Extensions of the large penetration strategy for contact problems with large load steps

The so-called large penetration strategy, proposed by the authors in previous investigations, has proved very e↵ective to deal with frictionless contact problems involving large load steps. The strategy is based on a sub- division of the solution process into two stages: in the first one, performed when the field of the unknowns is still far from the solution point, a predefined pressure limit is enforced and a simplified tangent sti↵ness with the exclusion of the geometric term is adopted in Netwon’s iterations; in the second stage, limited to the neighbourhood of the solution point, the standard consistent lin- earization is used, which guarantees in this phase an asymptotically quadratic convergence rate. Thus far, the e↵ectiveness and robustness of the strategy have been demonstrated in combination with the node-to-segment algorithm for linear finite elements.