Finite element procedures for virtual tribology

Abstract: The main purpose of this thesis is to use modern goal-oriented adap- tive ?nite element techniques in order to improve the numerical simulation of tribology. Two novel adaptive ?nite element methods for the Reynolds thin ?lm model, and Stokes model including cavitation are presented and their di?erent strategies are compared. The algorithms are inspired by an analogy with the obstacle problem and the cavitation problem that we con- sider is written as a variational inequality considering in the formulation the fact that the lubricant cannot stand negative stresses induced by sub- atmospheric pressure. A posteriori error estimates and adaptive algorithms are derived, and numerical examples illustrating the theory are supplied. The cavitation problem and calculations is introduced and put into his- torical and modern perspective. Modern thoughts and techniques around the oil-pocket idea in sheet metal forming are presented. The in?uence of oil pockets on the contact regime is assessed, and in particular the likely e?ect of oil-pocket-induced cavitation in order to produce lift, is discussed. The ultimate goal with the numerical simulation is to be able to optimize the surface structure so as to take advantage of cavitation e?ects in the lubricant.