Optimized Dual Algorithm with Automatic Penalty Parameter Selection for Elastoplastic Contact Analysis

Abstract

In this article, We examine a mechanical contact problem involving an elastoplastic body and a rigid foundation. The behavior of the material is characterized by Hencky's nonlinear elastic constitutive law. We present an iterative method based on Kacanov's method, with an augmented Lagrangian formulation at each iteration. To improve the algorithm in the discrete case, we propose an alternative approach consisting of automatic and optimal selection of the penalty parameter, accompanied by an approximate algorithm. To this end, we eliminate two unknowns, the principal and the auxiliary, and thus formulate a purely dual algorithm, enabling us to study the convergence of our method in depth. Finally, numerical experiments on two-dimensional problems are conducted to demonstrate the performance of the proposed method.