To the theory of elastic properties of isotropic magnetic gels. Effect of interparticle interaction
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Smart Materials and Structures 26 (9), 095028, 2017
SponsorshipL Iskakova and A Zubarev are grateful for the financial support of the Russian Fund for Basic Research, 16-58- 12003; the Program of Russian Federation Ministry of Science and Education, project 3.1438.2017/4.6. M Lopez-Lopez was supported by the project FIS2013- 41821-R (Plan Nacional de Investigación Científica, Desarrollo e Innovación Tecnológica, Ministerio de Economía y Competitividad, Spain, co-funded by ERDF, European Union). D Borin would like to acknowledge the support of DFG (Deutsche Forschungsgemeinschaft) under Grant Bo 3343/ 1-1.
The paper deals with theoretical study of elastic shear properties of a magnetic gel, consisting of spherical magnetizable particles, randomly (gas-like) distributed in an elastic matrix. We suppose that the composite is placed in a magnetic field, perpendicular to the direction of the sample shear. In order to get mathematically rigorous results, we have restricted ourselves by the analysis of the system with a low concentration of the particles. Magnetic and elastic (through the matrix deformation) interactions between them are considered in the framework of the regular pair approximation. Analysis shows that external magnetic field decreases the macroscopic shear modulus of the composite with a low concentration of the particles. The decreasing dependence of the modulus on the macroscopic shear is estimated. We believe that the suggested rigorous approach can be a robust background for the study of the systems with a high concentration of the particles.