Abstract:

A lattice Green’s function (LGF) framework is proposed to investigate the mechanical properties of nonlocal lattices (NLLs) with periodically distributed dense defects. The novelty lies in extending the periodic LGF (PLGF) to beam lattices and reformulating both dense defects and nonlocal elements as periodic equivalent nodal forces on a perfect counterpart. This enables displacement perturbation, stress redistribution, and long-range interaction among different unit cells (UCs) to be captured without repeated finite element modeling. With the superposition principle, the defective NLL is transformed into its perfect counterpart, and the effective moduli are derived via strain-energy equivalence. The accuracy of the proposed PLGF method in predicting displacement fields and moduli is verified against the finite element method (FEM) results. The effects of nonlocal interactions on deformation, anisotropic moduli, defect toughening, and stress redistribution are analyzed, providing an efficient theoretical tool for designing toughened lattice metamaterials.

Key words: lattice material, homogenization, effective property, nonlocal lattice (NLL), periodic lattice Green’s function (PLGF), defect toughening