A General Reduced Representation of One-Dimensional Frictional Interfaces

A physically-motivated, reduced representation of a general one-dimensional frictional interface is developed. Friction is introduced into the system as a state variable and is modeled by nonlinear springs of large but finite stiffness. The set of equations for the interface is reduced in a procedure similar to Guyan reduction by assuming that the system must deform in its quasistatic displacement shapes. The result of this reduction is that the degrees of freedom internal to the interface are removed from the analysis and only the boundary degrees of freedom are retained. The reduced system is then specialized to the case of a bar on a frictional surface. For this problem, a second reduction is made by noting that the time derivative of the friction force on the stuck block nearest the slip zone is much greater than the time derivatives of the friction forces elsewhere. Therefore only the friction force on the stuck block nearest the slip zone needs to be updated at each time step. The reduced representation developed in this paper is compared with a formulation from the literature and it is seen that the two match very closely and that the reduced representation is far less computationally intensive.