磁流变弹性体的力-磁耦合模型

A Theoretical Model for Magneto-Mechanical Coupling Behaviors of Magnetorheological Elastomers

以磁偶极子理论为基础,利用最小势能原理,从微观角度出发,研究了磁流变弹性体在单向载荷作用下的力-磁耦合行为,提出了可以描述该行为的数学模型,分析了磁致应力非线性变化的规律和机理.该模型从磁流变弹性体的微观结构出发,考虑了所有铁磁颗粒的磁化特性,以及颗粒之间、链结构之间的相互作用,推导了磁相互作用能的表达式,采用Mooney-Rivlin模型给出了弹性势能表达式.最后运用最小势能原理,建立了描述磁流变弹性体在均匀磁场中力-磁耦合行为的数学模型.该模型与实验结果吻合较好,并能从微观层面对磁流变弹性体的磁致应力变化规律做出解释.研究发现,磁流变弹性体的磁致应力在不同磁场下的变化规律不同,与材料内部的微结构紧密相关,铁磁颗粒之间及链结构之间的相互作用是导致磁致应力非线性变化的主要原因.

Based on the magnetic dipole interaction theory,a theoretical model was proposed to describe the magneto-mechanical coupling behaviors of magnetorheological elastomers with the principle of minimum potential energy. In this model,the fully coupled interaction among all particles and chains was considered according to the micro-structure of magnetorheological elastomers. The energy equations of magnetic interaction and the elastic potential energy equations based on the Mooney-Rivlin model were derived respectively. Then a theoretical model was developed to describe the stress-strain relationship of magnetorheological elastomers under uniaxial load. This model agrees well with existing experimental data and can be used to explain the micro-mechanism of magneto-induced stress. The results show that the mechanism of magneto-induced stress is closely related to the inner micro-structure,and the nonlinear property of magneto-induced stress mainly depends on the interaction among both particles and chains.