A continuation problem for finding successive solutions of discretised plane quasi-static contact problems with friction is proposed and studied. Various formulations of the first-order system are derived and results of existence and uniqueness of its solutions are obtained. Conditions guaranteeing continuation of a solution curve along a direction from the first-order system are given. Numerical continuation of solution curves is performed on examples with non-smooth folds.
A Continuation Problem for Computing Solutions of Discretised Evolution Problems. Part II -- Application to Quasi-Static Contact Problems with Friction.