Size-dependent contact mechanics via boundary element analysis

In classical Hertz theory, the peak failure stresses do not occur directly on the contacting area but beneath the surface, thus contradicting a common appearance of failures on the surfaces. In the present work, we examine the frictionless response of an elastic cylinder pressed between two rigid parallel plates under consistent couple stress theory, as an alternative view to that of Hertz. To address this problem, we develop a couple stress boundary element contact formulation to calculate the deformation and stresses in two-dimensional plane strain problems and find a quite different picture of contact stresses. The numerical investigation shows that the location of maximum effective stress may in fact occur directly on the contacting area, depending on the intrinsic length scale parameter l of couple stress elasticity. For failure analysis in this size-dependent couple stress contact theory, new effective-stress measures, which account for couple-stresses, also are defined. Most importantly, due to the role of asperities in contact behavior, this work is relevant to performance of macro-scale components, as well as micro- and nano-sized devices.