Numerical algorithms for two-dimensional dynamic frictional problems

•We illustrate drift phenomenon during stick for a conventional integration scheme.•We explore the difficulty for numerical solutions near slip–stick transition.•We propose approximate analytical solutions for recommencement of slipping.•We develop a state-variable algorithm to toggle between states of stick and slip.

Conventional integration schemes for the equations of motion encounter numerical problems near transitions between stick and slip in two-dimensional frictional contact problems. Here we explore the dynamical behaviour close to these transitions and develop analytical patches that can be used to develop a state-variable algorithm, where the system toggles between states of stick and slip.