Simple algorithms for solving steady-state frictional rolling contact problems in two and three dimensions

This paper presents simple, yet robust and efficient algorithms for solving steady-state, frictional, rolling/sliding contact problems, in two and three dimensions. These are alternatives to powerful, well established, but in particular instances, possibly ‘cumbersome’ general-purpose numerical techniques, such as finite-element approaches based on constrained optimization. The cores of the solvers rely on very general principles: (i) resolving motional conflicts, and (ii) eliminating unacceptable surface tractions. The proposed algorithms are formulated in the context of small deformations and applied to the cases of a rigid cylinder and a rigid sphere rolling on a linear viscoelastic layer of finite thickness, in two and three dimensions, respectively. The underlying principles are elucidated, relevant mathematical expressions derived and details given about corresponding implementation techniques. The proposed contact algorithms can be extended to more general settings involving a deformable indenter, material nonlinearities and large deformations.

► Simple, robust and efficient algorithms for 2D/3D steady-state frictional contact.
► Method: resolving motional conflicts and eliminating unacceptable surface tractions.
► Implementations: rigid cylinder and sphere on linear viscoelastic layer, in 2D and 3D.
► Two numerical examples, in 2D and 3D, are provided and discussed.
► Proposed algorithms can be extended to material nonlinearities and large deformations.