A new formulation for solving 3-D time dependent rolling contact problems of a rigid body on a viscoelastic half-space

•We propose a new formulation for the steady-state viscoelastic contact problem in rolling conditions without friction.•The numerical method is efficient for rollers of arbitrary shape.•The method is also valid for unstationnary rolling conditions.

The paper deals with a new formulation for solving the rolling contact problem without friction of a rigid body on a viscoelastic half-space in three dimensions. Assuming that the material behavior is independent of time for a sufficiently short time duration, the viscoelastic contact problem is transformed into elastic like problems. Then the contact problem is solved using a direct numerical method at each time step. The convergence of the method in time and space is good for a spherical indenter. The dissymmetry of the contact patch due to hysteresis was found in three dimensions for the spherical indenter and two cylinders of different width. Finally the method was tested for a sinusoidal varying speed and shows a good efficiency.