The reinforcement and defect interaction of two-dimensional lattice materials with imperfections

The defect interaction and reinforcement of imperfect two-dimensional lattice materials are studied by theoretical investigations and finite element (FE) simulations. An analytical model is proposed to predict the interaction of two defects in lattice materials based on a single defect model. An interaction coefficient is introduced to characterize the degree of interaction. The effects of defect type and defect distance on interaction coefficients are studied. The critical interaction distance of defects, beyond which the interaction of two defects can be neglected, is derived. FE calculations are performed to validate the theoretical model. The simulated results indicate that increasing the number of defects can reduce the stress concentration rather than weakening the strength of the residual parts in certain circumstances. Subsequently, several reinforcement methods are proposed to reduce the stress concentration in the triangular and Kagome lattice for the single-bar-missing defect and single-joint-missing defect. An analytical model is developed for the reinforced lattices, and the predicted stress concentration factors are in good agreement with those of FE simulations. By theoretical studies and FE simulations, optimal reinforcement methods are derived for the triangular and Kagome lattice under planar loading conditions.