A hybrid continuum-beam optimisation model: the virtual extensometer method for efficient optimisation of lattice materials

Additive manufacturing (AM) enables the fabrication of complex lattice structures that are infeasible with traditional manufacturing processes. These structures are typically implemented with constant cross-sectional strut elements; this strategy is expedient but leads to sub-optimal structural efficiency. Numerical continuum models allow robust mechanical modelling of complex lattice geometry but provide equally complex data fields that are ill-suited for traditional optimisation techniques. By contrast, numerical beam models represent the fundamental tensile and bending stress states but are incapable of capturing nuanced geometrical effects that lead to local stress concentrations. In this research, a hybrid continuum-beam method is proposed for the systematic optimisation of strut cross section: a representative unit cell is simulated by continuum elements, and the local strut stress tensor is acquired by embedded beam elements that act as virtual extensometers. By integrating a computationally inexpensive beam model into a more robust continuum model, the volume and the quality of data returned are significantly increased whilst being provided in a readily usable format for optimisation techniques, for a trivial increase in computational cost. The presented method is generalised and can be applied to any strut-based lattice structure. Body-centred cubic (BCC) and BCC with z-strut (BCCZ) lattice structures optimised by the proposed method are fabricated using laser-based powder bed fusion (LB-PBF) in AlSi10Mg and are mechanically evaluated. On average, performance for BCC lattice structures improves by 33% and 26% for relative yield strength and relative Young’s modulus respectively. BCCZ lattice structures saw a performance improvement of 25% and 19% for relative yield strength and relative Young’s modulus respectively, thus confirming superior performance at lower relative densities when compared to incumbent designs.