Materials with anisotropic microstructure as micropolar continua, statical and dynamical simulations

The mechanical behavior of materials endowed with specific microstructure can be properly described through a continuum model suitably derived by means of a multiscale approach. In this field, the Cosserat model proved effective, with respect to Cauchy continua, especially in cases of heterogeneous materials made of particles of prominent size and/or anisotropic media (particle composites, masonry, etc.). In this work we consider an energy equivalence criterion in order to built and calibrate a scaledependent continuum (the coarse model at the macro-scale) gathering the response of the original materials (the fine model at the micro-scale). As prototype material, a composite material of matrix and fibers/particles/crystals mutually interacting is adopted. The multiscale strategy is adopted to derive the constitutive relations of anisotropic composites endowed with periodic microstructure, with a ‘reasonable’ computational effort. A lattice system is employed to describe the microscale, thus the multiscale approach is performed to introduce the micropolar continuum modeling at the macro-scale. The derived constitutive relations take into account the shape, the texture and the orientation of the inclusions, and it is able to account for size effects by means of internal scale parameters. The coarse model and the fine one are compared in a linear static and dynamic framework, also showing how to model and how to inspect the inertial terms at both scales. Robustness and efficiency of the proposed multiscale strategy are evaluated by comparing the results of the macroscale model with those provided by numerical finite elements simulations, built in agreement with the ‘real’ microscale model. The investigations are developed by considering boundary conditions and parameters values varying within reasonable physical ranges. The computational effort and the performances of the proposed approach are investigated and discussed with comparisons to some classical benchmarks cases published in the technical literature. Novel potential applications are also presented.