Working in collaboration with Annie Colin and Philippe Poulin, researchers at the CRPP of Bordeaux, we aim to numerically simulate the behaviour of materials with special electrical features. Made embedding carbon nano-tubes in a polymeric matrix, this material has a dielectric constant which is strongly dependent of the mechanical deformation. Housed within a capacitor, they exhibits highly variable capacitance when subjected to vibration and, as a result, they can generate potential differences and store electric energy.
Our team is focused on the implementation of steady and unsteady efficient models, basically an elliptic problem, to allow the chemists to produce and simulate from simple to real complex materials behaviour.
The very first toy implementation of the steady model shows qualitative matches with the expected behaviour and at the same time it stresses the need for very high local resolution. High level of details could be expected considering the strong difference between the size of the nano-tubes and the dimension of the material sample. Moreover, the first results show very strong gradients of the electric potential demanding the use of locally refined computational meshes, such as quadtree/octree grids.
For this purpose, we are developing numerical methods for elliptic problems on quadtree/octree grids, using and developing a linear quadtree/octree manager called PABLO (Parallel Balanced Linear Octree) in collaboration with Optimad Engineering. PABLO is now integrated in bitpit, an open source modular C++ library for scientific computing.