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Description
Homogenization of lattice metamaterials enables modelling lattice cells as equivalent solid structures with anisotropic mechanical properties. This aspect enables performing preliminary structural analysis of mechanical components made of metamaterials without modelling the entire lattice cells thus saving computational cost. Elastic homogenization has been widely explored in the literature and many works identified elastic homogenized mechanical properties. On the contrary, elastic-plastic homogenization remains an open field, and it consists of modelling the anisotropic homogenized hardening behaviour of the cells. In this work the authors propose a mathematical framework to describe the anisotropic homogenized hardening behaviour of both 3D and 2D lattice cells. Finite element simulations were implemented by using the periodic boundary conditions, and, firstly, homogenized elastic properties were obtained. After, Hill yielding criterion, Levy-Mises plastic flow rule and a reference homogenized plastic curve along one of the directions of anisotropy were combined to describe the plastic homogenized properties. In particular, a scaling procedure was introduced, and this latter consisted of identifying Hill coefficients by scaling the homogenized plastic curves along the various directions of anisotropy to match the reference plastic curve, and the procedure was implemented in a plane with Hill equivalent stress and plastic strain on y and x axes, respectively. The proposed framework was validated both numerically and experimentally. The first validation was performed by comparing the tensile curves obtained by simulating the homogenized model and the whole lattice structures, while the second validation was performed through mechanical tests on manufactured graded lattice specimens. During mechanical tests digital image correlation (DIC) was also used for an adequate measure of the strains of lattice units. Different materials, i.e. polymeric and metallic, were considered for the manufacturing of the specimens, and the obtained results demonstrated a good overlap between experimental, numerical homogenized and numerical lattice results.