  This study numerically investigated the friction of viscoelastic objects with
grooves. A 3D viscoelastic block with grooves on a rigid substrate is slowly
pushed from the lateral side under uniform pressure on the top surface. The
local friction force at the interface between the block and the substrate obeys
Amontons' law. Numerical results obtained using the finite element method
reveal that the static friction coefficient decreases with increasing groove
width and depth. The propagation of the precursor slip is observed before bulk
sliding. Furthermore, bulk sliding occurs when the area of slow precursor slip
reaches a critical value, which decreases with increasing groove size. A
theoretical analysis based on a simplified model reveals that the static
friction coefficient is related to the critical area of the precursor, which is
determined by the instability of the precursor. A scaling law for the critical
area is theoretically predicted, and it indicates that the decrease in the
effective viscosity due to the formation of the grooves leads to a decrease in
the static friction coefficient. The validity of the theoretical prediction is
numerically confirmed.
