Critical wedging coefficient in planar frictional system

This report presents a method of determining the critical wedging coefficient in a planar elastic frictional system assuming a mixed presence of contact states and separation states for a given set of nodes of a contact surface. Wedging in a frictional system is defined as when the system remains in a state of sticking, a non-trivial state, even when the external loading on the system is completely removed. The proposed method is based on two factors: 1) a necessary and sufficient condition for wedging that can be interpreted as positive spanning of constraint vector sets comprising the contact stiffness and coefficient of friction and 2) a minimal positive basis that enables the determination of the minimum wedging coefficient. Then, nodes representing the case of imminent separation are changed from contact nodes to internal nodes, which in turn is reorganized to form a new set of contact stiffness matrix for the next iterative process. In this case, the normal contact force and normal displacement are examined to divide the contact region and separation region. The proposed method is advantageous in that it can be applied to models with numerous contact nodes and reduces the time required to compute the critical wedging coefficient.