## Computational Methods for Frictional Rolling Contact

 Bearbeitung: ext. M. Ziefle Förderung durch: This work is financed by the German Research Foundation (DFG), research group FOR492.

For the finite element analysis of rolling contact problems Arbitrary Lagrangian Eulerian (ALE) methods are well established. These techniques enable a time independent formulation for elastic bodies under stationary rolling conditions and for local mesh refinement concentrated to the contact region. A drawback is on the computation of history dependent material properties because the path of material points is not traced inherently. This affects inelastic constitutive behavior as well as frictional contact. In this project mathematically sound approaches for the treatment of frictional rolling within the ALE-description of rolling bodies are developed. By these novel and fully implicit algorithms the slip velocities are integrated along their path-lines which enables for the treatment of frictional contact as in a material picture. Quadratic convergence behavior and physical reliability can be demonstrated by computing rolling solid rubber wheels and typical car tire models.

Figure 1: Rolling kinematics (velocities: angular (w), convective (c), ground (vF)).

Figure 2: Integration of local slip velocities gives local slip.

Figure 3: FE-Mesh of rolling solid rubber disc.

Figure 4: Contact pressure in MPa.

Figure 5: Tangential contact stresses in MPa (5% braking slip): a) circumferential direction, b) lateral direction.

Figure 6: Circumferential contact stress for increasing braking slip: (left) simulation, (right) analytical solution of CARTER (1926).

Figure 7: Cornering: Deformed mesh and contact pressure distribution.

Figure 8: Cornering: Changes in footprint.

Figure 9: FE-model of a typical car tire.

Figure 10: Free rolling Tire: Contact pressure and circumferential contact stresses.

Figure 11: Free rolling Tire: Lateral contact stresses.

Figure 12: Changes in footprint of braking tire: Sticking elements (red), sliding elements (blue).