General equations describing elastic indentation depth and normal contact stiffness versus load

Continuum mechanics models describing the contact between two adhesive elas tic spheres, such as the JKR and DMT models, provide a relationship between the elastic indentation depth and the normal load, but the general interme diate case between these two limiting cases requires a more complex analysi s. The Maugis-Dugdale theory gives analytical solutions, but they are diffi cult to use when comparing to experimental data such as those obtained by s canning force microscopy. In this paper we propose a generalized equation b etween elastic indentation depth and load that approximates Maugis' solutio n very closely. If the normal contact stiffness can be described as the for ce gradient, that is the case of the force modulation microcopy, then a gen eralized equation between normal contact stiffness and load can be deduced. Both general equations can be easily fit to experimental data, and then in terfacial energy and elastic modulus of the contact can be determined if th e radius of the indenting sphere is known. (C) 2000 Academic Press.