Continualization method of lattice materials and analysis of size effects revisited based on Cosserat models

The homogenized classical and higher-order mechanical properties of repetitive lattice materials are evaluated using Timoshenko beam models at a microlevel, and a continualization method towards a Cosserat homogenized substitution medium is applied. The proposed method combines a reduced number of degrees of freedom at a unit cell level with the continuous set of kinematic variables, which are representative of a Cosserat continuum at the macroscale. The homogenized classical and Cosserat moduli are obtained as closed-form expressions of the lattice microstructural and mechanical parameters for the specific case of honeycomb lattices. The proposed continualization method proves to be accurate and computationally efficient in comparison with fully resolved finite element simulations. One main hallmark of this paper is the quantification of edge effects in the response of lattice structures, relying on the surface formulation of the extended Hill macrohomogeneity condition. The bending moment to curvature relation involves a classical term and a micropolar bending moment, the impor-tance of which is decreasing asymptotically up to a nil value by increasing the number of unit cells in the height of the macrostructure.

Automated summary

This paper evaluates the mechanical properties of repetitive lattice materials using Timoshenko beam models and a continualization method. It also proposes a surface formulation to quantify the edge effects in lattice structures. The results show that the proposed method is accurate and computationally efficient.