Sage Journals: Discover world-class research

Abstract

Cellular solids have superior energy absorption capabilities as compared to monolithic materials. Within this category of materials, lattice materials are of particular interest since their periodicity offers repeatable – and thus predictable – behavior. In combination with the advancements in additive manufacturing technologies, these lattice materials can be highly customized for a desired response. In this paper, the crashworthiness of unique multi-layer, multi-topology (MLMT) lattices is investigated. First, the nylon-carbon fiber composite material properties within a developed numerical model were tuned based on strut orientation. Then, the response of single-layer and three-layer cubic and octet lattices was investigated, where all lattices were designed with a relative density of 30%. Following the characterization of single-topology lattices, the response of MLMT lattices were investigated. Stress-strain, efficiency-strain, and multiple crashworthiness parameter data was collected for all lattices to facilitate in the comparison of those lattices. It was found that, experimentally, the unique MLMT lattices did not absorb more energy than their constituent layers combined, though modifications to the interface between layers could increase the energy absorption capability; the prediction of energy absorption of the MLMT lattices based on constituent layers was similar to actual numerical results. As all lattices were designed at the same relative density, the mass-specific energy absorption of the cubic-octet-cubic MLMT lattice (1.56 x10³ J/kg) outperforms the single-topology octet lattice by 19% to 36% (1.15–1.31 x10³ J/kg). While the octet-cubic-octet MLMT lattice (0.71 x10³ J/kg) is outperformed by the single-topology cubic lattices (1.69–3.76 x10³ J/kg), they see an increase of 59% to 77% in plateau stress (5.1–9.2 MPa) as compared to the MLMT lattice (2.1 MPa).

Graphical Abstract

Keywords

Energy absorption performance finite element analysis experimental techniques fused filament fabrication composite filament cellular materials

Introduction

The unique properties of natural cellular materials have inspired the research and development of similarly engineered solids for a variety of industries including biological and medical sciences, aviation and aerospace, and automotive and defense industries.^1–9 However, such materials are generally irregular and random in nature, making it difficult or impossible to obtain predictable, repeatable properties, a characteristic that can be quite important in advanced engineering applications.^10,11 As a solution, the regular, repetitive cells of lattice materials allow for reiterative and controllable mechanical, thermal and electrical properties.^10–12 This improvement, along with characteristics such as high specific strength and stiffness, and high energy absorption capabilities, means that periodic lattice materials are of increasing interest for a new generation of materials in numerous fields, including weight-critical applications in the aerospace, defense and automotive sectors.^13,14

The properties of lattice materials are controlled by the careful manipulation of a variety of parameters, including: the parent material from which they are fabricated (also, “bulk material”); the relative density; and the geometry – or topology – of the unit cell.¹⁴ However, due to the highly geometrically complex nature of these materials, traditional manufacturing methods are generally not capable of fabricating such material.^10,15 Additionally, the dimensions of the characteristics of these materials may be on the order of micro- or nano-meters.^16,17 The advent and then rapid advancement of alternative manufacturing techniques, specifically additive manufacturing (AM) technologies, has allowed for the investigation and use of such complex periodic cellular solids.^{1,3,11,18–20}

Analytical,^21–26 experimental,^26–30 and numerical^26,28,29,31 approaches are all methods of investigating cellular solids and, more specifically, lattice materials. And such investigations have been plentiful and widespread in the last few decades, especially after the publication of “Cellular Solids: Structure and Properties” by Gibson and Ashby,³² which collected and summarized much of the early work on cellular materials. Andrew et al.²⁷ varied impact energy, relative density (and plate thickness), cell orientation, and impact number during low-velocity experiments on elementary and hybrid polymeric plate-lattices (elementary cells included simple cubic (SC), body-centered cubic (BCC), and face-centered cubic (FCC), while hybrid lattices were combinations of those elementary cells). They found that the hybrid cells outperformed the elementary cells and also showed a direction-independent response; the SC-BCC-FCC hybrid had a higher specific energy absorption than a conventional aluminum lattice. Tancogne-Dejean et al.²⁹ looked at the static and dynamic response of octet lattices where the circular strut cross-section area was varied along the length of the strut. They found that the introduction of a slight taper in the struts of the octet lattice increased the macroscopic yield strength. In their following work,³³ strut tapering was investigated for BCC lattices both numerically and experimentally; the tapering of struts increased the specific mechanical properties, including Young’s modulus and energy absorption. Ozdemir et al.^30,31 experimentally and numerically investigated the quasi-static and dynamic response of multiple lattices, respectively. First,³⁰ the experiments were performed on three types of AM titanium alloy lattices – cubic, diamond, and re-entrant cube – finding that there was some rate-dependence for results. Then,³¹ using the experimental results as validation, they developed a numerical model using beam elements for the struts of the lattices (this time for diamond and re-entrant cube lattices). While the model assumed a perfect fabrication of the lattices (i.e. it did not account for any imperfections that may have been present in AM samples), they were still able to accurately predict experimental results with the numerical model. Here, they found that while a multi-layered re-entrant cube lattice showed some rate sensitivity, a single-layer re-entrant cube lattice did not (i.e., appeared rate-insensitive).

Literature concerning the use of lattice materials as core materials within sandwich and tube structures is also underway.^34–37 Zhang et al.³⁴ manufactured three versions of a sandwich panel: one with only polyurethane foam; one with a pyramidal lattice; and a hybrid, combination of the polyurethane foam and pyramidal lattice. They found that the hybrid core sandwich panel had a greater load-carrying capacity in relation to the other two sandwich panels. Yet, they also found that in low-velocity impact tests, the hybrid samples did not show any significant increase in impact resistance. Mines et al.³⁵ performed drop-weight testing on sandwich panels with titanium and stainless-steel BCC lattice cores. They saw that the panels with the stainless-steel lattice core were of better quality and less sensitive to the build parameters during manufacturing, as compared to the titanium alloy cores. However, the stainless-steel panels had lower specific strength. In addition, the titanium alloy samples were said to be able to compete with current aluminum honeycomb used in aerospace sandwich panels. Li et al.³⁶ presented three analyses methods for a sandwich panel with a core made of AM aluminum alloy BCC-Z lattice: theoretically, numerically employing finite element, and experimentally. They found good correlation between results from all three approaches. They also concluded that the number of layers within the core had a significant effect on the mechanical properties of the panel; the crushing strength decreased with an increase in number of layers. Hou et al.³⁷ considered the 3D printed polyamide-carbon fiber lattice core of an aluminum tube, testing four different lattice topologies separately and finding the Kagome achieves the highest energy absorption. They then optimized the design of the Kagome and tube to increase the specific energy absorption by 16%, decreasing the mass by 17%.

Yet, to the best of the authors’ knowledge, the investigation of multi-layer, multi-topology (MLMT) lattice structures – in the form of layers of differing topologies – is practically non-existent, lending to the novelty of this work, which compares single- and multi-layer cube and octet lattice material results with the performance of MLMT lattices, all designed at a relative density of 30%. Both numerical and experimental analyses are performed to characterize a variety of crashworthiness parameters for those lattices, where the material model within the developed numerical model was tuned based on strut orientation.

This paper is organized into five main sections following this introduction. The first section following this introduction describes the numerical model set up, including the material model utilized, as well as the experimental testing set up. The second section outlines the crashworthiness parameters calculated for data analysis and comparison while the third section presents and discusses single-layer and multi-layer lattice experimental and numerical results, where all lattices were designed with a relative density of 30%. A conclusion and references are the final sections.

Numerical model and experimental testing set up

Lattice geometry and design

The numerical study consisted of making models from two topologies – cube and octet – at a relative density of 30%; the relative density was kept constant throughout this work. This relative density value was selected following testing of the production capability of the Onyx One 3D printer used for sample manufacturing. For angled struts at relative densities less than 30%, it was observed that the surface quality of the struts significantly deteriorated and that there was residual material in areas outside of the design space. Such a comparison of print quality is shown in Figure 1.

Figure 1.

Visual comparison of the print quality of three-unit cells at 20%, 25%, and 30% relative density, used to determine the production capability of the 3D printer utilized for experimental samples.

With a constant original unit cell height of 10 mm, the design radii for these topologies was 2.05 mm and 0.87 mm, respectively. Models consisted of either one or three layers in the impact direction; a three-unit cell width in the other two orthogonal directions was kept constant for each layer. The visual representation of the single- and multi-layer, single-topology lattice numerical model configurations is provided in Figure 2.

Figure 2.

Finite element model for octet single-layer lattice (a, orange) and multi-layer lattice (b, orange) to be compressed between stationary plate (gray) and moving impactor (green). Boundary conditions are applied to the lattice and an initial velocity is applied to the green impactor in the negative y-direction (downwards). The gray plate has boundary conditions applied such that no movement is permitted.

Finite element model

Altair’s HyperMesh (v2020) was used to develop the finite element model for the explicit finite element solver Radioss (v2020). All models were developed with a flat, stationary bottom plate (“plate”) and a flat, moving top plate (“impactor”), as illustrated in Figure 2. Both the impactor and the plate were modeled as rigid bodies, and have identical dimensions of 35 mm × 35 mm, with a thickness of 1 mm. However, while the impactor is assigned a constant speed in the downward y-direction (see Figure 2), the bottom plate is stationary and boundary conditions prevented any translational or rotational movement. Consequently, the lattice was compressed between the two rigid plates during the simulation.

The lattices in all models were defined by solid tetrahedron elements with a tabulated plastic material law, where numerical values were determined by material testing, as detailed in the section Lattice parent material model. Nodal boundary conditions were applied to the lattices to represent the same restrictions experienced by printed lattice samples in uniaxial compression experiments. There were two sets of nodes – top surface and bottom surface – that had boundary conditions applied. The degrees of freedom (DOFs) are specified for those node sets as follows, where translational restrictions (T_a) or rotational restrictions (ω_a) to the DOF are given as “1’s” (i.e. they are fixed) and free translational or rotational DOFs are given as “0’s”. For the top nodes of the lattice unit cell: $[\begin{array}{l} \begin{array}{l} T_{x} & T_{y} & T_{z} \end{array} & \begin{array}{l} ω_{x} & ω_{y} & ω_{z} \end{array} \end{array}] = [\begin{array}{l} \begin{array}{l} 1 & 0 & 1 \end{array} & \begin{array}{l} 1 & 1 & 1 \end{array} \end{array}]$ where the subscripts represent the axis for the translational or rotational motions. As such, the top nodes of the lattices were only permitted translational motion along the y-axis. For the bottom nodes: $[\begin{array}{l} \begin{array}{l} T_{x} & T_{y} & T_{z} \end{array} & \begin{array}{l} ω_{x} & ω_{y} & ω_{z} \end{array} \end{array}] = [\begin{array}{l} \begin{array}{l} 1 & 1 & 1 \end{array} & \begin{array}{l} 1 & 1 & 1 \end{array} \end{array}]$ meaning that they were not permitted to translate or rotate about any axis. During experimental testing no restrictions were applied to the sides of the lattice specimens; the numerical model also did not apply any translational or rotational restrictions to the sides of the lattices.

The contact between impactor-lattice and plate-lattice was each described by a solid contact interface between the master surface (in this case, impactor or plate) and slave nodes (that is, the lattice). For the self-contact of the lattice during compression, a single-surface interface was used.

Lattice parent material model

In previous work,³⁸ the lattice parent material was uniform regardless of strut orientation and was based on the tensile testing results of a nylon-based composite carbon fiber filament Onyx™ (hereafter referred to as simply Onyx) from Markforged. While the base parent material is the same for this work (i.e., Onyx), based on the large percent errors between experiments and the numerical predictions, the material model was further refined to obtain one which more accurately represented experiments. Since actual mechanical properties and performance of 3D printed material can vary based on printing parameters and is generally anisotropic (and therefore sensitive to print orientation),^39–43 the data from a simple characterization of the Onyx material was used to obtain a starting point for estimating lattice material properties and was then tuned to better compare to the known experimental results. Tensile samples were fabricated per the specifications of ISO 527-2,⁴⁴ illustrated in Figure 3, on an Onyx One 3D printer (also from Markforged), which uses a Fused Filament Fabrication (FFF) technique to manufacture parts. All samples were printed with a layer thickness of 0.1 mm at 100% infill and at a speed of 20 mm/sec. The nozzle temperature was set to 275°C.

Figure 3.

(a) ISO 527-2 Type B standard tensile test specimen dimensions in [mm]. (b) sample specimen printed on an Onyx One with Onyx filament (nylon-base with carbon fiber whiskers).

The specimens were tensile tested at a rate of 1 mm/min on an MTS machine as in Figure 4 until failure and tests were repeated three times to ensure the accuracy of results. The load-displacement data was collected directly from the MTS machine, where an extensometer was used to obtain the strain data. As mentioned, due to the nature of the additive manufacturing technique, struts with different orientations with respect to the print direction (e.g., the vertical struts of the cube topology as compared to the diagonal struts of the octet topology) would have different mechanical properties. Consequently, tuning of the material model included accounting for these differences; struts belonging to the cubic topology were defined with different parameters as compared to those struts of the octet topology. General mechanical properties of the Onyx material are summarized in Table 1.

Figure 4.

MTS machine for bulk material and lattice testing.

Table 1.

Mechanical properties of Onyx nylon-carbon fiber filament.

Property	Value
Young’s modulus, E	1200–1400 MPa
Yield strength $σ_{y}$	8.5–60 MPa
Poisson’s ratio $ν$	0.4
Density $ρ_{0}$	1200 kg/m³

Experimental testing set up

The experimental quasi-static compression testing of the lattices was performed on an 810 MTS machine with a maximum capacity of 25 kN, the same as used for the bulk material testing, shown in Figure 4. Since the lattice samples were not conducive to the direction collection of strain data by extensometer, the force-displacement data was collected directly from the measurements recorded by the MTS machine. Sample photos of single-layer octet and cubic Onyx lattices are provided in Figure 5. These samples were tested at the quasi-static compression strain rate of 0.001/s (0.01 mm/s). The lattice sample dimensions, including relative density, were the same as in the numerical model. For clarity, parameters associated with the experiments (including manufacturing parameters) have been summarized in Table 2.

Figure 5.

3x3 single-layer sample of (a) octet and (b) cubic lattices printed with Onyx nylon-carbon fiber filament.

Table 2.

Experimental design parameters for tensile test specimens and lattice samples.

Property	Value
Lattice height	10 mm
Lattice relative density	30%
Layer thickness	0.1 mm
Infill	100%
Print speed	20 mm/sec
Nozzle temperature	275°C
Tensile test rate, tensile test specimens	1 mm/min
Compressive test rate, lattice samples	0.001/sec (0.01 mm/sec for single-layer, 0.03 mm/sec for 3-layer)

For multi-layer lattice clusters, to keep the strain rate the same as those single-layer specimens, the quasi-static test speed was set to 0.03 mm/s. Photos of multi-layer samples are shown in Figure 6 for single-topology lattices and Figure 7 for the MLMT lattices.

Figure 6.

3 × 3 × 3 multi-layer cluster of (a) octet and (b) cubic lattices printed with Onyx nylon-carbon fiber filament.

Figure 7.

(a) 3 × 3 × 3 sample of an octet-cube-octet MLMT lattice printed with Onyx filament. (b) 3 × 3 × 3 sample of a cube-octet-cube MLMT lattice printed with Onyx filament.

Crashworthiness parameters for data analysis

Data collected from the numerical and experimental analyses included the following crashworthiness parameters, of which their calculation allows for the quantification of the performance of lattice materials, in addition to stress-strain and efficiency-strain data over the course of the compression event.

Energy absorption efficiency

Also, “efficiency” or $η$ is calculated from the stress-strain ( $σ$ - $ε$ ) curve as: $η (ε) = \frac{1}{σ (ε)} \int_{0}^{ε} σ (ε) d ε$ (1)where the stress is obtained from the overall compressive force divided by the surface area of the upper surface of the lattice unit cell envelope and the strain is obtained from the displacement of the uppermost surface of the lattice divided by the original lattice unit cell height, a method utilized in other literature.^38,45,46

Densification strain

Per the energy absorption efficiency method, the densification strain, $ε_{D}$ , is: ${\frac{d η (ε)}{d ε} |}_{ε = ε_{D}} = 0$ (2)which is the strain at the maximum efficiency point.^45,47,48

Plateau stress

The plateau stress, $σ_{p l}$ , along with densification strain, are considered to be the most important values with regards to the energy absorption of materials.⁴⁷ This parameter is calculated as:⁴⁵ $σ_{p l} = \frac{\int_{0}^{ε_{D}} σ (ε) d ε}{ε_{D}}$ (3)

Energy absorption

Energy absorption, EA or IE (internal energy), is calculated as: $E A = V \int_{0}^{ε_{D}} σ (ε) d ε$ (4)

It should be noted that while equation (4) utilizes the densification strain as the final integration point, the selected strain value within this integral does vary across literature.^{29,45,49–51}

Specific energy absorption

Specific Energy Absorption (SEA) can be calculated either per unit volume – ${S E A}_{V}$ – or per unit mass – ${S E A}_{m}$ . Equations for both of these SEAs are provided as follows:^45,51,52 ${S E A}_{V} = \frac{E A}{V} = \int_{0}^{ε_{D}} σ (ε) d ε$ (5) ${S E A}_{m} = \frac{E A}{m} = \frac{\int_{0}^{ε_{D}} σ (ε) d ε}{\bar{ρ} ρ_{0}}$ (6)where $V$ is the volume of the lattice structure and $m$ is the mass of the lattice structure. It should be noted that these values are also calculated up to the densification strain, as with EA.

Lattice cluster results and discussion

Single-layer lattice clusters

Experimental and numerical model stress-strain and efficiency-strain results are presented in Figure 8 for the single-layer cubic and octet truss lattices, while Figures 9 and 10 present, respectively, images from the compression event, from both experiments and the numerical simulation animation. Table 3 and Figure 18 (at the end of the section “Multi-layer, multi-topology lattice clusters”) summarize crashworthiness parameters calculated from experimental and numerical simulation data for all lattices.

Figure 8.

Stress versus strain and efficiency versus strain curves for experiments and numerical model for (left) cubic lattice and (right) octet lattice printed in Onyx. See Figures 9 and 10, respectively, for photos relating to letter labels.

Figure 9.

Progressive compression of experimental sample and numerical model of single-layer cube lattice printed with Onyx filament. Color contour for numerical model is of plastic strain, units of [mm/mm].

Figure 10.

Progressive compression of experimental sample and numerical model of single-layer octet lattice printed with Onyx filament. Color contour for numerical model is of plastic strain, units of [mm/mm].

Table 3.

Summary of crashworthiness parameters for all lattices investigated.

Size	Topology^a	Source^a	Max. Effb	Dens. Strain^b (mm/mm)	EAb (J)	${S E A}_{V}$ b [x10⁶ J/m³]	${S E A}_{m}$ b [x10³ J/kg]	Plat. Stress^b (MPa)
3 × 3 × 1	C	E	0.38	0.49	12.2	4.51	3.76	9.2
	C	N	0.40	0.40	9.5	3.54	2.95	8.8
	O	E	0.39	0.45	3.8	1.40	1.15	3.1
	O	N	0.46	0.51	5.6	2.07	1.72	4.0
3 × 3 × 3	C	E	0.77	0.39	16.5	2.03	1.69	5.1
	C	N	0.41	0.39	19.8	2.45	2.04	6.2
	O	E	0.38	0.51	12.7	1.57	1.31	3.1
	O	N	0.41	0.52	15.2	1.88	1.57	3.6
3 × 3 × 3 MLMT	O-C-O	E	0.28	0.40	6.9	0.85	0.71	2.1
	O-C-O	N	0.34	0.55	21.7	2.68	2.23	4.9
	C-O-C	E	0.77	0.48	15.1	1.87	1.56	3.9
	C-O-C	N	0.38	0.42	17.3	2.14	1.78	5.0

^aTopology: C = Cube, O = Octet. Source: E = Experiment, N = Numerical Model.

^bOnly average values are summarized in this table.

In Figure 8 (left) for the cubic lattice, the numerical model showed good correlation with the experiments for most of the compression event, through both the elastic region (up to a strain of about 0.05 mm/mm) and into the plateau region until a strain of approximately 0.45 mm/mm. The efficiency of the numerical model also shows good correlation with the experiments, though it reaches the maximum sooner (strain of 0.40 mm/mm vs 0.49 mm/mm) and at a slightly higher value (0.40 vs 0.38) than shown in experiments.

For the octet topology single-layer lattice (Figure 8 (right)), there is also a good correlation between experimental and numerical results, though the plateau region predicted by the numerical simulation is not as flat and has a higher peak; the plateau stress from experiments is 3.1 MPa versus 4.0 MPa per the numerical data. However, the differences are small and the general form of the stress-strain results from the numerical model match quite closely with experiments: first, a curved elastic-like region, where the increase in stress is mostly non-linear with increase in strain; then, a brief plateau region; and, finally, a slight dip in stress before a sharp increase in stress at the densification point. The efficiency-strain experimental results for the octet topology are also well predicted by the numerical model (18% and 14% difference for maximum efficiency and densification strain, respectively).

In observing snapshots from each of the compression events, the same general deformation mechanisms are seen for the experiments and numerical model. In Figure 9, for the cubic topology, the vertical struts of the outer unit cells bend and bow outwards, withstanding compressive loads; the deformation behavior is bending-dominated. In Figure 10, for the octet topology, the struts stretch and the lattice squishes outwards in the same manner whether observed by experiments or seen in the numerical model animation; its deformation behavior is stretching-dominated, with the struts carrying mostly tensile loads.

In comparing the single-layer lattice results from both topologies, the anticipated difference in deformation behavior – bending for cube, stretching for octet – is clearly depicted in the images of Figures 9 and 10. Additionally, the stress carried by the cubic lattice is larger than that of the octet lattice, which can be understood as a consequence of the direct alignment of the vertical struts of the cubic topology with the load direction and that the struts of the cubic topology are over two times larger in radius than the struts of the octet topology, which has only angled struts with respect to the compressive load direction. As a consequence of the higher stresses, the cubic lattice also absorbed more energy than the octet lattice. However, the maximum efficiencies of these lattices are quite similar, at 0.38 and 0.39 for the cube and octet, respectively (experimentally).

Based on qualitative and quantitative data collected from the experiments and numerical simulations, the numerical model well predicts the reality of experiments for these single-layer lattices; the material model tuning successfully accounts for variations in strut material properties based on orientation.

Multi-layer lattice clusters

Crashworthiness parameter results for the multi-layer specimens are summarized in Table 3 and Figure 18 (at the end of the section “Multi-layer, multi-topology lattice clusters”), while experimental and numerical model stress-strain and efficiency-strain results are depicted in Figure 11. Figures 12 and 13 present snapshots of the compression event for the cubic and octet multi-layer samples, respectively.

Figure 11.

Stress versus strain and efficiency versus strain curves for experiments and numerical model for (left) cubic lattice and (right) octet multi-layer lattices printed with Onyx filament. See Figures 12 and 13, respectively, for photos relating to letter labels.

Figure 12.

Progressive compression of experimental sample and numerical model of multi-layer cubic lattice printed with Onyx filament. Color contour is of plastic strain, units of [mm/mm].

Figure 13.

Progressive compression of numerical model of multi-layer octet lattice printed with Onyx filament. Color contour is of plastic strain, units of [mm/mm].

Looking first at the cubic topology results (Figure 11 (left)), the initial responses of experiments and the numerical model are very similar. After a strain of approximately 0.1 mm/mm, the experiments and numerical model begin to diverge, though the results of Experiment #1 and the numerical model are notably similar; the numerical model and Experiment #1 stress-strain curves both decrease after a strain of about 0.1 mm/mm, before a brief plateau region and a sharp increase in stress at densification. The numerical model slightly overpredicts the stress carried by the lattice (6.2 MPa vs 5.1 MPa), though the experimental and numerical simulation deformation photos presented in Figure 12 do show good similarity. Beginning with Figure 12(a) and (a), each layer of the experimental sample deformed in the same manner, with outward bending of the vertical struts, while the numerical model showed only some bending of individual vertical struts. With further deformation, both the experimental sample and numerical model showed a local layer-by-layer collapse phenomenon, with the vertical struts of the upper layer buckling first. By Figure 12(c) and (c), the bottom layer had collapsed and the middle layer of the cluster has begun to deform further.

For the octet multi-layer lattice (Figure 11 (right)), experimental-numerical differences were generally smaller than for the 3-layer cubic lattice and more in-line with the observations of the single-layer octet lattice. While the stress carried by the octet lattice in the numerical model at a given strain was slightly larger than in experiments, the overall shape of the stress-strain curves were very similar: a gradual, non-linear increase in stress with increase in strain at the beginning; the appearance of a plateau region, though with some minimal variations in stress; and finally a sharp increase in stress at the densification strain, which was well predicted by the numerical model, with only a 2% difference (and only a 9% difference in maximum efficiency). Images of the compression event for an experiment and the numerical simulation are compared and contrasted in Figure 13. The numerical simulation snapshots shows an acceptable correlation to the photos of the progressive deformation of the experimental sample; with progressive compression, the sample first squishes, with the struts under tensile load as expected for the stretching-dominated topology, and the sample width grows larger. Nearing densification, the material has been neatly compacted with few strut failures.

Multi-layer, multi-topology lattice clusters

Stress-strain and efficiency-strain results are provided in Figure 14 for the MLMT lattices and snapshots from the compression event are provided in Figure 15 for the octet-cube-octet (O-C-O) lattice and Figure 16 for the cube-octet-cube (C-O-C) lattice. Table 3 and Figure 18 (at the end of this section) provide the crashworthiness parameters for these lattices for both experimental and numerical approaches.

Figure 14.

Stress versus strain and efficiency versus strain curves for experiments and numerical model for MLMT: octet-cube-octet (left) and cube-octet-cube (right) printed with Onyx filament. Refer to Figures 15 and 16, respectively, for photos relating to letter labels.

Figure 15.

Progressive compression of experimental sample and numerical model of octet-cube-octet MLMT lattice printed with Onyx filament. Color contour is of plastic strain, units of [mm/mm].

Figure 16.

Progressive compression of experimental sample and numerical model of cube-octet-cube MLMT lattice printed with Onyx filament. Color contour is of plastic strain, units of [mm/mm].

For the O-C-O lattice (Figure 14 (left)), the numerical model generally overpredicts the stress carried by the lattice, while the efficiency-strain results are much closer to experiments. However, this numerical model does not predict the overall trend of the experimental stress-strain curves well; while the numerical model shows no obvious plateau region and has numerous peaks and valleys as the overall trend is an increase in stress, the experimental model has a distinguishable, smooth plateau region. Yet, the compression behavior observed from experiments and in the animation of the numerical model (Figure 15) show better correlation. In both experiments and the numerical simulation, the octet layers deform first – almost completely – before the cubic layer deforms in any significant manner. The octet and cubic layers, on their own, show similar deformation behavior as the single-layer lattices discussed earlier. Additionally, both the numerical model and experiments have points of high stress where the octet layers connect with the cubic layer. As is visible in the experimental compression images of Figure 15, the octet struts connected to the cubic layer disconnected and broke free from their original connection points, while those same struts in the numerical model are shown to carry much more load than other struts within the lattice (particularly visible in Figure 15(a) through (c)).

For the C-O-C lattice (Figure 14 (right)), the numerical model overpredicts the stress carried by the lattice, though there is a good prediction of results prior to a strain of approximately 0.1 mm/mm and the general peak-valley trends are similar (for both the stress-strain and efficiency-strain curves, particularly prior to a strain of 0.3 mm/mm). For example, both experiments and the numerical simulation show a local stress peak at a strain of approximately 0.25 mm/mm and a local valley around a strain of 0.4 mm/mm (though experiments briefly level-out around this strain point whereas the numerical model does not). Regardless of experiments or numerical simulations, the C-O-C experimental stress-strain curves don’t show an obvious plateau region, with variations in stress as strain increases. In observing the deformation behavior of the lattices from experiments and the numerical model (Figure 16), there is a good correlation between the two approaches, even with a global buckling phenomenon around point “C” and “c” in Figure 16. As in the O-C-O lattice, the octet layer deforms first, before the cubic layer shows any significant deformation.

For both MLMT lattices the contribution of each layer – octet or cubic – to the overall compressive strain was determined from the numerical model by measuring the distance between the top and bottom of each layer throughout compression. Results are illustrated in Figure 17, with letter labels referring back to snapshots from the animation of the numerical simulation in Figures 15 and 16. The data in Figure 17 validates the observations of the snapshots; the octet layers compress much more quickly than the cubic layers. From single-layer and three-layer investigations, the densification strain (from numerical models) is from 0.39 to 0.40 mm/mm for the cubic topology and 0.51 to 0.52 mm/mm for the octet topology. With this knowledge, it’s seen that the cubic layer(s) don’t deform until the octet layer(s) have at least reached their densification point; the cubic layers begin to deform at an approximate overall lattice strain of 0.2 mm/mm for the C-O-C lattice (octet layer at 40% original height) and 0.5 mm/mm for the O-C-O lattice (octet layers at <40% original height).

Figure 17.

Layer height compression versus overall lattice strain for O-C-O MLMT lattice (black) and C-O-C lattice (gray). Octet layers shown with dashed lines, cube layers shown with solid lines. Data is from numerical models. Letter labels correspond to numerical model images in Figure 15 for the O-C-O lattice and Figure 16 for the C-O-C lattice. Note that for clarity the letter labels are only pointing at one of the three curves associated with the respective lattice.

Figure 18.

Energy absorption and specific energy absorptions (per by mass and by volume) from experiments (black) and numerical studies (gray) for cubic (C) and octet (O) single-layer and multi-layer samples.

In comparing three-layer, single- and multi-topology lattice results, it is immediately noted that both the experiment and numerical model results suggest that MLMT lattices printed from Onyx do not completely outperform single-topology three-layer lattices of the same relative density. Experimentally, the cubic and octet three-layer lattices absorb 16.5 J and 12.7 J, respectively. By switching the middle layer to an octet or cubic topology, the energy absorptions become 15.1 J (C-O-C) and 6.9 J (O-C-O) – only one of these MLMT lattices outperforms the octet lattice and neither absorb more energy than the cubic lattice. While it is possible to modify the maximum efficiency and densification strain slightly by using multi-topology lattices, the loss in energy absorption capacity up to densification strain by switching from the cubic multi-layer lattice would not be beneficial for energy absorption applications. Table 4 shows energy absorption approximations for the MLMT lattices (O-C-O and C-O-C) using single-topology lattice results and three-layer lattice averages. Interestingly, using the experimental single- and three-layer cubic and octet results to predict the experimental MLMT lattice performance shows an overprediction of energy absorption capability. As with the previously noted differences between experimental and numerical simulation results for the MLMT lattices, this discrepancy appears to be due to the print quality and the interface of dissimilar layers, which is assumed to be “ideal” within the numerical model while the samples for experiments see reduced strut print quality in this area since portions of the bottom struts of the cubic layer go unsupported by the octet layer below it and vice versa. Indeed, imperfections between layers for the MLMT lattices can be seen Figure 7, where there is some filament stringing.

Table 4.

Estimates for MLMT energy absorption based on single-layer and three-layer cubic and octet lattices.

Size	Top^a	Actual results		Single-layer Avg		MLMT Calculations^b
		Actual results		Single-layer Avg		O-C-O^a		C-O-C^a
		E^a	N ^a	E	N	E	N	E	N
3 × 3 × 1	C	12.2	9.5	12.2	9.5	19.7	17.1	28.1	22.8
3 × 3 × 1	O	3.8	5.6	3.8	3.8
3 × 3 × 3	C	16.5	19.8	5.5	6.6	14.0	16.8	15.2	18.3
3 × 3 × 3	O	12.7	15.2	4.2	5.1
3 × 3 × 3 MLMT^c	-	-	-	-	-	6.9	21.7	15.1	17.3

^aTop. = Topology, C = Cube, O = Octet, E = Experiment, N = Numerical Model.

^bEstimates are provided based on the results from the single-layer and three-layer results.

^cActual results from experiments/numerical model as indicated.

Note: All values provided have energy units of [J].

Conclusion

This research examines the crashworthiness of cubic and octet lattices and unique multi-layer, multi-topology (MLMT) lattices, designed as a combination of cubic and octet lattice layers. The lattices were designed and manufactured with a relative density of 30% from a nylon-carbon fiber composite material (Onyx). Initially, the quasi-static mechanical properties of this material were characterized using tensile test specimens of different orientations. The material results were used to develop a tuned numerical model, with properties dependent on strut orientation. Then, the compressive response of cubic and octet single-layer and three-layer lattices was studied. Additionally, the response of the MLMT lattices was investigated and comparisons based on stress-strain, efficiency-strain, and other crashworthiness parameters were performed for each lattice.

Some key conclusions from this work include:

• As observed in experiments and the numerical simulations, a bending-dominated behavior was noted for the cubic lattices and a stretching-dominated behavior was seen for the octet lattices. In MLMT lattices, the dominant behavior was layer-specific.

• The three-layer cubic lattices generally had smaller densification strains (0.39 mm/mm) than octet lattices (0.51–0.52 mm/mm). However, the cubic lattices had higher plateau stresses, by 30% to 64%, and, consequently, higher energy absorptions. By mass, the specific energy absorption increase is between 7% and 36% for the cubic lattices (1.69–2.04 x10³ J/kg) as compared to the octet lattices (1.31–1.57 x10³ J/kg).

• The cubic-octet-cubic MLMT lattice absorbed 1.56 x10³ J/kg, a 19% to 36% increase as compared to the octet-only lattices (1.15–1.31 x10³ J/kg). While the octet-cubic-octet (O-C-O) MLMT lattice has the lowest absorption at 0.71 x10³ J/kg and the cubic-only lattices have the highest (1.69–3.76 x10³ J/kg), the plateau stress of the cubic-only lattices is 59% to 77% greater than the O-C-O MLMT lattice.

Footnotes

Acknowledgments

The authors would like to thank the financial support from BOMBARDIER INC. Montreal,in collaboration with MITACS Canada,grant number IT29280.

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research,authorship,and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research,authorship,and/or publication of this article: This work was supported by BOMBARDIER INC. Montreal,in collaboration with MITACS Canada,grant number IT29280.

ORCID iDs

Autumn R. Bernard

Muhammet Muaz Yalcin

Mostafa S.A. El Sayed

References

Banhart

. Manufacture, characterisation and application of cellular metals and metal foams. Prog Mater Sci 2001; 46: 559–632.

Ashby

Medalist

RFM

. The mechanical properties of cellular solids. Metall Trans A 1983; 14: 1755–1769.

Schaedler

Carter

. Architected cellular materials. Annu Rev Mater Res 2016; 46: 187–210.

Bari

Bollenbach

. Spiderweb cellular structures manufactured via additive layer manufacturing for aerospace application. J Compos Sci 2022; 6: 133.

Najmon

Dehart

Wood

, et al. Cellular helmet liner design through bio-inspired structures and topology optimization of compliant mechanism lattices. SAE Int J Transp Saf 2018; 6: 217–235.

Fuganti

Lorenzi

Grønsund

, et al. Aluminum foam for automotive applications. Adv Eng Mater 2000; 2: 200–204.

Murr

Gaytan

Medina

, et al. Next-generation biomedical implants using additive manufacturing of complex, cellular and functional mesh arrays. Philos Trans A Math Phys Eng Sci 2010; 368: 1999–2032.

Borsellino

Bella

. Paper-reinforced biomimetic cellular structures for automotive applications. Mater Des 2009; 30: 4054–4059.

Grunenfelder

Suksangpanya

Salinas

, et al. Bio-inspired impact-resistant composites. Acta Biomater 2014; 10: 3997–4008.

10.

du Plessis

Razavi

Benedetti

, et al. Properties and applications of additively manufactured metallic cellular materials: a review. Prog Mater Sci 2022; 125: 100918.

11.

Somera

Poncelet

Auffray

, et al. Quasi-periodic lattices: pattern matters too. Scr Mater 2022; 209: 114378.

12.

Ngo

Kashani

Imbalzano

, et al. Additive manufacturing (3D printing): a review of materials, methods, applications and challenges. Compos B Eng 2018; 143: 172–196.

13.

Wadley

HNG

. Cellular metals manufacturing. Adv Eng Mater 2002; 4: 726–733.

14.

Ashby

. The properties of foams and lattices. Philos Trans A Math Phys Eng Sci 2006; 364: 15–30.

15.

Benedetti

du Plessis

Ritchie

, et al. Architected cellular materials: a review on their mechanical properties towards fatigue-tolerant design and fabrication. Mater Sci Eng R Rep 2021; 144: 100606.

16.

Mieszala

Hasegawa

Guillonneau

, et al. Micromechanics of amorphous metal/polymer hybrid structures with 3D cellular architectures: size effects, buckling behavior, and energy absorption capability. Small 2017; 13: 1602514.

17.

Rashed

Ashraf

Mines

RAW

, et al. Metallic microlattice materials: a current state of the art on manufacturing, mechanical properties and applications. Mater Des 2016; 95: 518–533.

18.

Thompson

Moroni

Vaneker

, et al. Design for additive manufacturing: trends, opportunities, considerations, and constraints. CIRP Annals 2016; 65: 737–760.

19.

Zhang

Liu

, et al. Lattice structures of Cu-Cr-Zr copper alloy by selective laser melting: microstructures, mechanical properties and energy absorption. Mater Des 2020; 187: 108406.

20.

Nagesha

Dhinakaran

Varsha Shree

, et al. Review on characterization and impacts of the lattice structure in additive manufacturing. Mater Today: Proc 2020: 916–919.

21.

Yang

Shan

Zhao

, et al. Multiple strut-deformation patterns based analytical elastic modulus of sandwich BCC lattices. Mater Des 2019; 181: 107916.

22.

Ptochos

Labeas

. Elastic modulus and Poisson’s ratio determination of micro-lattice cellular structures by analytical, numerical and homogenisation methods. Jnl of Sandwich Structures Materials 2012; 14: 597–626.

23.

Hedayati

Sadighi

Mohammadi-Aghdam

, et al. Analytical relationships for the mechanical properties of additively manufactured porous biomaterials based on octahedral unit cells. Appl Math Model 2017; 46: 408–422.

24.

Mahbod

Asgari

. Elastic and plastic characterization of a new developed additively manufactured functionally graded porous lattice structure: analytical and numerical models. Int J Mech Sci 2019; 155: 248–266.

25.

Zadpoor

Hedayati

. Analytical relationships for prediction of the mechanical properties of additively manufactured porous biomaterials. J Biomed Mater Res 2016; 104: 3164–3174.

26.

Tancogne-Dejean

Mohr

. Elastically-isotropic truss lattice materials of reduced plastic anisotropy. Int J Solids Struct 2018; 138: 24–39.

27.

Andrew

Schneider

Ubaid

, et al. Energy absorption characteristics of additively manufactured plate-lattices under low- velocity impact loading. Int J Impact Eng 2021; 149: 103768.

28.

Park

K-M

Min

K-S

Roh

Y-S

. Design optimization of lattice structures under compression: study of Unit cell types and cell Arrangements. Materials 2021; 15: 97.

29.

Tancogne-Dejean

Spierings

Mohr

. Additively-manufactured metallic micro-lattice materials for high specific energy absorption under static and dynamic loading. Acta Mater 2016; 116: 14–28.

30.

Ozdemir

Hernandez-Nava

Tyas

, et al. Energy absorption in lattice structures in dynamics: experiments. Int J Impact Eng 2016; 89: 49–61.

31.

Ozdemir

Tyas

Goodall

, et al. Energy absorption in lattice structures in dynamics: nonlinear FE simulations. Int J Impact Eng 2017; 102: 1–15.

32.

Gibson

Ashby

. Cellular solids: structure & properties. 1st ed. Oxford: Pergamon Press, 1988.

33.

Tancogne-Dejean

Mohr

. Stiffness and specific energy absorption of additively-manufactured metallic BCC metamaterials composed of tapered beams. Int J Mech Sci 2018; 141: 101–116.

34.

Zhang

Wang

, et al. Energy absorption and low velocity impact response of polyurethane foam filled pyramidal lattice core sandwich panels. Compos Struct 2014; 108: 304–310.

35.

Mines

RAW

Tsopanos

Shen

, et al. Drop weight impact behaviour of sandwich panels with metallic micro lattice cores. Int J Impact Eng 2013; 60: 120–132.

36.

Lei

Liu

, et al. Crushing behavior of multi-layer metal lattice panel fabricated by selective laser melting. Int J Mech Sci 2018; 145: 389–399.

37.

Hou

Yang

, et al. Crashworthiness optimization of crash box with 3D-printed lattice structures. Int J Mech Sci 2023; 247: 108198.

38.

Bernard

Yalcin

ElSayed

. Development of numerical model for the crashworthiness of additively manufactured sandwich lattices. AIAA SCITECH 2023 Forum. DOI: 10.2514/6.2023-2200.

39.

Wauthle

Vrancken

Beynaerts

, et al. Effects of build orientation and heat treatment on the microstructure and mechanical properties of selective laser melted Ti6Al4V lattice structures. Addit Manuf 2015; 5: 77–84.

40.

Dong

Liu

, et al. Orientation dependency for microstructure, geometric accuracy and mechanical properties of selective laser melting AlSi10Mg lattices. J Alloys Compd 2019; 791: 490–500.

41.

Delroisse

Jacques

Maire

, et al. Effect of strut orientation on the microstructure heterogeneities in AlSi10Mg lattices processed by selective laser melting. Scr Mater 2017; 141: 32–35.

42.

Obadimu

Kourousis

. Compressive behaviour of additively manufactured lattice structures: a review. Aerospace 2021; 8: 207.

43.

Gautam

Idapalapati

Feih

. Printing and characterisation of Kagome lattice structures by fused deposition modelling. Materials and Design. 2018; 137: 266–275. doi:10.1016/j.matdes.2017.10.022.

44.

ISO 527-2:2012. Plastics — Determination of Tensile properties — Part 2: test conditions for moulding and extrusion plastics.

45.

Yang

. Advanced lattice material with high energy absorption based on topology optimisation. Mech Mater 2020; 148: 103536.

46.

Bernard

Elsayed

MSA

. Impact resistance and specific energy absorption efficiency limits of periodic cellular solids. AIAA SCITECH 2022 Forum. DOI: 10.2514/6.2022-1093.

47.

Chen

Wang

Zhou

, et al. Novel negative poisson’s ratio lattice structures with enhanced stiffness and energy absorption capacity. Materials 2018; 11: 1095.

48.

Magkiriadis

Harrigan

. Compressive strain at the onset of densification of cellular solids. J Cell Plast 2006; 42: 371–392.

49.

Mueller

Matlack

Shea

, et al. Energy absorption properties of periodic and Stochastic 3D lattice materials. Adv Theory Simul 2019; 2: 1900081.

50.

Nasrullah

AIH

Santosa

Dirgantara

. Design and optimization of crashworthy components based on lattice structure configuration. Structures 2020; 26: 969–981.

51.

Yang

Peng

, et al. Cut-out grooves optimization to improve crashworthiness of a gradual energy-absorbing structure for subway vehicles. Mater Des 2016; 103: 132–143.

52.

. Thin-walled corrugated structures: a review of crashworthiness designs and energy absorption characteristics. Thin-Walled Struct 2020; 157: 106995.

Crashworthiness investigations for 3D printed multi-layer multi-topology carbon fiber nylon lattice materials

Abstract

Keywords

Introduction

Numerical model and experimental testing set up

Lattice geometry and design

Finite element model

Lattice parent material model

Experimental testing set up

Crashworthiness parameters for data analysis

Energy absorption efficiency

Densification strain

Plateau stress

Energy absorption

Specific energy absorption

Lattice cluster results and discussion

Single-layer lattice clusters

Multi-layer lattice clusters

Multi-layer, multi-topology lattice clusters

Conclusion

Footnotes

Acknowledgments

Declaration of conflicting interests

Funding

ORCID iDs

References