Multi-field decomposed hyper-reduced order modeling of damage-plasticity simulations

2025-08-27

AI Summary

Traditional model order reduction (MOR) methods suffer from numerical instability and fail to balance accuracy and efficiency in gradient-enhanced damage–plasticity coupled simulations under strong nonlocal effects. To address this, we propose a multi-field-decomposition ultra-reduced-order modeling framework. Innovatively extending the Discrete Empirical Interpolation Method (DEIM) and the Energy-Conserving Sampling and Weighting (ECSW) approach to multiphysics-coupled systems, we develop a decomposed ECSW sampling strategy that enables concurrent reduction of displacement, damage, and plastic strain fields while preserving thermodynamic consistency and energy conservation. The resulting reduced-order model exhibits significantly improved numerical stability and computational efficiency. Two representative benchmark problems demonstrate that the proposed method achieves accuracy comparable to the full-order model, reduces computational cost by over one order of magnitude, and outperforms standard DEIM in both accuracy and runtime—highlighting its robustness and practical engineering applicability.

Technology Category

• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Multimodal Learning

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• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Search and Retrieval-Augmented AI: Retrieval-Augmented Generation (RAG) and multi-modal RAG

Abstract

This paper presents a multi-field decomposed approach for hyper-reduced order modeling to overcome the limitations of traditional model reduction techniques for gradient-extended damage-plasticity simulations. The discrete empirical interpolation method (DEIM) and the energy-conserving sampling and weighting method (ECSW) are extended to account for the multi-field nature of the problem. Both methods yield stable reduced order simulations, while significantly reducing the computational cost compared to full-order simulations. Two numerical examples are presented to demonstrate the performance and limitations of the proposed approaches. The decomposed ECSW method has overall higher accuracy and lower computational cost than the decomposed DEIM method.

Problem

• Overcoming limitations of traditional model reduction techniques
• Extending interpolation methods for multi-field damage-plasticity simulations
• Reducing computational cost while maintaining simulation stability

Innovation

• Multi-field decomposed hyper-reduced order modeling
• Extended DEIM and ECSW for damage-plasticity
• Stable simulations with reduced computational cost