A finite element formulation based on the theory of a Cosserat point

This dissertation presents a two- and a three-dimensional finite element formulation for the field of solid mechanics. This continuum finite element formulation for large deformations is based on the theory of a Cosserat point and therefore named Cosserat point element. In this thesis, the originally introduced Cosserat point element formulation by Nadler & Rubin (2003) is generalized for different nonlinear hyperelastic material formulations and for distorted initial mesh geometries. Special about the Cosserat point element formulation is the fact that it is neither limited to nor designed for specific applications but generally applicable to almost any problem within the field of solid mechanics. It is an exceptionally stable, robust and efficient finite element formulation that can handle many different situations arising in case of bending dominated problems, materials in the near incompressible range, thin structures, sensitive geometries as well as coarse or distorted meshes.