Friction and fracture

Consider a block placed on a table and pushed sideways until it begins to slide. Amontons and Coulomb found that the force required to initiate sliding is proportional to the weight of the block (the constant of proportionality being the static coefficient of friction), but independent of the area of contact(1). This is commonly explained by asserting that, owing to the presence of asperities on the two surfaces, the actual area in physical contact is much smaller than it seems, and grows in proportion to the applied compressive force(1). Here we present an alternative picture of the static friction coefficient, which starts with an atomic description of surfaces in contact and then employs a multiscale analysis technique to describe how sliding occurs for large objects. We demonstrate the existence of self-healing cracks(2-4) that have been postulated to solve geophysical paradoxes about heat generated by earthquakes(5-11,25-27), and we show that, when such cracks are present at the atomic scale, they result in solids that slip in accord with Coulomb's law of friction. We expect that this mechanism for friction will be found to operate at many length scales, and that our approach for connecting atomic and continuum descriptions will enable more realistic first-principles calculations of friction coefficients.