Computational homogenization of soft matter friction: Isogeometric framework and elastic boundary layers

A computational contact homogenization framework is established for the modeling and simulation of soft matter friction. The main challenges toward the realization of the framework are (1) the establishment of a frictional contact algorithm that displays an optimal combination of accuracy, efficiency, and robustness and plays a central role in (2) the construction of a micromechanical contact test within which samples of arbitrary size may be embedded and which is not restricted to a single deformable body. The former challenge is addressed through the extension of mixed variational formulations of contact mechanics to a mortar-based isogeometric setting where the augmented Lagrangian approach serves as the constraint enforcement method. The latter challenge is addressed through the concept of periodic embedding, with which a periodically replicated C1-continuous interface topography is realized across which not only pending but also ensuing contact among simulation cells will be automatically captured. Two-dimensional and three-dimensional investigations with unilateral/bilateral periodic/random roughness on two elastic micromechanical samples demonstrate the overall framework and the nature of the macroscopic frictional response. Copyright (c) 2014 John Wiley & Sons, Ltd.