Numerical analysis of homogenized hexagonal-shaped composite as Cosserat continua

Composite materials are utilized in a several engineering fields, they can be studied by modelling interactions among their constituents or by homogenizing an equivalent continuum, the first approach requires an high computational cost to model the particles and their interactions. The aim of this work is to study the behavior of a structure with a regular microstructure: different textures are considered to understand the effects of the geometry on the mechanical response and it is also evaluated the in uence of geometry's scale. Furthermore, another purpose is to show how different materials, such as masonry assemblies, can be described through micropolar continua theory, wherein the continuum has additional degrees of freedom with respect to classical elasticity and it is able to more accurately describe heterogeneous materials taking into account size effects. In this thesis various numerical examples are illustrated in which various structures are loaded in different conditions and three different mathematical models are assumed: a discrete model, where the microstructure is formed by rigid blocks with elastic interfaces, a Cosserat continuum model and lastly a Cauchy continuum model. The continuum models are obtained by a homogenization technique which is able to carry out constitutive parameters using a principle of energetic equivalence: starting from a representative volume element (RVE) is obtained the constitutive matrix. In literature it's possible to find a numerical tests with a rectangular shape of blocks, so it is interesting to prove that the procedure is expandable to other geometries. The models are studied by numerical simulation using a MATLAB FEM code and the FEM analysis software Abaqus through the use of Python code script. In a second moment the dynamic behavior is studied as well, comparing the frequencies and the deformed shape of the ways to vibrate for the different models.