Model of a Magnetoactive Elastomer with Structure Parameter

Abstract

Purpose. To propose a simple and physically reasonable way to describe basic properties of magnetoactive elastomers under the action of magnetic field and/or mechanical loading.Methods. A phenomenological approach is developed, in the framework of which the aggregation of ferroparticles in a magnetoactive elastomer is interpreted as the appearance of an order parameter whose physical meaning resembles, although does not coincide entirely with, the number of the particles dwelling in aggregates normalized by the total number of the particles. The corresponding functional contribution to the free energy of the system is constructed in the form similar to that of the Landau-de Gennes expansion, as it is used in the theory of phase transitions. Depending on the presence of the cubic term in this expansion, the transition may develop along the scenarios of either I or II order.Results. In a model 1D calculation it is shown that the dependences of the main characteristics of the composite, viz. magnetization and deformation, on the applied field and mechanical load, might be in a unified manner described as being entailed by the evolution of the above-introduced order parameter. A specific feature manifested by the model system is its ability to display quasi-plastic response that exists as long as the external field is on, and to get back to elastic behavior as soon as the field is switched off.Conclusions. The results obtained are found to be in good agreement with the data obtained from the direct numerical modelling of the mesoscopic variant of the considered problem. In qualitative aspect, the discovered specific features of the rheological bahavior closely resemble the results of experimental studies om mechanical loading of magnetoactive composites consisting of a silicone rubber filled with micron-size particles of carbonyl iron.