• International Journal of Technology (IJTech)
  • Vol 13, No 5 (2022)

A Novel Lattice Structure for Enhanced Crush Energy Absorption

A Novel Lattice Structure for Enhanced Crush Energy Absorption

Title: A Novel Lattice Structure for Enhanced Crush Energy Absorption
Chang Yuan Seek, Chee Kuang Kok, Chong Hooi Lim, Kia Wai Liew

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Cite this article as:
Seek, C.Y., Kok, C.K., Lim, C.H., Liew, K.W., 2022. A Novel Lattice Structure for Enhanced Crush Energy Absorption. International Journal of Technology. Volume 13(5), pp. 1139-1148

Chang Yuan Seek STMicroelectronics Sdn. Bhd., Kawasan Perindustrian Tanjung Agas, 84007 Muar, Johor, Malaysia
Chee Kuang Kok Center for Advanced Mechanical and Green Technology, Faculty of Engineering and Technology, Multimedia University, Jalan Ayer Keroh Lama, 75450 Bukit Beruang, Melaka, Malaysia
Chong Hooi Lim Center for Advanced Mechanical and Green Technology, Faculty of Engineering and Technology, Multimedia University, Jalan Ayer Keroh Lama, 75450 Bukit Beruang, Melaka, Malaysia
Kia Wai Liew Center for Advanced Mechanical and Green Technology, Faculty of Engineering and Technology, Multimedia University, Jalan Ayer Keroh Lama, 75450 Bukit Beruang, Melaka, Malaysia
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A Novel Lattice Structure for Enhanced Crush Energy Absorption

Lightweight and stiff lattice structures are good energy absorbers. This study evaluates the energy absorption capacity of a few common lattice structures printed out of PLA using fused deposition  modeling and proposes an improved lattice structure. Simple cubic (SC), honeycomb (HC),  body-centered cubic (BCC), and  novel PeckGy80 (PG80) lattice structures were subjected to compressive tests. The quasi-static load-displacement  behavior of lattice specimens was characterized in terms of specific energy absorption and crush load efficiency. The damage mechanisms were then related to energy absorption. Cracks and brittle fractures occurred in all lattice structures during the crush test. Different lattice structures induced different damage mechanisms,  significantly affecting their energy absorption. SC lattice structure showed structural separation at a small displacement, rendering it an ineffective energy absorber. BCC and HC lattice structures demonstrated almost identical shear band failure modes. The PG80 lattice structure, although made of brittle PLA, displayed progressive failure from the bottom layer to the upper layers, exhibiting both a high peak load and  stable post-yield behaviour. This damage mode enabled the PG80 lattice to be far superior in terms of specific energy absorption to HC, SC, and BCC lattice structures.

3D Printing; Energy absorption; Lattice structures; PLA; Quasi-static crush


Three-dimensional lattices, having replicated structures like those of cellular solids, draw much attention owing to their high stiffness, strength and ultra-lightweight (Dong et al., 2020). Besides, the capability of lattice structures to undergo considerable deformation at a relatively low transmitted stress makes them good energy absorbers. Lightweight and large energy absorption capacity are currently the main design priorities in the automobile and aerospace sectors to minimize the amount of material and hence fuel consumption (Helou & Kara, 2017; Ye et al., 2020). Traditionally, the role of energy absorption has been filled by thin-walled tubes (Malawat et al., 2019). Recent findings indicated that polylactic acid (PLA) lattice structures might be used as sacrificial claddings as material and structure protection gear (Santos et al., 2021; Sun et al., 2021).

The advancement in additive manufacturing provides design freedom in printing lattices, yet the effective design strategies of complex lattices suitable for various  applications are still under research (Panesar et al., 2018).   Three   types   of   lattices   are common, namely strut-based lattices, planar lattices, and surface-based lattices. The typical strut-based (a.k.a. bending dominated) lattices suffer from low structural stiffness, whereas the typical surface-based (a.k.a. stretch-based) lattices demonstrate low energy absorption (Riva et al., 2021). Common strut-based lattices include simple cubic (SC) and body-centered cubic (BCC), whereas honeycomb (HC) is a common planar lattice. These common latices had been printed using different materials (Obadimu & Kourousis, 2021). In a similar study, Park and Park (2020) made functionally graded lattices, including BCC and hexagonal HC structures, with photo-curable polyurethane resin. They found that the compressive stiffness of the lattice structures varied greatly, up to five orders of magnitude depending on design parameters. And all the structures displayed predominantly bending mode in compression. Santos et al. (2021) fabricated PLA and polyethylene terephthalate glycol-modified (PETg) lattice structures out of honeycomb and auxetic?type hexagonal unit cells to investigate their low-velocity impact response. They found that PETg was superior to PLA in terms of energy absorption.  A hybrid design combining an octet and a  bending-dominated structure printed in PLA showed a desirable stable post-yield stress plateau, which could hardly be achieved by the octet structure alone.  The latest trend also included the use of cell topology and its modification (Sun et al., 2021).

Previous work demonstrated the feasibility of SC, HC, and BCC lattices for energy absorption. Liu et al. (2021b) explored the mechanical performance of an SC lattice structure fabricated using titanium alloys through selective laser melting (SLM) technology. They found that the SC lattice structure showed manageable plateau stress and excellent energy-absorption capability, and it can be utilized in vibration damping machines and biomedical transplants (Liu et al., 2021b). It has been long observed that the HC lattice possesses a superior energy absorption ability. When loaded uniaxially, the honeycomb cells would bend and fold over steadily as demonstrated in (Ashby, 2006). On the other hand, BCC is a traditional form of bending-dominated strut-based structure, which has gained significant attention and has been experimentally and scientifically studied for its unique mechanical and energy-absorbing properties (Mines et al., 2013; Ushijima et al., 2010; Gümrük et al., 2013; Tancogne-Dejean & Mohr, 2018). The mechanical performance of the BCC lattice structure was examined under numerous loading conditions (Gümrük et al., 2013; Tancogne-Dejean & Mohr, 2018), and the classical beam hypothesis approach was used to forecast its mechanical performance (Ushijima et al., 2010; Ushijima et al., 2013). In addition, drop-weight impact tests revealed that the BCC lattice structure made of Ti–6Al–4V demonstrated superiority over the honeycomb (Mines et al., 2013), and compression tests indicated that the BCC lattice structure made of Ti–6Al–4V seemed to be suitable for energy absorption systems owing to the extended plateau region and low hardening period before densification (Tancogne-Dejean & Mohr, 2018).

Compared to other printable materials such as ABS, nylon and (PETg), PLA possesses the advantages of being biodegradable and cost-effective (Lololau et al. 2021, Santos et al. 2021). Yet, there appears to be a lack of a comprehensive evaluation of the performance of PLA-printed lattices for energy absorption, which prompted this study. There are two objectives in this study. First, the energy absorption capability of different lattice structures, namely SC, HC, BCC, and a novel PG80, was characterized experimentally to establish the basis for comparison. PG80 was not a pre-existing lattice structure but was the result of trial-and-error in the course of this work. Secondly, the structural failures of the lattice structures were related to energy absorption to elucidate the superiority of the novel lattice structure.

Experimental Methods

2.1. Lattice Structures and Specimen Design

       The SC, BCC, and PG80 lattice structures have proper strut placement in a unit cell of 10 mm X 10 mm x 10 mm. These lattice structures, together with the HC lattice structure, have equal overall sizes of 40 mm X 40 mm X 40 mm, as shown in Fig 1. The theoretical relative density of the SC, HC, BCC, and PG80 are 0.16, 0.36, 0.26, and 0.38, respectively. The actual relative density of the printed specimens turned out to be 0.17, 0.28, 0.20, and 0.34, respectively, for the same lattice structures. The relative density is the density of the lattice structure (i.e., the mass of the lattice over its apparent volume, namely 6.4X104 mm3) over the theoretical density of the PLA, 1240 kg/m3. To measure the actual relative density of the lattice structures, only the masses of the printed lattice structures need to be measured. The deviations in relative density may have resulted from imperfect support material removal and printing parameters. In as much as humanly possible, the printed specimens were all inspected for unintended sharp corners so that they were removed before crushing.

Figure 1 Printed lattice structures. (a) SC; (b) HC; (c) BCC; (d) PG80

Figure 2 shows the unit cells of SC, HC, and BCC. The SC lattice is lined with square struts having a cross-section of 2 mm X 2 mm (i.e., L = 9.5 mm and d = 1 mm in Figure 2(a)). The HC lattice was made of honeycombs in a hexagonal arrangement. Each unit cell has a perimeter of 30 mm (i.e., L = 5 mm each side, Lc = 10 mm, t = 1 mm in Figure 2(b)). When one cell is laid hexagonally with another cell, the joining side forms a honeycomb wall of 2 mm thick. The BCC lattice has eight struts per unit cell. Every strut has a cross-section of 2 mm X 2 mm, whose corners are rounded by a radius of 0.3 mm. The strut begins at the cell  center and diverges to eight corners. Its length is  before joining a corner prism (i.e., four prisms from neighboring unit cells make a cube of 4 mm X 4 mm X 4 mm). The crossing points between trusses were made into smooth bends (see Figure 2(c)) instead of sharp corners to reduce stress concentration.

        While SC, HC, and BCC lattice structures were used in this study primarily for their prevalence in previous studies, the PG80 lattice structure was designed specifically in this study to retain the existing advantage of strut-based lattice architecture, namely outstanding energy absorption, with enhancement in strength or stiffness. The PG80 unit cell comprises nodes (n) and struts (S), as shown in Figure 3. The "X" configuration nodes are generated when four struts meet at the hollow cylinder. The "#" configuration nodes are located at the struts' intersection points. The hollow cylinder that exists at the middle of the unit cell serves as a connector that links three (3) of "X" configurations and two (2) "#" configurations in series. There are 20 struts and 20 nodes in total within a unit cell.  

Figure 2 Unit cells of (a) SC, (b) HC, (c) BCC lattice structures


Figure 3 PG80 lattice; (a) Unit cell, (b) “X” configuration, (c) “#” configuration

Based on the number of nodes and struts, the Maxwell number (Maconachie, et al., 2019) turned out to be negative, making this structure exhibit a predominantly bending mode. The solid struts on the "X" have a thickness of 1.4-1.7 mm (i.e., 2 mm diameter cylinders truncated by 0.3 mm on either side and by 0.6 mm when sandwiched in the unit cell, see Figure 3 (a) (right)), whereas those hollow struts on the "#" have a mean diameter of 1.5 mm and thickness of 0.5 mm. The hollow cylinder has a mean diameter of 4 mm and is 1 mm thick.

2.2. PLA materials and printing Parameters

The lattice structures were printed out of a PLA filament with a diameter of 1.75±0.05 mm (produced by RoHS SGS (China), Brand name: LanDu). The slicing program module was used to regulate the Makerbot Replicator desktop 3D printer, which horizontally sliced the lattice structure into thin layers. The lattice structures were printed in a flat orientation, with each layer deposited in either a 0° or 90° direction, layer by layer from the bottom up. In other words, the printing direction is perpendicular to the compression direction. Printing parameters include feeding speed (3 mm/s), printing temperature (210oC), printing orientation, support building, and layer thickness. Quality was set to the default "Standard", and the layer height was set at 0.2 mm with an infill of 10%. Table 1 summarizes the typical properties of the PLA as provided by Makerbot.

Table 1 Typical PLA properties



Theoretical density ( )


Flexural strength ( )


Tensile strength, printed ( )


Compressive strength, printed ( )


2.3. Quasi-static crush Test and Energy Metrics

       Universal testing machine Instron model 3367 was used to conduct quasi-static crushing of the specimens. The test speed was set at 0.5 mm/min. The machine, specimen, and compression jigs are shown in Figure 4.

Figure 4 Photograph of compression machine, specimen, and jigs

Specific energy absorption (SEA) (in unit kJ/kg or J/g) and the dimensionless crush force efficiencies (CFE) are two metrics of particular interest in this study, as defined in Equations (1) and (2).

where EA is the total energy absorbed (i.e., the area under the curve of the force-displacement curve before the sign of densification, in unit N-m or J), Mm is the crushed mass, Fm is the mean crush load (i.e., EA divided by crush length in unit N) and Fmax is the maximum crush load throughout the loading history (also in unit N).

    A higher specific energy absorption means a greater amount of energy absorbed per unit of mass of the crushed lattice, which indicates a more efficient absorber. Crush force efficiency is an indicator of crushing steadiness. In fact, higher crush force efficiency means lower acceleration damages (Ma et al., 2019).

Results and Discussion

        The maximum crushing load can be acquired from the load-displacement curves in Fig 5. The curves were terminated either at the point of densification (i.e., sharp increase in load due to the compaction of crushed elements instead of structural resistance) or failure (i.e., a sudden drop in load due to structural breaking, usually visible and sometimes audible). It could be observed that SC lattice structures failed rather prematurely at small loads. HC and BCC lattice structures had lower peak loads, with HC demonstrating better energy absorption. PG80 outperformed the other three lattice structures by a wide margin in terms of the magnitude of the peak force and the stability of the post-yield behavior. The latter is favorable to energy absorption and was achieved by Sun et al. (2021) by using a hybrid lattice. The results for the samples were sufficiently consistent. 

Figure 5 Load-displacement curves of different lattice structures. Specimens are designated by lattice type (e.g., SC) followed by sample number in the legend

Table 2 Energy absorption of lattice specimens


Energy Absorption ( ),

Specific Energy Absorption ( ), k

Average , k