Mathematical Modelling of Metal Forming
Metal forming involves permanently deforming metal into a required shape. Many forms of metal forming are used in industry: rolling, stamping, pressing, drawing, etc; for example, 99% of steel produced globally is first rolled before any subsequent processing. Most theoretical studies of metal forming use Finite Elements, which is not fast enough for real-time control of metal forming processes, and gives little extra insight. As an example of how little is known, it is currently unknown whether a sheet of metal that is squashed between a large and a small roller should curve towards the larger roller, or towards the smaller roller. In this talk, I will give a brief overview of metal forming, and then some progress my group have been making on some very simplified models of cold sheet rolling in particular. The mathematics involved will include some modelling and asymptotics, multiple scales, and possibly a matrix Wiener-Hopf problem if time permits.