Elastic behavior of contacting surfaces under normal loads: A computer simulation using three‐dimensional surface topographies

Abstract

It is very important to understand the potential and limitation of the contact theories in order to apply them to geophysical problems. Using three‐dimensional topographies, a computer simulation concerning the behavior of contacting surfaces under normal loads was performed to examine the contact models previously proposed. Two models, the Brown and Scholz (B&S model) and the Yamada et al. (Y model), were compared in detail. It is found that the Y model neglects the contacts between asperities and valleys or shoulders, which results in a smaller area of contact and smaller stiffness than with the B&S model. The contact area formed between asperities and shoulders or valleys is estimated at about 20% of the total contact area, a value that does not depend on either normal stress or surface roughness. The real area of contact is proportional to normal load even under purely elastic conditions, as originally proposed by Archard, and it is much smaller than 1% of the total area of contact up to the normal stress of 30 MPa. Average area of contact, contact density, mean contact pressure, and maximum contact pressure were also calculated as a function of normal stress, which revealed the detailed process of contact mechanics under normal loads.