A Stick-Slip Model Based on Granular Flow Theory

It is well known that stick-slip phenomena are prevalent in all types of mechanical systems and present one of the greater challenges to tribology. Stick-slip is widely studied and occurs at length scales from kilometers in techtonic movements to nanometers in MEMS applications. Granular flows are likewise widely studied and are known to exhibit stick-slip behavior. The purpose of this paper is to extract a straightforward result from the continuum granular flow theory due to Aranson and Tsimring (Phys Rev E 65:0161303, 2002) to obtain a simple and accessible model which can predict, or at least describe, stick-slip. A relatively simple formula for effective viscosity is provided and some typical results portrayed. The perspective of the paper is that a continuum stick-slip model which incorporates some basic principles may be useful in the modeling of real engineering systems.