The project is called QUANTHOM, which is short for quantitative method in stochastic homogenization. The aim is to develop mathematical tools to allow for more realistic modelling of composite materials, in particular when they are subjected to physical deformation (stretching, compression, shearing, etc.) Initially, I will examine the behaviour of the materials at the microscopic level, in order to establish the mathematical laws that govern them at the macroscopic level. This change of scale is called the principle of homogenisation. The materials are composed of microscopic patterns which are repeated randomly (or "stochastically"). Modelling their behaviour is therefore naturally more complex than with materials that have identical patterns. To get around this, I am going to rely on probability theory, statistical physics, and on the analysis of partial derivatives equations: a combination which should yield innovative results.
This project will not be merely theoretical: the study should also shed light on the non-linear elasticity of rubber. Finally, I am going to take on the problems posed by changes of scale to much larger levels of observation, like oil extraction according to the geological environment, for example.
I wish to provide mathematical tools to the community of physics researchers.
Since at the microscopic level rubber is composed of chains of polymers linked to each other randomly, it is a material that fits in perfectly with my project. I learned about this material while working for Hutchinson, which is a world leader in the field. Hutchinson's research teams were developing very refined methods of calculation to simulate the behaviour of rubber. However, I noticed that the composition law they were using was itself very simple, which left room for improvement in the quality of their calculations. Straight away, I saw this as an interesting challenge, because understanding how things work from a mathematical point of view is simply part of my nature. I need that understanding to grasp the physical behaviour of the objects I study.
I got a lot out of this prize even before winning it! Before I could submit an entry, I had to take a step back and think about what I wanted to do, that helped me to formalise my project. Beyond just the pride of winning, the grant will provide me with funding for a project based at two locations: ULB and Inria Lille, incorporating QUANTHOM, but also with a bearing on larger issues in the area of mathematical methods for the physical sciences. It will provide me with the support of four PhD students and an engineer for two years. I would also like to be able to host one guest per month, for one week, in Lille or Brussels, to create a centre of expertise on these subjects and take advantage of fresh perspectives on our work.
