Art of Modeling in Contact Mechanics

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 modeling process. A wide overview will be given on the art of modeling in contact mechanics under its various aspects: contact laws, their mechanical basics, various scales, underlying concepts, mathematical analysis, solvers, identification of the constitutive parameters and validation of the models. Every point will be illustrated by one or several examples. 1 Modeling: the bases It would be ambitious to try to give a general definition of the concept either of a model itself or of model processing. Modeling relates to the general process of production of scientific knowledge and also to the scientific method itself. It could be deductive (from the general to the particular, as privileged by Aristotle) or inductive (making sense of a corpus of raw data). Descartes (38) saw in the scientific method an approach to be followed step by step to get to a truth. Modeling can be effectively regarded as a scientific method that proceeds step by step, but its objective is more modest: to give sense of an observation or an experiment, and above all to predict behaviors within the context of specific assumptions. This concept of ”proceeding step by step” is fundamental in modeling. In this first section, we will examine the notion of model in the general context of mechanical systems. The main features of these models are their ∗ The author is grateful to Prof. Marius Cocou for his very constructive comments on the mathematical aspects and Prof. Alfredo Soldati for our very interesting discussion on the general topic.