Friction and Fracture

e this picture applies, we wish to point out an alternative way to explain the same basic fact. Suppose two solids are in close contact over some distance. Suppose further that a wave of separation, a self--healing crack, can run along the interface, like a bump on rug, leading one solid to slip over the other (Fig. 1). And suppose finally that the condition for such self--healing cracks to arise depends only upon the ratio of horizontal to compressive stress. Then sliding begins in accord with Coulomb's law, and is naturally independent of the area of contact. We can demonstrate in a simple but realistic setting that these suppositions are correct. To explain how the task is performed, we begin by describing a calculation that employs standard techniques from continuum mechanics . Imagine a semi--infinite elastic solid atop a rigid substrate, impose vertical and horizontal stresses far from the boundary, and suppose that there is a self--healing crack of length