Microstructural modelling of hard-magnetic soft materials: Dipole-dipole interactions versus Zeeman effect

Abstract

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.