An ALE formulation for implicit time integration of quasi-steady-state wear problems

A fully coupled implicit scheme is developed for quasi-steady-state wear problems. The formulation admits finite configuration changes due to both deformation and wear. The unconditionally stable implicit backward-Euler scheme is used for time integration of the shape evolution problem. Thus, the solution may proceed with large time increments, contrary to the commonly used explicit forward-Euler scheme, in which the time increment is restricted by the stability condition. This comes at the cost that the shape transformation mapping constitutes an additional unknown. As a result, a kind of an arbitrary Lagrangian–Eulerian (ALE) formulation is obtained in which the problem is solved simultaneously for the nodal positions and displacements. The incremental coupled problem is solved using the Newton method which leads to a highly efficient computational scheme, as illustrated by two- and three-dimensional numerical examples.