The numerical solution of 2D elastoplastic contact problems by dual mortar method, dualization, and optimal quadratic programming solvers

Abstract

This paper contributes a novel and complete pipeline for solving 2D elastoplastic contact problems by integrating dual mortar methods for contact handling, the von Mises criterion with bilinear isotropic hardening for modeling plasticity, and optimal quadratic programming algorithms with projector-based preconditioning for solving the discretized equations. While these components have been individually studied, their structured combination into an efficient framework has not been systematically examined in existing research. The method assumes plane stress conditions and employs a dual mortar formulation to manage non-conforming meshes. Contact constraints are treated in the dual formulation and the pseudoinverse of the stiffness matrix required for the dualization is obtained via a generalized Cholesky factorization. Performance evaluation is carried out in MATLAB, focusing on the impact of plasticity and mortar contact discretization on computational efficiency. A systematic analysis investigates how these features affect the iterative behavior of the quadratic solver, particularly in terms of the number of Hessian multiplications and solution time. Additionally, the scalability is examined to assess how individual algorithmic components influence the overall performance, and the overall performance is compared with the primal–dual active-set method. Finally, the proposed framework is applied to a realistic engineering problem, demonstrating its robustness and practical applicability.

The authors' abstract, as published at the source. Computers & Structures, 2026 · DOI ↗