### Functionally Graded Lattice Structures Incorporating a Thickness Gradient under Compressive Loads  
An easily controlled grading variable is the thickness of strut-based lattices while the cell type and size are kept constant. Several publications have considered the thickness-grading styles of lattices in quasi-static or dynamic compressive load cases and noted potential performance improvements compared with uniform lattices of the same relative density. [PERSON] et al. [14] studied six different lattice types at 50% porosity made of Formlabs Elastic 50 A resin in quasi-static compression, comparing them with four linearly varying thickness distributions along a single axis. The lattices were loaded along or perpendicular to the gradient direction to assess potential differences. They concluded that the uniform lattices were mostly capable of higher stress levels and absorbing more energy than the graded lattices at low compression strains; however, this trend was reversed at higher compressive strain levels. Furthermore, applying a gradient perpendicular to the loading direction appeared to outperform a parallel gradient in most of the model configurations. The performance of lattices under compressive loads is commonly assessed via specific energy absorption (SEA), a measurement dividing the absorbed compressive energy by the structure's mass. [PERSON] et al. [15] investigated a two-dimensional hexagonal aluminium honeycomb at 5% relative density under dynamic compression. At low speeds, the uniform configuration showed the largest energy absorption and the graded variants the lowest. During high-velocity compression, differences in behaviour start to occur at different compression stages. Up to 25% compression, a positive gradient with more mass located near the moving plate shows significantly increased energy absorption compared with the inverted gradient, while the uniform distribution's absorption level is nearly the average of the graded lattices' performance. At approximately 55% compression, all graded lattices have reached comparable energy absorption levels only to diverge again at higher compression levels. Between 60 and 80% compression, lattices with a negative gradient (less mass near the moving plate) show the greatest energy absorption capabilities. The same study also considered a honeycomb Voronoi lattice structure in the same load case, and similar findings were reported. [PERSON] et al. [16] studied two cuboid lattice structures at a relative density of 19% made of polyamide 12 produced with a Selective Laser Sintering (SLS) machine. A constant gradient was applied to BCC and BCCz lattices (which are BCC unit cells with additional vertical struts) along the compression direction. In quasi-static compression, the uniform lattice structures exhibit long, flat plastic plateaus, whereas the graded structures show pronounced sequential layer collapses. Both types of graded structures outper  
Figure 1: (**a**) Examples of bending-dominated (left) and stretching-dominated (right) unit cell categories; (**b**) schematic reaction force development of compressed lattice composed of ductile material with stretching-dominated cells (solid line), bending-dominated cells (dashed line) and a brittle lattice exhibiting sequential layer collapse (dotted line). Three distinct regions are visible—(1) linear elastic part, (2) plateau region, (3) densification. formed the uniform counterparts vastly with 80% (BCC) and 114% (BCCz) higher specific energy absorption. In a similar study by [PERSON] et al. [17], a BCC lattice structure made of Al-Si10-Mg produced via Selective Laser Melting (SLM) with heat treatment was tested under quasi-static compression. A relative density of 22% was set for both the uniform lattice and a linearly changing thickness distribution. The graded lattice showed a slight increase in SEA of approximately 10%. A uniform, non-heat-treated specimen failed because of shear band formation and large-scale diagonal failure in the early compression stages with 10% strain.