NDLI: A Cascading Mean-Field Approach to the Calculation of Magnetization Fields in Magnetoactive Elastomers

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A Cascading Mean-Field Approach to the Calculation of Magnetization Fields in Magnetoactive Elastomers

Content Provider	MDPI
Author	Romeis, Dirk Saphiannikova, Marina
Copyright Year	2021
Description	We consider magnetoactive elastomer samples based on the elastic matrix and magnetizable particle inclusions. The application of an external magnetic field to such composite samples causes the magnetization of particles, which start to interact with each other. This interaction is determined by the magnetization field, generated not only by the external magnetic field but also by the magnetic fields arising in the surroundings of interacting particles. Due to the scale invariance of magnetic interactions ( $O(r-3)$ in $d=3$ dimensions), a comprehensive description of the local as well as of the global effects requires a knowledge about the magnetization fields within individual particles and in mesoscopic portions of the composite material. Accordingly, any precise calculation becomes technically infeasible for a specimen comprising billions of particles arranged within macroscopic sample boundaries. Here, we show a way out of this problem by presenting a greatly simplified, but accurate approximation approach for the computation of magnetization fields in the composite samples. Based on the dipole model to magnetic interactions, we introduce the cascading mean-field description of the magnetization field by separating it into three contributions on the micro-, meso-, and macroscale. It is revealed that the contributions are nested into each other, as in the Matryoshka’s toy. Such a description accompanied by an appropriate linearization scheme allows for an efficient and transparent analysis of magnetoactive elastomers under rather general conditions.
Starting Page	1372
e-ISSN	20734360
DOI	10.3390/polym13091372
Journal	Polymers
Issue Number	9
Volume Number	13
Language	English
Publisher	MDPI
Publisher Date	2021-04-22
Access Restriction	Open
Subject Keyword	Polymers Magnetic Polymers, Magneto-active Elastomers Dipole Approximation Dipole Model Self-consistent Field Magnetization Field
Content Type	Text
Resource Type	Article

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