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We develop a theory of static friction by modeling the homogeneous surfacesof contact as being composed of a regular array of compressible elastic smoothmicroscopic inclines. Static friction is thought of as the resistance due tohaving to push the load over these smooth microscopic inclines that share acommon inclination angle. As the normal force between the surfaces increases,the microscopic inclines would be compressed elastically. Consequently, thecoefficient of static friction does not remain constant but becomes smaller fora larger normal force, since the load would then only need to be pushed oversmaller angles. However, a larger normal force would also increase theeffective compressed area between the surfaces, as such the pressure isdistributed over this larger effective compressed area. The relationshipbetween the normal force and the common angle is therefore non-linear. Overall,static friction is shown to depend on the normal force, apparent contact area,Young's modulus, and the compressed efficiency ratio (effective compressed areaper apparent contact area). Experimental measurements using teflon were carriedout, and the results confirm predictions of this theory.

A theory of static friction between homogeneous surfaces based on compressible elastic smooth microscopic inclines