Determination of the shakedown limit for large, discrete frictional systems

• Presents a method for calculating the shakedown limit for large, discrete frictional systems.
• Applies calculation a FE model with 50,000 degrees of freedom and 128 contact nodes.
• Presents the results of over 1000 transient simulations.
• Demonstrates that the steady state can be very sensitive to initial conditions.

It has been shown that complete frictional contacts subjected to cyclic loads can shake down such that the interface becomes fully stuck after some number of cycles (even if partial-slip occurs at the onset of loading). However, if the amplitude of the cyclic load is greater than a particular value (the shakedown limit), it is impossible for shakedown to occur. In this paper, we examine a numerical approach for determining the shakedown limit for elastic frictional systems subjected to quasi-static loads using a discrete formulation. We then use this technique to determine the shakedown limit for a finite element model of a (coupled) complete contact with ∼50,000 total degrees of freedom and ∼250 along the contact interface. Finally, we compare the calculated value of the shakedown limit to a series of over 1000 transient simulations and investigate the influence of initial conditions on steady state frictional energy dissipation. The results demonstrate that the dissipative properties of complete contacts can be highly dependent on the initial residual slip displacement state.