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

TL;DR

This paper introduces a neural network-based multiscale modeling approach for anisotropic magneto-elastic materials, capturing microscale responses and predicting macroscopic behavior with physical consistency.

Contribution

It develops a data-driven, physics-augmented neural network scheme that automatically detects material anisotropy and enforces physical laws for magneto-elasticity modeling.

Findings

Accurate prediction of magnetization and stress within training data range

Plausible extrapolation results for larger magnetic fields

Demonstration of magnetostrictive contraction in a spherical MRE sample

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.