Elastic Incompressibility and Large Deformations: Numerical Simulation with adaptive mixed FEM

This thesis investigates the numerical simulation of three-dimensional, mechanical deformation problems in the context of large deformations. The main focus lies on the prediction of non-linearly elastic, incompressible material. Based on the equilibrium of forces, we present the weak formulation of the large deformation problem. The discrete version can be derived by using linearisation techniques and an adaptive mixed finite element method. This problem turns out to be a saddle point problem that can, among other methods, be solved via the Bramble-Pasciak conjugate gradient method or the minimal residual algorithm. With some modifications the resulting simulation can be improved but we also address remaining limitations. Some numerical examples show the capability of the final FEM software. In addition, we briefly discuss the special case of linear elasticity with small deformations. Here we directly derive a linear weak formulation with a saddle point structure and apply the adaptive mixed finite element method. It is shown that the presented findings can also be used to treat the nearly incompressible case