A review of the latest theoretical advances in the description of magnetomechanical effects and phenomena observed in magnetoactive elastomers (MAEs), i.e., polymer networks filled with magnetic micro- and/or nanoparticles, under the action of external magnetic fields is presented. Theoretical modeling of magnetomechanical coupling is considered on various spatial scales: from the behavior of individual magnetic particles constrained in an elastic medium to the mechanical properties of an MAE sample as a whole. It is demonstrated how theoretical models enable qualitative and quantitative interpretation of experimental results. The limitations and challenges of current approaches are discussed and some information about the most promising lines of research in this area is provided. The review is aimed at specialists involved in the study of not only the magnetomechanical properties of MAEs, but also a wide range of other physical phenomena occurring in magnetic polymer composites in external magnetic fields.
Keywords: magnetic particles; magnetoactive elastomers; magnetodeformation; magnetorheological effect; magnetorheological elastomers; mechanical properties; theoretical modeling.