A family of simple two-pass dual formulations for the finite element solution of contact problems

Simple, stable, unbiased algorithms for two-pass, two-body contact have until now eluded researchers in computational mechanics. This work examines the subject, starting from an interpolation scheme proposed in an earlier work. This method, though stable and unbiased, results in an exceedingly complex algorithm in three-dimensions. Motivated by the need for simplicity, a new formulation of the contact problem is introduced, which results in a family of simple, stable, geometrically unbiased elements. The starting point of these elements is any algorithm which is stable for the Signorini problem. A number of example problems are presented to compare the performance of the elements.