1D Modelling of BCC Lattice Mechanical Behaviour Using Optimised Neural Networks

Abstract: Lattice structures find extensive use in multiple engineering sectors due to their tailored high specific mechanical properties. These structures are characterised by the repetition of one, or multiple, unit cell(s). Starting from a standard Body-Centered Cubic (BCC) unit cell, this study presents a new numerical approach for modelling lattice structures from the single unit cell. Specifically, a novel 1D numerical model is presented featuring custom-defined area and inertia values for the beam elements of the cell struts, independent of their nominal diameter value. The mechanical properties are evaluated through uniaxial compression and in-plane shear tests. Numerical analyses were carried out using Ansys 2023 R2 implementing a custom Ansys Parametric Design Language (APDL) routine. Subsequently, custom-made and commercial neural networks, trained using 3D finite element method simulations, were used to optimise the user-integrated area and inertia values. By comparing their results is possible the identification of the most suitable parametric values for different strut diameters. The proposed 1D method is aimed at reducing the modelling and computational complexity associated with traditional 3D FEM approaches while retaining the ability to predict mechanical behaviour accurately. By simplifying lattice struts into 1D beam elements, computational costs can be reduced, allowing the analysis of full-scale lattice structures and parametric studies across various designs and loading conditions. The method was validated through comparisons of 3D and 1D numerical simulations and with well established approaches in the literature through a three-point bending test with variable spans. The results demonstrated that the proposed approach provides accurate predictions while saving computational time, proving its effectiveness for practical use.