In this chapter, we will first address general issues of the art and craft of modeling contents, concepts, methodology. Then, we will focus on modeling in contact mechanics, which will give the opportunity to discuss these issues in connection with non-smooth problems. It will be shown that the non-smooth character of the contact laws raises difficulties and specificities at every step of the m...

The role of surface roughness in contact mechanics is relevant to processes ranging from adhesion to friction, wear and lubrication. It also promises to have a deep impact on applied science, including coatings technology and design of microelectromechanical systems. Despite the considerable results achieved by indentation experiments, particularly in the measurement of bulk hardness on nanomet...

The 120-year old so-called Painlevé paradox involves the loss of determinism in models of planar rigid bodies in point contact with a rigid surface, subject to Coulomb-like dry friction. The phenomenon occurs due to coupling between normal and rotational degrees-of-freedom such that the effective normal force becomes attractive rather than repulsive. Despite a rich literature, the forward evolu...

Significance Knots, knits, and weaves have been technologically essential across civilizations, their significance remains undiminished today. In these systems, it is challenging to understand the equilibria of deformable filaments with tight contacts due intricate geometry touching tubular volumes small, but nonvanishing, radius. This article considers a specific canonical context for in conta...