Data-Free Weak-Form Staggered Neural Operators for Magneto-Mechanical Coupling in Finite-Strain Elastomers

2026-10-02

AI Summary

This study addresses the high computational cost and reliance on labeled data in magneto-mechanical coupling simulations for magnetically active elastomers undergoing large deformations. To this end, a data-free physics-informed operator learning framework is proposed. The framework constrains neural operator training using finite element weak-form residuals and introduces a weak-form alternating optimization strategy to decouple the strongly coupled saddle-point problem while preserving physical correlations. Furthermore, a neural-initialized Newton solver is incorporated to accelerate convergence. Experimental results demonstrate that the proposed method accurately captures coupled responses across diverse parameterized scenarios, significantly reducing computational costs and enhancing generalization capability.

Abstract

Magneto-active elastomers, as a class of smart materials, exhibit strongly coupled magnetic and mechanical behavior at finite strains. Considering variations in microstructure, material properties, and geometry can lead to computationally expensive analyses. Building on the finite operator learning (FOL) framework, this study develops a data-free, physics-informed operator-learning framework for families of coupled finite-strain magneto-mechanical boundary-value problems. The governing magnetostatic and mechanical equations are enforced through finite-element weak-form residuals, allowing the neural operators to be trained without labeled finite-element solution data. The main contribution of this study is the development of a weak-form staggered neural operator (WSNO) framework for strongly coupled magneto-mechanical saddle-point problems. Separate magnetic and mechanical neural operators are trained alternately using a staggered optimization strategy, while their physical coupling is retained through the constitutive relations and residual evaluations. The resulting framework learns mappings from parameterized material and geometric descriptions to the corresponding coupled magnetic and mechanical solution fields. The proposed framework is investigated across several settings, including heterogeneous random-inclusion microstructures, varying magnetic phase contrast, area-fraction-dependent geometries, strongly out-of-distribution material morphologies, and three-dimensional geometry-parametric problems. In addition, the learned operator is combined with a neural-initialized Newton strategy, in which the nonlinear finite-element solver is initialized using the neural prediction. The results demonstrate that the proposed operator-learning framework can accurately capture coupled magneto-mechanical responses across a broad range of parametric problem settings.

Problem

• magneto-mechanical coupling
• finite-strain elastomers
• data-free learning
• saddle-point problems
• operator learning

Innovation

• Data-Free Operator Learning
• Weak-Form Staggered Neural Operator
• Physics-Informed
• Magneto-Mechanical Coupling
• Neural-Initialized Newton Strategy