A Fully Implicit Approach for the Numerical Treatment of Tractive Rolling

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 contribution a mathematically sound approach for the treatment of frictional rolling within the ALE description based on a spatially fixed finite element mesh is suggested. By this novel and fully implicit algorithm 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 will be demonstrated as well as the computability of large scaled finite element tire models.

Key words: Rolling contact, tire, Arbitrary Lagrangian Eulerian (ALE) method, frictional contact.