Representative volume element size, length-scale identification, and stop-band frequencies in magnetorheological elastomers

Smart composite materials have garnered a great interest from the engineering community, and been the subject of many studies in the last few decades. Specifically, magnetorheological elastomers (MREs) are examples of such smart composites, typically they consist of ferromagnetic particles embedded in a polymer network. The underlying microstructure is a fundamental property in the analysis of heterogeneous materials’ behaviour. Microstructural information needs to be taken into account in the macroscopic continuum to accurately describe and predict the material response. Therefore, the main aim of this study is to develop numerical models and investigate the static and dynamic behaviour of MRE materials by considering the influence of microstructural properties. In the static aspect, microstructural effects have been introduced to macroscopic magneto-elastic continua via additional material parameters: Representative Volume Elements (RVE). Hence, a numerically-statistical procedure has been presented to define and determine the RVE sizes for an MRE material. Thereafter, length-scale enriched generalised gradient magneto-elastic continuum model has been used with the determined RVE sizes to study the effectiveness of the model compared to a classical magneto-elastic continuum formulation that lacks of microstructural information. In the dynamic aspect, the effects of geometrical properties and magneto-elastic coupling on the longitudinal wave propagation have been investigated, in particular, from appearance of band gap phenomenon .