Computational dynamics for anisotropic homogenized materials

Materials endowed with microstructure, such as particle composites, show a peculiar mechanical behavior, where discontinuities and heterogeneities cannot be neglected. In detail, aiming to depict the structural response at the macroscopic scale, a non-local description is required to keep into account the microscopic one [1]. In this contribution materials with anisotropic microstructure are described as micropolar (Cosserat) continua. Compared to classical (Cauchy) continua, the latter encompass more kinematical descriptors, and then more stress and strain measures. These enriched fields can be revealed of pivotal significance when concentrated forces and/or geometric discontinuities are of interest [2]. As discussed in [3], non-classical and non-local continua can be deducted through multi-scale approaches relying on eligible energy equivalence criteria. Here, anisotropic materials with irregular hexagonal microstructure are considered. The proposed model is able to expose the macroscopic effects of particle size and orientation [2,4]. It is a suitable enhancement of the one recently presented by the Authors in [2], where the statics of two dimensional bodies made of hexagonal rigid particles interacting via elastic interfaces has been analyzed. It is shown how the dynamics at the macroscopics scale is driven by the microstructure. The effect of material anisotropy is investigated with the help of numerical sensitivity analyses, showing how an increasing in the level of material anisotropy alters both frequencies and mode-shapes. Some reliability threesholds for the Cosserat- and Cauchy-like homogenized continua are deduced and discussed in order to address further developments on this research line.