New Applications of Mortar Methodology to Extended and Embedded Finite Element Formulations

Abstract

The past decade or so has shown the mortar method to be a helpful foundation for formulation of new methods for contact/impact analysis. As originally formulated, the advantage of the mortar method is that it preserves inf-sup conditions associated with interfacial constraints, such that stability and convergence are more or less guaranteed, at least when some regularity of the solution is expected. In more recent work, interest has been shown by a number of researchers in extending many of these ideas to treatment of interfaces in extended finite element frameworks, and also to embedded surface techniques. In these cases, use of the mortar method with naïve multiplier space choices can readily lead to instability. This paper highlights some of these issues, and contemplates stabilization methods which seem to be effective in such settings.