A region of micro-slip may develop at the interface of two contacting bodies subjected to compression and shear.
Prediction of a slip response to the applied system of loads is of great interest in structural dynamics as shear microdisplacements
are found to be a source of energy dissipation in jointed elements. Such prediction is challenged by
the fact that slip evolution (and therefore damping of the entire system) is highly influenced by the history of
loading. The present study aims to develop memory rules for the generalized contact of two axi-symmetric bodies
with an irregularity of shape Arα. At each step of the loading, three characteristic domains are identified in the force
space to differentiate different scenarios of the contact response. The tangential and normal compliances are used to
obtain the incremental equations in each of these domains that constitute the memory rules for micro-slip evolution.