A finite volume penalty based segment-to-segment method for frictional contact problems

•The finite volume segment-to-segment contact method is developed.•Simultaneous calculation of the contact force without the need for surface-to-surface interpolation.•The method is tested on a number of relevant mechanical contact problems.•The proposed contact calculation method demonstrates good accuracy and robustness. This paper presents a new contact boundary condition for finite volume simulations of frictional contact problems involving geometrical and material non-linearities. Deformation of bodies in contact is described by the updated Lagrangian form of the momentum equation which is discretised in space using the cell-centred finite volume method. The proposed contact boundary condition is based on the finite volume implementation of the penalty based segment-to-segment contact force calculation method in which normal contact pressure, governed by a penalty law, is integrated across the discretised contact surface, enforcing contact constraints in an integral manner. Such an approach, as opposed to the pointwise contact force calculation algorithm, allows for more accurate and more robust treatment of the contact area edge, simultaneous calculation of contact forces on both contact surfaces as well as smoother contact force during large sliding. The proposed numerical method is tested on challenging mechanical contact problems showing very good agreement with the available benchmark results.