A theoretical method to analyze the effect of stress distribution on compressive strength of periodic lattices

The lattice structures or lattice metamaterials have been widely used in aerospace and medical fields, and the mechanical properties were mostly evaluated based on simulated stress distribution. However, the evaluation of stress distribution of lattice structures often relies on personal experience and lacks quantitative analysis methods. In this study, a theoretical method to quantitatively analyze the relationship between compressive strength of periodic lattices and the simulated stress distribution is proposed. The methodology is based on the periodic stress distribution of periodic lattices, to derive the formulas of structural efficiency and stress concentration coefficient. Then, we discovered that lattice strength is determined by the product of structural efficiency, stress concentration coefficient, relative density, and material strength. In this derivation, the characteristic parameters related to stress distribution are introduced into the formula for lattice strength for the first time. Finally, the theoretical method has been used to analyze the effects of structure parameters, including strut diameter, cell size, and cell pose, on stress distribution and mechanical properties in periodic lattices. The results demonstrate the formula of lattice strength is applicable to analyze the effects of stress distribution.