The present work deals with continuum mechanical considerations for deformable and rigid solids as well as for fluids. A common finite element framework is used to approximate all systems under considerations. In particular, we present a standard displacement based formulation for the deformable solids and make use of this framework for the transition of the solid to a rigid body in the limit of infinite stiffness. At last, we demonstrate how to immerse a discretized solid into a fluid for fluid-structure interaction problems.
In the present work, a tire model is derived based on geometrically exact shells. The discretization is done with the help of isoparametric quadrilateral finite elements. The interpolation is performed with bilinear Lagrangian polynomials for the midsurface as well as for the director field. As time stepping method for the resulting differential algebraic equation a backward differentiation formula is chosen. A multilayer material model for geometrically exact shells is introduced, to describe the anisotropic behavior of the tire material. To handle the interaction with a rigid road surface, a unilateral frictional contact formulation is introduced. Therein a special surface to surface contact element is developed, which rebuilds the shape of the tire.