‘The aim of OxMOS is to revitalize the study of mathematical solid mechanics in the U.K. through a simultaneous attack on three key areas: microstructure morphology; fracture; and applications in medicine,’ said Professor Sir Ball. ‘These areas share more or less the same governing equations, those of nonlinear elasticity theory, and we hope that lessons learnt in one area will prove fruitful in the others.’
The first area of research, microstructure morphology, will help to determine the everyday properties and behaviour of alloys by studying how to predict the patterns of microstructure that arise when the crystal lattice structures underlying these materials change their geometric shapes at certain temperatures. This could assist engineers and materials scientists in understanding microscopic and macroscopic changes in the alloys and in designing new materials and nanodevices.
The second area of research will examine mathematical models for the accurate prediction of fracture formation, which could assist in the prediction and prevention of catastrophic failure of materials. If will also examine the question of fatigue in metals, by shedding light on the formation of ‘dislocation ladders’, banded patterns which form when materials such as copper are cyclically loaded. The computational simulation and reliable prediction of material failure is particularly important in safety-critical applications, such as the fracture of aircraft-engine blades as a result of a bird-strike or the fracture of glass on impact.
Thirdly, researchers with OxMOS will study soft tissue deformation and growth in the human body to improve the understanding, detection and imaging of tumours, especially in the breast and colon. These efforts will encompass and assist other researchers and clinicians in institutions including the Faculty of Engineering and the Medical Imaging Group at Oxford and the international Integrative Biology Project.
It is often difficult to interpret and to match images taken of the breast with ultrasound, magnetic resonance imaging (MRI) and X-ray mammography because the breast is distorted differently during each type of test. Researchers with OxMOS will develop mathematical models of breast deformation and tissue elasticity to overcome this obstacle. Biological materials can be more difficult to understand and to predict than alloys because they frequently contain residual stress, are inhomogeneous, may be actively moving or growing, and are prone to extensive deformation.
The research activities of OxMOS will foster the development of new analytical, mathematical and computational approaches and will improve training and undergraduate provision in related areas within the United Kingdom.
‘The project is focused on training a new generation of young mathematicians in this key field for the engineering, physical and life sciences,’ said Professor Sir Ball.
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