Construction of micropolar continua from the asymptotic homogenization of beam lattices

► Development of homogenization techniques for discrete lattice structures. ► Calculation of the effective elastic micropolar properties. ► Design of a lattice with a hierarchical double scale microstructure. ► Validation of the calculated micropolar moduli by comparison with FE simulations. The asymptotic homogenization of periodic beam lattices is performed in an algorithmic format in the present contribution, leading to a micropolar equivalent continuum. This study is restricted to lattices endowed with a central symmetry, for which there is no coupling between stress and curvature. From the proposed algorithms, a versatile simulation code has been developed, relying on an input file giving the lattice topology and beam properties, and providing as an output the equivalent stiffness matrix of the effective continuum. The homogenized moduli are found in close agreement with the moduli obtained from finite element simulations performed over extended lattices. The obtained results are exploited to design and calculate a lattice endowed with a hierarchical double scale microstructure, leading to a dominant micropolar effect under bending at the macroscopic scale.