On regularization of the convergence path for the implicit solution of contact problems

Following up to a previous investigation, this paper proposes a strategy to deal with frictionless contact problems involving large penetrations, in the context of the node-to-segment formulation and of the penalty method. The rationale is based on two main considerations: the first one is that, within an iteration scheme, the use of consistent linearization is only convenient when the field of the unknowns is sufficiently close to the solution point; the second one is that, if the order of magnitude of the maximum contact pressure can be estimated a priori, this information can be exploited to approach the solution in a faster and more reliable way. The proposed strategy is based on a check of the nodal contact pressure, to select the technique that has to be used to perform each iteration. If the contact pressure is smaller than a predefined limit, the problem is solved in the standard way, using consistent linearization and Newton’s method. When the contact pressure exceeds the limit, a modified method is used. This one is based on the enforcement of a contact pressure limit and on the use of a simplified secant stiffness, where the geometric stiffness term is disregarded. The strategy has to be integrated with a specific “safeguard algorithm” to guarantee convergence to the correct solution also in cases where the maximum contact pressure has been underestimated. Two alternative procedures for this purpose are proposed.