Composites with different material symmetries. Discrete-micropolar continuum description

Particle composites include materials like ceramic, metal composites, poly-crystals, and masonry. Due to the presence of different heterogeneities (rigid or soft inclusions, voids, microcracks, etc.) whose size may have an important impact on their behaviour at the macroscopic scale, mechanical modelling is a challenging task. Non-local theories offer a solution to this problem while maintaining memory of the microstructure, especially the internal length. Differently to local classical models, non-local models (micropolar/Cosserat might be considered non-local continua of implicit type [1]) can account for internal lengths in the field equations, which are significant in many cases. The aim of this work is the mechanical characterization of anisotropic composites made of rigid particles and thin elastic interfaces at different level scale for investigating both statical and dynamical behaviour [2-3]. To find the anisotropic constitutive properties of those materials, a homogenization technique based on an energy equivalence criterion between a discrete model of the material and a continuum one is adopted [4]. Two continuum model descriptions, one micropolar and the other classical, are compared to the discrete system, assumed as benchmark. Different material symmetry classes, both centrosymmetric and non-centrosymmetric, are considered and the advantages of micropolar modelling are highlighted. [1] Trovalusci, P., Molecular Approaches for Multifield Continua: Origins and Current Developments. In Multiscale Modeling of Complex Materials; T. Sadowski, P. Trovalusci, Eds.; Springer: Vienna, Austria, 2014; pp. 211–27, DOI:10.1007/978-3-7091-1812-2_7 [2] Colatosti, M., Fantuzzi, N., Trovalusci, P. and Masiani, R., New insights on homogenization for hexagonal-shaped composites as Cosserat continua. Meccanica, 2021. https://doi.org/10.1007/s11012-021-01355-x [3] Colatosti, M., Fantuzzi, N. and Trovalusci, P., Dynamic Characterization of Microstructured Materials Made of Hexagonal-Shape Particles with Elastic Interfaces. Nanomaterials 2021, 11, 1781, DOI: doi.org/10.3390/nano11071781 [4] Trovalusci, P. and Masiani, R., Material symmetries of micropolar continua equivalent to lattices, International Journal of Solids and Structures, 36(14), 2091-2108, 1999. DOI:10.1016/S0020-7683(98)00073-0