The project is aimed to apply the methods of quasiconformal analysis to the various problems of nonlinear elasticity theory. In particular, the use of so-called mappings of finite distortion, rather than those traditionally used in such a context, should confer significant benefits since they directly encode much of the underlying physics. Furthermore, the project will look at analytical and geometrical problems associated with the modeling of various continua such as magnetoelastic materials and nematic elastomers and will make use of mixed Eulerian/Lagrangian formulations. The work will devote proper attention to the physical interpretation of the mathematical properties of our analyses.
The project has been carried out at the Faculty of Mathematics of the University of Vienna., 1.06.2019-14.01.2020, and at the Institute of Analysis and Scientific Computing of TU Wien, 15.01.2020-30.04.2021.