Microstructure in multi-phase solids has long been a research interest of mine. RecentlyAnja Schloemerkemper and I have shown that Monoclinic-I martensite is capable of exhibiting T3 microstructures (which are infinite-rank laminates). Moreover we show that there is an open set of points for which this is possible. This is the first "real-world" example (we are aware of) of these theoretically much-investigated microstructures. As a consequence the lamination convex-hull of this material is strictly smaller than its quasiconvex-hull, again the first such "real-world" example.
Along the way we also discovered that there are in fact two kinds of Monoclinic-I martensites, group-theoretically indistinguishable but with different convex polytope structures, and thus also different semi-convex hulls/envelopes. Curiously all known Monoclinic-I martensites lie in one of these groups. This work is part of a larger programme to understand the zero-energy states of monoclinic-I martensite and is funded by the Royal Society.
While I'm interested in several aspects of the mechanics of growth of biological materials I am currently focused on investigating continuum limits of discrete growing systems. Some preliminary results were presented at Banff in October 2010. For computational investigations I collaborate with Dariyash Kurenkeyeva who is supported by a Bolashak presidential scholarship. I've had many valuable discussions with Patrick Shipman on these and related matters. Pardeep Bahra joined me over summer for an undergraduate research project on this topic which was funded by the School of Mathematics.
Jonathan Robbins and I are interested in vortex motion on Riemannian manifolds. Chiara Liverani joined us for four months this Spring.
