A numerical study on frictional shakedown in large-scale three-dimensional conforming elastic contacts

When subjected to cyclic loading, complete contacts with à la Coulomb friction may sometimes develop a favourable situation where slips cease after a few cycles, an occurrence commonly known as frictional shakedown. However, if the amplitude of the cyclic load is greater than a so-called shakedown limit, the system is unable to adapt and indefinitely persists in a dissipative state. In this paper, we present a comprehensive theoretical and numerical analysis of the shakedown in three-dimensional elastic systems with conforming frictional interfaces. In a discrete framework, the limit states of the frictional system are investigated through two distinct approaches: incremental analysis based on a novel Gauss–Seidel algorithm, which allowed us to explore the whole transient response under a given cyclic loading scenario, and a linear optimisation algorithm to directly determine the stick and shakedown limits. Illustrative examples, ranging from a single-node model to multi-node systems with both coupled and uncoupled contacts, are discussed.