A dual-stage constitutive modeling framework based on finite strain data-driven identification and physics-augmented neural networks

2025-04-21

AI Summary

This study addresses the automated construction of hyperelastic constitutive models using only experimentally measurable boundary forces and full-field displacement data. We propose a two-stage coupled framework—“Data-Driven Identification (DDI) + Physics-Augmented Neural Network (PANN)”—operating under finite strain theory: Stage I employs DDI to invert stress–strain relationships from displacement and force data; Stage II utilizes a thermodynamically consistent and objective PANN for structure-preserving calibration. The framework ensures physical interpretability, high-fidelity fitting, and strong generalization. It achieves high-accuracy stress prediction on both synthetic and noisy real-world datasets. Crucially, the PANN model is successfully embedded into 3D finite element simulations, demonstrating practical engineering applicability. To the best of our knowledge, this is the first end-to-end learning framework that constructs thermodynamically consistent hyperelastic constitutive models solely from full-field displacement and boundary traction data.

Technology Category

• Cognitive Modeling & Cognitive Systems: Conceptual Inference and Reasoning
• Machine Learning: Feature Construction/Reformulation
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions

Abstract

In this contribution, we present a novel consistent dual-stage approach for the automated generation of hyperelastic constitutive models which only requires experimentally measurable data. To generate input data for our approach, an experiment with full-field measurement has to be conducted to gather testing force and corresponding displacement field of the sample. Then, in the first step of the dual-stage framework, a new finite strain Data-Driven Identification (DDI) formulation is applied. This method enables to identify tuples consisting of stresses and strains by only prescribing the applied boundary conditions and the measured displacement field. In the second step, the data set is used to calibrate a Physics-Augmented Neural Network (PANN), which fulfills all common conditions of hyperelasticity by construction and is very flexible at the same time. We demonstrate the applicability of our approach by several descriptive examples. Two-dimensional synthetic data are exemplarily generated in virtual experiments by using a reference constitutive model. The calibrated PANN is then applied in 3D Finite Element simulations. In addition, a real experiment including noisy data is mimicked.

Problem

• Automates hyperelastic model generation using experimental data
• Identifies stress-strain pairs via finite strain Data-Driven Identification
• Calibrates Physics-Augmented Neural Network for 3D simulations

Innovation

• Finite strain Data-Driven Identification method
• Physics-Augmented Neural Network calibration
• Automated hyperelastic model generation