Multi-scale dispersive gradient elasticity model with rotation for the particulate composite

Research on the characteristics of composites material has received enormous interest in recent years. The multiscale nature of composite material leads to employing advanced techniques. Moreover, the presence of a wave with the high-frequency source adds complexity to the analysis. In this paper, a novel multi-scale elasticity model was developed to predict the wave dispersion property of particulate composites. The methodology was based on the simultaneous participation of translational and rotational degrees of freedom in motion equations. The method scheme of gaining motion equations was accomplished by using Taylor's expansion as a continualization method. The framework of the motion equations and restrictions determined the layout of the lattice. The obtained lattice was a network of polydispersive particles in three-dimensional as a unit cell. The model proposed the inertia coefficient and dimension coefficient, which reflected the heterogeneity on the particulate composite. The theoretical results were then validated with experimental results. For this aim, concrete and mortar with the various classes of heterogeneity were nominated as a sample of particulate composite material. The nominated composites were prepared with different mixture schemes from geopolymer paste. The wave dispersion behavior of geopolymer specimens was established by measuring phase velocity in various frequencies. In addition to geopolymer products, experimental results from independent literature were scrutinized for concrete and mortar with cement binder. In the end, the capability of the presented parameters was indicated for realizing the state of concrete curing and features of the binder.