A First Violation Contact Algorithm that Correctly Captures History Dependence

Abstract

Problems of elastic frictional contact are of great engineering relevance playing major roles in many fields such as tribology, attachment integrity, and even structural dynamics. These problems are historically extremely difficult to analyze either theoretically or numerically. A quick review of the literature provides insight as to a major cause of the numerical difficulty specifically that traditional algorithms search for contact solutions that satisfy all equality and inequality constraints using iterative processes that pass through states that do not satisfy those constraints and are physically inadmissible. A novel contact algorithm - the Method of First Violation - is introduced to address the deficiency identified in traditional methods by choosing load steps precisely so as to avoid iterations through inadmissible states. The new algorithm is demonstrated on multiple contact problems and the results compared to those of a conventional algorithm and to analytic solutions where available. Finally, the Method of First Violation is demonstrated on a contact problem with a nontraditional friction model (Dahls model) to demonstrate generality and robustness.