Dynamics for anisotropic homogenized materials

Materials such as ceramic and metal composites, poly-crystals, masonry, porous rocks are examples of particle composites: their macroscopic behavior is strongly dependent on the internal microstructure, moreover discontinuities and heterogeneities cannot be neglected. For these reasons, a non-local description is necessary to take into account the microscopic influence on the mechanical response. In this work the goal is to highlight the advantages of a description of these materials as micropolar continua compared to the classical continua. A homogenization technique, based on an energy equivalence criterion, between the discrete model, assumed as the benchmark, and the continuum model, is adopted to detect the anisotropic constitutive characteristics [1]. A possible numerical approach is presented in order to have a right identification of the representative volume element, needful for a correct homogenization [2]. Starting from other works of the same authors where the statics of two-dimensional bodies has been analysed [3-5], this study goes to further enrich the discussion and shows the influences of the material internal length on the dynamic response and consequently the necessity of a micropolar description. Particle composites with an internal microstructure made of three different hexagonal rigid blocks and thin elastic interfaces are considered at three different scale level, the numerical tests bring out how an increasing in the level of material anisotropy affect both frequencies and mode-shapes. [1] P. Trovalusci and R. Masiani, “Material symmetries of micropolar continua equivalent to lattices,” Int. J. Solids Struct., vol. 36, no. 14, pp. 2091–2108, 1999, doi: 10.1016/S0020-7683(98)00073-0. [2] M. Colatosti, N. Fantuzzi, P. Trovalusci, and R. Masiani, “New insights on homogenization for hexagonal-shaped composites as Cosserat continua”. Meccanica, 2021. https://doi.org/10.1007/s11012-021-01355-x [3] N. Fantuzzi, P. Trovalusci, and R. Luciano, “Multiscale analysis of anisotropic materials with hexagonal microstructure as micropolar continua,” Int. J. Multiscale Comput. Eng., vol. 18, no. 2, pp. 265–284, 2020, doi: 10.1615/IntJMultCompEng.2020032920. [4] N. Fantuzzi, P. Trovalusci, and R. Luciano, “Material symmetries in homogenized hexagonal-shaped composites as cosserat continua,” Symmetry, vol. 12, no. 3, pp. 1–21, 2020, doi: 10.3390/sym12030441. [5] L. Leonetti, N. Fantuzzi, P. Trovalusci, and F. Tornabene, “Scale effects in orthotropic composite assemblies as micropolar continua: A comparison between weak and strong-form finite element solutions,” Materials, vol. 12, no. 5, 2019, doi: 10.3390/ma12050758.