A discretization method for predicting the equivalent elastic parameters of the graded lattice structure

Abstract

In recent years, cellular materials have been widely studied and applied in aerospace and other fields due to the advantages of lightweight and multi-function. However, it is difficult to predict the equivalent elastic properties of the graded lattice structure and other non-uniform cellular materials because of the complex configuration and non-uniformity. A new discretization method for predicting the equivalent elastic parameters of the graded lattice structure is proposed based on the strain energy equivalent method and the discretization method in this paper. The graded lattice structure is discretized into lattice cells, the equivalent elastic properties are predicted by calculating the global equivalent elastic parameters with the parameters of lattice cells, and the calculation formulas are derived. After that, taking edge cube, face-centered cubic and body-centered cubic lattice as examples, the effectiveness and accuracy of the method are verified by theoretical calculation, numerical analysis, and experiment. The results show that the calculation errors of equivalent elastic parameters are between 4.5%–9.7%, and the errors can be significantly improved by reducing the graded factor. It proves that the proposed discretization method can predict the equivalent elastic parameters of the graded lattice structure effectively, and is suitable for different lattice structures.

Predictions of the Elastic–Plastic Compressive Response of Functionally Graded Polymeric Composite Lattices Manufactured by Three-Dimensional Printing

“…The authors observed a good agreement of the FEN model with the experimental data. Besides the explicit geometric models, the homogenisation approach [12,[15][16][17][18][19] served as a computationally efficient alternative to determine the equivalent effective properties of a heterogeneous lattice. In [17,19], it was coupled with the modified Hill yield criterion and showed good agreement for variable density and surface-based lattices.…”