Model-Informed Joint Material-Structural Optimization of Hard-Magnetic Soft Materials

2026-07-15

AI Summary

This study addresses the challenges in predicting deformation and achieving co-optimized design of hard-magnetic soft materials under magnetic actuation by proposing a unified effective shear modulus framework. This framework integrates classical inclusion theory, the Hill self-consistent model, and constrained kinematic relations, and employs an experimentally calibrated Mooney strain energy function to formulate a multiphysics constitutive model. Building upon this foundation, a material–structure concurrent topology optimization method is developed to simultaneously tailor structural density, magnetic particle distribution, and remanent magnetization orientation. The proposed framework successfully generates non-intuitive designs capable of achieving prescribed deformations—such as rotation, translation, and recovery—demonstrating its versatility and precise controllability across single- and multi-loading scenarios and diverse design objectives.

Abstract

This work develops a model-informed framework for predictive analysis and optimal design of hard-magnetic soft materials (hMSMs). These materials undergo contact-free, field-driven deformation, making them attractive for soft robotics, adaptive structures, and bio-inspired systems. Accurate prediction requires effective structure--property relations, while optimal design requires simultaneous control of structural density, magnetic particle distribution, and remanent magnetization direction. To address these issues, this work makes two main contributions. First, classical rigid-inclusion relations, a Hill self-consistent relation, and constrained-kinematics models are placed into a unified effective shear-modulus framework for particle-filled elastomers. With one default control relation, seven shear-modulus relations are combined with three strain-energy density functions to obtain 21 constitutive models. The results show that the strain-energy density form has a relatively small effect for the actuation problems considered, whereas the effective shear-modulus relation can significantly affect deformation when magnetic material overlaps with highly deforming regions. Experimental stress--strain data are then used to select a representative shear-modulus relation, with the Mooney relation giving the best overall agreement. Second, using the selected constitutive model, a joint material--structural optimization framework is developed for simultaneous design of structural density, magnetic particle volume fraction, and remanent magnetization direction. Rotational, translational, and restorative examples show that the framework handles different active design fields, objectives, and single- or multi-load-case formulations, producing non-intuitive hMSM designs with prescribed deformation responses. The framework is implemented in the open-source \texttt{CEADpx/top\_optim} repository.

Problem

• hard-magnetic soft materials
• material-structural optimization
• effective shear modulus
• remanent magnetization
• constitutive modeling

Innovation

• hard-magnetic soft materials
• constitutive modeling
• effective shear modulus
• joint material-structural optimization
• magnetic actuation