Hard-magnetic soft materials are a class of magneto-active polymers (MAPs) where the fillers are composed of hard-magnetic (magnetised) particles. These materials present complex magneto-mechanical couplings, which require the development of modelling frameworks in understanding their responses at the very beginning of conceptualisation and design. Most of the current constitutive approaches available in the literature for hard-magnetic MAPs do not consider dipole–dipole interactions of the embedded particles. However, such interactions among the magnetised particles generate internal forces within the composite that need to be balanced by mechanical stress from the polymeric matrix networks. This fact may imply an initial stretch of the polymeric network and suggests that such dipole–dipole interactions may be important during the MAP deformation process. To address these crucial points, in this contribution, we propose a novel constitutive model relating microstructural characteristics of hard-magnetic MAPs. The model accounts for polymeric network pre-stretch, dipole–dipole interactions, Zeeman effect as well as viscous mechanisms which are formulated on the finite deformation theory. The results obtained herein highlight the importance of accounting for the dipole–dipole interactions and the polymeric network pre-stretch to understand the complex magneto-mechanically coupled behaviour of hard-magnetic MAPs.

硬磁软材料是一类磁活性聚合物 (MAP)，其中填料由硬磁（磁化）颗粒组成。这些材料呈现复杂的磁-机械耦合，这需要开发建模框架以在概念化和设计之初就理解它们的响应。硬磁 MAP 文献中可用的大多数当前本构方法不考虑嵌入粒子的偶极-偶极相互作用。然而，磁化颗粒之间的这种相互作用会在复合材料内产生内力，这些内力需要通过来自聚合物基质网络的机械应力来平衡。这一事实可能意味着聚合物网络的初始拉伸，并表明这种偶极-偶极相互作用在 MAP 变形过程中可能很重要。为了解决这些关键点，在本文中，我们提出了一种与硬磁 MAP 的微观结构特征相关的新型本构模型。该模型考虑了聚合物网络预拉伸、偶极-偶极相互作用、塞曼效应以及根据有限变形理论制定的粘性机制。本文获得的结果强调了考虑偶极 - 偶极相互作用和聚合物网络预拉伸的重要性，以了解硬磁 MAP 的复杂磁机械耦合行为。我们提出了一种新的本构模型，该模型与硬磁 MAP 的微观结构特征相关。该模型考虑了聚合物网络预拉伸、偶极-偶极相互作用、塞曼效应以及根据有限变形理论制定的粘性机制。本文获得的结果强调了考虑偶极 - 偶极相互作用和聚合物网络预拉伸的重要性，以了解硬磁 MAP 的复杂磁机械耦合行为。我们提出了一种新的本构模型，该模型与硬磁 MAP 的微观结构特征相关。该模型考虑了聚合物网络预拉伸、偶极-偶极相互作用、塞曼效应以及根据有限变形理论制定的粘性机制。本文获得的结果强调了考虑偶极 - 偶极相互作用和聚合物网络预拉伸的重要性，以了解硬磁 MAP 的复杂磁机械耦合行为。