Hyper-reduction of nonlinear hardening plasticity models using Petrov–Galerkin projection and gappy POD

Alireza Ashkpour; Ahmad Raeisi Najafi

doi:10.1016/j.cma.2026.119155

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Hyper-reduction of nonlinear hardening plasticity models using Petrov–Galerkin projection and gappy POD

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Hyper-reduction of nonlinear hardening plasticity models using Petrov–Galerkin projection and gappy POD

Alireza Ashkpour and Ahmad Raeisi Najafi

Computer methods in applied mechanics and engineering, v 461(Part A), 119155

01 Nov 2026

DOI: https://doi.org/10.1016/j.cma.2026.119155

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Abstract

Reduced Order Model

Nonlinear hardening plasticity

Petrov–Galerkin projection

We present a projection-based reduced-order modeling (ROM) framework for nonlinear plasticity that combines a Least-Squares Petrov–Galerkin (LSPG) formulation with hyper-reduction via the Gauss–Newton with Approximated Tensors (GNAT) method. The framework addresses both associative von Mises and non-associative Drucker–Prager formulations with nonlinear isotropic hardening. At each integration point, a local Newton–Raphson method updates the stress state and plastic multiplier using history-dependent internal variables. Dimensional reduction is achieved with Proper Orthogonal Decomposition (POD), while gappy POD, combined with a greedy sampling strategy enables reconstruction of nonlinear residuals and Jacobian actions from a subset of sampled nodes, significantly reducing online evaluations. The ROM is trained over a parameter space encompassing variations in load magnitude and six elasto-plastic material parameters. We evaluated the method on two- and three-dimensional benchmark problems, demonstrating computational speedups of up to relative to full-order models, despite the limitations imposed by the Kolmogorov barrier. Finally, we assess the robustness of the LSPG formulation in the presence of non-symmetric, non-positive definite Jacobians arising from non-associative plasticity, showing that the proposed ROM maintains convergence under these challenging conditions.

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Title: Hyper-reduction of nonlinear hardening plasticity models using Petrov–Galerkin projection and gappy POD
Creators: Alireza Ashkpour - Drexel University, Mechanical Engineering and Mechanics
Ahmad Raeisi Najafi (Corresponding Author) - Drexel University, Mechanical Engineering and Mechanics
Publication Details: Computer methods in applied mechanics and engineering, v 461(Part A), 119155
Publisher: Elsevier
Number of pages: 27
Grants: CAREER: A Holistic Framework for Designing Multifunctional Materials and Structures Using Computational Optimization Methods, 2143422, U.S. National Science Foundation (United States, Alexandria) - NSF
Grant note: NSF CAREER Award: CMMI-2143422 Department of Mechanical Engineering and Mechanics at the Drexel University, United States
The work is supported by the NSF CAREER Award CMMI-2143422. Alireza Ashkpour was also supported by a faculty start-up funding from the Department of Mechanical Engineering and Mechanics at the Drexel University, United States. All simulations were performed on the high-performance computing clusters in the Computational Mechanics and Biomechanics (MCMB) Lab at Drexel University, United States.
Resource Type: Journal article
Language: English
Academic Unit: Mechanical Engineering and Mechanics
Web of Science ID: WOS:001799150700001
Other Identifier: 991022189375404721

Hyper-reduction of nonlinear hardening plasticity models using Petrov–Galerkin projection and gappy POD

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