Research

OxMOS conducted a broadly based programme of research on the mathematics of solid mechanics and computation of solutions, concentrating on three important areas of applications.

The first area concerned the formation of patterns of microstructure in alloys, arising from phase transformations in which the underlying crystal lattice undergoes a change of shape (for example, from cubic to tetragonal) at a critical temperature. These patterns are of importance for determining the everyday properties of the material. The research attempted for the first time to describe mathematically how these patterns form. More details on the microstructure page.

The second area was fracture mechanics, which is the study of when and how materials crack and break. This is a large scientific field of great technological importance. The research here focused on new mathematical models of fracture, which avoid making guesses as to the position and form of new fracture surfaces, and which allow effective numerical computation of these surfaces. More details on the fracture page.

The third area concerned applications of solid mechanics to medicine. Mechanics is becoming increasingly important for the understanding of many parts of the human body. Models of bone and tissue growth were studied, with applications to tumours and in particular colon cancer, as was the detection of breast tumours aided by observing changes in the elastic properties of the breast. More details on the biomaterials page.

The programme linked with many other departments and groups in Oxford. We collaborate closely with OCIAM, the Oxford Centre for Industrial and Applied Mathematics, and also welcomed discussions with industrial and other researchers concerning interesting solid mechanics problems.