A contact mechanics model for quasi-continua
R. A. Sauer and S. F. Li
International Journal for Numerical Methods in Engineering, 71, 931-962 (2007).

ABSTRACT
A computational multiscale contact mechanics model is proposed to describe the
interaction between deformable solids based on the interaction of individual
atoms or molecules belonging to the solids. The contact model, formulated in the
framework of large deformation continuum mechanics, is derived from coarsening
the molecular dynamics (MD) description of a large assembly of individual atoms,
and it thus bears some of the characteristics of the underlying atomic
structure. The multiscale contact model distinguishes between atoms interacting
within a small neighbourhood within the solids and atoms interacting over large
distances between remote regions of the solids. The former furnishes a
constitutive relation for the continuum, like the Cauchy-Born Rule, while the
latter is used to model the interaction between distinct bodies. The proposed
contact model is formulated as a variational weak form and implemented within an
updated Lagrangian finite element method. It is shown that, as the problem size
increases, the description of the model can be simplified to yield more
efficient computational algorithms. In this respect, the proposed multiscale
formulation leads to a smooth transition from MD to continuum contact mechanics.
The general behaviour of the contact model is studied, and some numerical
examples are given.