An atomistically enriched continuum model for nanoscale contact mechanics and its application to contact scaling

This work provides a comprehensive exposition and extension of an atomistically enriched contact mechanics model initially proposed by the present authors. The contact model is based on the coarse-graining of the interaction occurring between the molecules of the contacting bodies. As these bodies may be highly compliant, a geometrically nonlinear kinematical description is chosen. Thus a large deformation continuum contact formulation is obtained which reflects the attractive and repulsive character of intermolecular interactions. Further emphasis is placed on the efficiency of the proposed atomistic-continuum contact model in numerical simulations. Therefore three contact formulations are discussed and validated by lattice statics computations. Demonstrated by a simple benchmark problem the scaling of the proposed contact model is investigated and some of the important scaling laws are obtained. In particular, the length scaling, or size effect, of the contact model is studied. Due to its formal generality and its numerical efficiency over a wide range of length scales, the proposed contact formulation can be applied to a variety of multiscale contact phenomena. This is illustrated by several numerical examples.