Explicit frictional stick–slip dynamics of elastic contact problem incorporating the LuGre model

Dynamical contact problem with friction is of continuous concern and have been investigated over the years. The effective and accurate description of the development of the friction force is the key to this problem. However, the stick–slip phenomenon, as typical dynamical behaviour, has rarely been considered when developing contact algorithms for frictional contact problems of elastic bodies. The conventionally used Coulomb’s model, with differentiating the static and kinetic coefficient of friction, can lead to inaccurate results due to errors generated when switch between the stick or slip states. In this work, a three-dimensional mortar-based frictional contact algorithm is proposed in an explicit scheme. The proposed algorithm incorporates the LuGre model to account for dynamical frictional behaviours such as stick–slip. The effectiveness and accuracy of the proposed algorithm are validated through several simplified two-dimensional cases. The sticking time ratio and the evolution of the global coefficient of friction with time of a three-dimensional contact problem with a randomly rough contact interface are investigated as an application.