AI 中文总结
针对硬磁软材料，开发模型驱动框架，将多种关系纳入统一剪切模量框架获多个本构模型，经实验选代表性关系，再用所选模型开发联合材料-结构优化框架，可处理不同设计情况，产生规定变形响应设计并开源实现。
AI 中文摘要
本文为硬磁软材料（hMSMs）的预测分析和优化设计开发了一个模型驱动框架。这类材料通过非接触、场驱动变形，在软机器人、自适应结构和仿生系统中有应用潜力。准确预测需有效结构-性能关系，优化设计需同时控制结构密度、磁颗粒分布和剩余磁化方向。为此，一是将经典关系和模型纳入统一有效剪切模量框架得到多个本构模型，经实验数据选代表性关系；二是用所选模型开发联合材料-结构优化框架，能处理不同设计领域等，产生规定变形响应的设计，该框架已开源实现。
英文摘要
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.
Comments53 pages, 20 figures, 8 tables; Repository: https://github.com/CEADpx/top_optim
