Research: Crystalline Defects

Since my PhD studies, I have had a particular interest in understanding and better modelling dislocations. These are mathematically interesting due to their complex topological and geometric nature, since they are imperfections in the crystalline structure localised along lines in the material. The mathematical language needed to describe dislocations and their reactions accurately is complex, involving ideas from Geometric Measure Theory and non-smooth manifolds, and many new analytical techniques in this area are in development.

From a more practical point of view, dislocations are interesting since their motion is one key way in which metals plastically (or irreversibly) deform. While humans have known how to form metal for several thousand years, our ability to theoretically predict the outcome of novel processing techniques for new alloys is still poor. This is in part due to the vast complexity of dislocation networks found in these materials. A key challenge for researchers in this area is to work to connect the modelling techniques used at different scales together, and thereby provide efficient theoretical predictions which can be used in the development of new materials and manufacturing processes.