Second-order homogenization of 3-D lattice materials towards strain gradient media: numerical modelling and experimental verification

Abstract The literature in the field of higher-order homogenization is mainly focused on 2-D models aimed at composite materials, while it lacks a comprehensive model targeting 3-D lattice materials (with void being inclusion) with complex cell topologies. For that, computational scheme based Mindlin (type II) strain gradient elasticity theory developed here. variational formulation periodic boundary conditions, implemented open-source software FreeFEM to fully characterize effective classical elastic, coupling, and elastic matrices materials. Rigorous mathematical derivations equilibrium equations Hill–Mandel lemma are provided, resulting introduction macroscopic body forces modifications tensors which eliminate spurious effects homogeneous material. obtained homogenized positive definite, leading energy density value—an important criterion that sometimes overlooked. employed study size square cubic case material, verified using full-field simulations, isogeometric analysis, experimental three-point bending tests. results through simulations show good agreement mechanical generic can be used derive second-grade continuum for any architectured material arbitrary geometry. However, identification proper type generalized continua analysis different architectures yet an open question.