A Large-Deformation Phase-Field Approach for the Modeling of Magneto-Sensitive Elastomers

Magneto-sensitive materials show magneto-mechanical coupled response and are thus of increasing interest in the recent age of smart functional materials. Ferromagnetic particles suspended in an elastomeric matrix show realignment under the influence of an external applied field, in turn causing large deformations of the substrate material. The magneto-mechanical coupling in this case is governed by the magnetic properties of the inclusion and the mechancial properties of the matrix. The magnetic phenomenon in ferromagnetic materials is governed by the formation and evolution of domains on the micro scale. A better understanding of the behavior of these particles under the influence of an external applied field is required to accurately predict the behavior of such materials. In this context it is of particular importance to model the macro scopic magneto-mechanically coupled behavior based on the micro-magnetic domain evolution. The key aspect of this work is to develop a large-deformation micro-magnetic model that can accurately capture the microscopic response of such materials. Rigorous exploitation of appropriate rate-type variational principles and consequent incremental variational principles directly give us field equations including the time evolution equation of the magnetization, which acts as the order parameter in our formulation. The theory presented here is the continuation of the work presented in [1, 7] for small deformations. A summary of magneto-mechanical theories spanning over multiple scales has been presented in [4]. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)