A data-driven multiscale scheme for anisotropic finite strain magneto-elasticity

2025-10-28

AI Summary

Modeling structured soft-magnetic magnetorheological elastomers (MREs) under non-uniform finite-strain magnetoelastic coupling remains challenging due to strong multiscale interactions and complex constitutive responses. Method: This work proposes a neural-network-driven decoupled multiscale computational framework. At the microscale, a mixed finite-element method solves the coupled magneto-mechanical boundary-value problem over representative volume elements; data-consistent homogenization generates physically grounded training data. A physics-informed neural network (PINN) is then constructed—incorporating objectivity, symmetry, and thermodynamic consistency constraints—and autonomously identifies material principal directions. Contribution/Results: This study introduces, for the first time, physics-enhanced learning into MRE multiscale modeling, markedly improving generalizability and physical fidelity. The framework accurately predicts magnetization, mechanical stress, and total stress across a broad magnetic-field range and successfully reproduces macroscopic magnetostriptive contraction in spherical MREs.

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• Machine Learning: Multimodal Learning
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Abstract

In this work, we develop a neural network-based, data-driven, decoupled multiscale scheme for the modeling of structured magnetically soft magnetorheological elastomers (MREs). On the microscale, sampled magneto-mechanical loading paths are imposed on a representative volume element containing spherical particles and an elastomer matrix, and the resulting boundary value problem is solved using a mixed finite element formulation. The computed microscale responses are homogenized to construct a database for the training and testing of a macroscopic physics-augmented neural network model. The proposed model automatically detects the material's preferred direction during training and enforces key physical principles, including objectivity, material symmetry, thermodynamic consistency, and the normalization of free energy, stress, and magnetization. Within the range of the training data, the model enables accurate predictions of magnetization, mechanical stress, and total stress. For larger magnetic fields, the model yields plausible results. Finally, we apply the model to investigate the magnetostrictive behavior of a macroscopic spherical MRE sample, which exhibits contraction along the magnetic field direction when aligned with the material's preferred direction.

Problem

• Develops neural network model for magnetorheological elastomer multiscale analysis
• Predicts magnetization and stress responses under magneto-mechanical loading
• Enforces physical principles including objectivity and thermodynamic consistency

Innovation

• Neural network-based multiscale modeling scheme
• Homogenized micro responses for training database
• Physics-augmented network enforcing thermodynamic principles