Abstract
Purpose
Most support surfaces in comfort applications and sporting equipment are made from pressure-relieving foam such as viscoelastic polyurethane. However, for some users, foam is not the best material as it acts as a thermal insulator and it may not offer adequate postural support. The additive manufacturing of such surfaces and equipment may alleviate these issues, but material and design investigation is needed to optimize the printing parameters for use in pressure relief applications. This study aims to assess the ability of an additive manufactured flexible polymer to perform similarly to a viscoelastic foam for use in comfort applications.
Design/methodology/approach
Three-dimensional (3D) printed samples of thermoplastic polyurethane (TPU) are tested in uniaxial compression with four different infill patterns and varying infill percentage. The behaviours of the samples are compared to a viscoelastic polyurethane foam used in various comfort applications.
Findings
Results indicate that TPU experiences an increase in strength with an increasing infill percentage. Findings from the study suggest that infill pattern impacts the compressive response of 3D printed material, with two-dimensional patterns inducing an elasto-plastic buckling of the cell walls in TPU depending on infill percentage. Such buckling may not be a beneficial property for comfort applications. Based on the results, the authors suggest printing from TPU with a low-density 3D infill, such as 5% gyroid.
Originality/value
Several common infill patterns are characterised in compression in this work, suggesting the importance of infill choices when 3D printing end-use products and design for manufacturing.
Keywords
Citation
Nace, S.E., Tiernan, J., Holland, D. and Ni Annaidh, A. (2021), "A comparative analysis of the compression characteristics of a thermoplastic polyurethane 3D printed in four infill patterns for comfort applications", Rapid Prototyping Journal, Vol. 27 No. 11, pp. 24-36. https://doi.org/10.1108/RPJ-07-2020-0155
Publisher
:Emerald Publishing Limited
Copyright © 2021, Susan Erica Nace, John Tiernan and Donal Holland Aisling Ni Annaidh.
License
Published by Emerald Publishing Limited. This article is published under the Creative Commons Attribution (CC BY 4.0) licence. Anyone may reproduce, distribute, translate and create derivative works of this article (for both commercial and non-commercial purposes), subject to full attribution to the original publication and authors. The full terms of this licence may be seen at http://creativecommons.org/licences/by/4.0/legalcode
1. Introduction
According to an analysis conducted by Grand View Research Inc. in 2017, the size of the global pressure relief devices market will rise from US$2.53bn in 2015 to US$4.14bn in 2025 (Grand View Research Inc., 2017). This rise is expected due to an increasing geriatric and limited-mobility population who are at an increased risk of pressure injury development, which pressure relief devices are designed to prevent or help heal. Viscoelastic polyurethane foams (VPFs) are commonly used in various comfort cushioning applications related to pressure relief, including hospital or long-term care beds, wheelchair seating, office furniture, shoe sole inserts and aircraft and vehicle seating. VPFs are commonly used in these applications due to their ability to conform to the user’s body shape with increased usage time, increasing the surface area over which body pressure is distributed, thus lowering peak pressures experienced by the user.
Other key factors contributing to increased risk of pressure injury development are shear and friction at the surface interface, local temperature and local humidity at the user-surface interface (Lachenbruch, 2005; Lachenbruch et al., 2015; Schwartz et al., 2018). Foams thermally insulate users from their surrounding environment over the surface area of the foam. At times, this insulation can lead to an increase in localised moisture and temperature that heightens the risk of pressure injury development in that region (Jan et al., 2013), which can present a severe health and financial risk (Stroupe et al., 2011; Dealey et al., 2012). The heightened temperature can also lead to increased discomfort in environments such as offices, home bedding, personal vehicles and in the use of protective clothing and gear for sports (Finn et al., 2012; Kumar et al., 2015; Dotti et al., 2016; Califano et al., 2017). The use of materials other than VPF and the development of new support surface designs may allow for better control of the microclimate at the support surface-user interface while still offering pressure and shear relief to the tissues at risk of pressure injury or discomfort. With the development of three-dimensional (3D) printing in clinical settings, the appropriateness of 3D printed cushioning materials should be examined, especially qualifying their ability to support weight-bearing loads encountered in comfort applications.
1.1 Fused filament fabrication
Additive manufacturing through fused filament fabrication (FFF), commonly referred to as 3D printing, is a relatively inexpensive manufacturing process that builds a part up in thin layers. To attain flexible, elastic or energy-absorbent parts made using FFF, materials such as thermoplastic elastomers, specifically thermoplastic polyurethanes (TPUs), are more effective to use as they are inherently flexible. Bulk TPU material has been modelled by Qi and Boyce (2004) as a hyperelastic, rubbery network with a viscoelastic-plastic element. When 3D printed, its behaviour in compression is similar to that of elastomeric foams (Avalle et al., 2001). The effect of 3D printing parameters on the elasticity and energy-absorption of TPU has been investigated recently (Bates et al., 2016, 2018; Rossiter et al., 2019) and multi-material prints including TPU are on the rise for use in biomedical applications (Tsai et al., 2017; Verstraete et al., 2018; Lin et al., 2019). Whether TPU is suitable for use as an alternative to VPF in comfort applications is yet to be determined and is the goal of the current study. Herein TPU specimens of varying infill percentages and infill patterns are tested in compression and compared to a soft fire-retardant grade SunMate foam (Dynamic Systems, Inc., USA). This VPF is commonly used in comfort applications, including hospital bedding, Formula One headrests, custom prosthetics and wheelchair seating and aircraft and motorcycle seating.
1.2 Infill patterns
The internal infill percentage and infill pattern of the object are usually defined in the slicing software and the patterns available to the manufacturer vary depending on the slicing software used. Two-dimensional (2D) structures are the most common type of FFF infill patterns. From layer to layer in the normal direction to the printer build plate, the inner area of a 2D infill pattern does not change. Examples of 2D infill patterns are shown in Figure 1. 2D patterns cause anisotropy in the mechanical properties of the printed part, making print direction an important design factor when using such patterns (Kozior and Kundera, 2017).
Some slicing software also offers 3D infill patterns, such as those shown in Figure 2. A 3D infill pattern has cells with 3D built from sliced flat layers that vary in the direction normal to the printer build plate. Some 3D infill patterns are made up of triply periodic minimal surfaces (TPMS), such as the gyroid infill shown in Figure 2. TPMS are commonly found in natural structures, do not self-intersect and are isotropic (Domínguez-Rodríguez et al., 2018; Podroužek et al., 2019).
When 3D printing end-use parts, being able to predict how printing parameters such as infill pattern and infill percentage will affect the performance of the part is necessary. This need has motivated research into the behaviour of 3D printed materials in various loading states. Recent studies have investigated the ability of the 2D honeycomb structure to absorb energy in compression (Bates et al., 2016, 2018), characterised 3D printed TPMS-based infill patterns in uniaxial compression (Abueidda et al., 2019; Podroužek et al., 2019) and investigated the ability to print custom shoe-insoles with varying mechanical properties through tailored 3D infill pattern design (Amorim et al., 2019). Podrouzek et al compared the behaviour of different 3D infill patterns in compression (Podroužek et al., 2019), while Wang et al. compared one 3D infill pattern – gyroid infill – to two common 2D infill patterns for energy absorption through the finite element method (Wang et al., 2020). Rossiter et al. (2020) assessed the effects of varying several geometric design variables on the behaviour of FFF nylon samples infilled with truncated octahedron lattices in compression, indicating the importance of infill geometry on the performance of 3D printed flexible polymers and rubber like materials. A study comparing commercially available 2D and 3D infill patterns in uniaxial compression as an alternative to VPF in comfort applications, as proposed for this study, has not yet been pursued.
2. Material and methods
2.1 Sample preparation
2.1.1 Printing parameters
A cuboid sample was modelled in Autodesk Inventor Professional 2020 CAD software (Autodesk, Inc., USA) with 25 mm depth and 50 mm width and length. This digital model was exported as an .STL file from the CAD software and imported into Ultimaker Cura slicing software version 4.5 (Ultimaker B.V., The Netherlands) for copying and slicing three models per testing group for 3D printing. The printing parameters used in the slicing software in this study are listed in Table 1. The sample groups and their infill patterns and infill percentages for TPU are shown in Figure 3. The four infill patterns chosen for testing in this study are recommended by Ultimaker to use with flexible filaments, such as the TPU in this study.
Concentric infill has not yet been tested in compression in the literature, though studies show it exhibits lower strengths in tension and flexion than other infill patterns when printed using acrylonitrile butadiene styrene or polyactic acid composites (Khan et al., 2017, 2018; Kesavarma et al., 2020), a characteristic that may be beneficial for comfort applications. Cross infill has also not been tested in the literature; thus, a formal study of its behaviour is beneficial. Cross3D infill and gyroid infill have shown beneficial elastic properties (Abueidda et al., 2019; Pecho et al., 2019), but comparisons to the concentric infill and cross infill have not been conducted in the same flexible material.
The infill percentages chosen were based on previous studies investigating the effects of infill density on performance in compression that showed that infills above 40% exhibited high strengths (Rodríguez-Panes et al., 2018; Podroužek et al., 2019; Tezel et al., 2019) and the estimated pressures in comfort applications (Apatsidis et al., 2002; Global et al., 2009). Samples were printed on an Ultimaker2 + 3D printer (Ultimaker B.V., The Netherlands) using SpoolWorks FlexD 2.85 mm green filament (E3D-Online, UK).
3D printed samples were compared to soft SunMate fire retardant grade VPF (Dynamic Systems, Inc, USA). This VPF is used in a variety of applications, including military aircraft seating, wheelchair seating, custom vehicle seating and Formula One vehicle seating. Samples were cut from sheets of 25 mm-thick, 400 mm by 400 mm VPF supplied from the manufacturer to measure 50 mm × 50 mm × 25 mm (L × W × H). Three samples were cut to size for compression testing, as set in standard ISO 3386–1 standard for determining the stress-strain characteristics of low-density polymeric materials in compression. The properties of each constituent material tested are listed in Table 2.
2.1.2 Sample conditioning
Before testing, all samples were conditioned according to ISO 3386–1. Conditioning consisted of storing samples after preparation for at least 72 h unloaded at room temperature and relative humidity of 50% ± 5%.
2.2 Compression testing
Testing flexible TPU samples was conducted according to ISO 3386–1. Three specimens were tested for each sample group, as required by ISO 3386–1 and a 30 kN load cell was used on a Lloyd LR30K Plus Materials Testing Machine (Lloyd Instruments Ltd, England). Data were collected during testing using NEXYGEN MT Materials Testing Software version 4.5.1 Issue 3 (Lloyd Instruments Ltd, England). Before testing, each sample was preconditioned by loading and unloading the sample to 70% of its initial height three times at a strain rate of 6.67 × 10−4 s−1. Immediately after preconditioning, each sample was again loaded to 70% of its initial height and then unloaded at a strain rate of 3.33 × 10−3 s−1. All sample data were then averaged for each testing group (n = 3). Testing of VPF was conducted following the same procedure with a 5 kN load cell on the same machine, using a smaller load cell due to the lower forces required to compress the VPF to high strains. All data collection was performed at room temperature with a relative environmental humidity of 50% ± 5%.
3. Results and discussion
Important material characteristics, as defined in Figures 4 and 5, can be identified from the stress-strain data of flexible VPF and 3D printed TPU. Figure 4 is specific to elastomeric polymers, such as VPF, while Figure 5 is typically seen in elastoplastic materials (Gibson and Ashby, 1997; de Vries, 2009). The important material characteristics for the flexible materials are as follows: the average stiffness in the linear elastic region (Ei); the average collapse stress (σc) defined as the stress due to which the cells in the polymer structure begin to collapse in compression; the average hysteresis loss at the collapse strain (hc) of each testing group defined as the average per cent of energy loss in a loading cycle or one minus the ratio of the collapse stress when unloading the specimen (σu) and the collapse stress when loading the specimen; the plateau stiffness (Epl) defined as the average stiffness in the plateau region; and the average densification stress (σd) due to which the cell walls in the polymer structure begin to touch in compression, leading to the structure collapsing fully on itself and a steep increase is seen in the stress-strain data. Note that after the collapse stress in elastoplastic materials, there is a notable drop in the stress before the plateau region begins. This effect is due to the buckling of cell walls in polymer structures with Euler column-like walls
The average characteristic material values for each flexible material testing group from the study results are illustrated in Figures 6–10.
Two-way analysis of variances (ANOVAs) were conducted to assess if the differences between the variances of Ei, σc, hc, Epl and σd due to infill pattern, infill percentage and material were statistically significant with 99% confidence. The results of the two-way ANOVAs and post hoc Tukey honestly significant difference (HSD) tests are summarised in Tables 3–Table 7.
3.1 Effect of infill percentage
The compression test stress-strain results for all TPU groups are shown in Figure 11(a)–11(d) for a strain rate of 3.33 × 10−3 s−1. The TPU groups printed with higher infill percentages exhibit higher stiffness, collapse stress, plateau stiffness and densification stress than their lower infill counterparts, as seen in Figures 6–10. However, higher infill also correlates to a lower densification strain, as seen in Figure 11(a)–(d). These effects are expected as there is a higher material mass in the same sample volume. A higher material mass offers more material over which to distribute the compression load, lending strength and stiffness to samples. There is less void space in the structural cells of the higher infill sample groups such that cell walls compress together at a lower strain than in the lower infill sample groups with less material mass. The results here confirm that as infill percentage is increased, the behaviour of the 3D printed specimen moves towards that of the constituent material, TPU, as found in related literature (de Vries, 2009; Bates et al., 2018). Notably, the behaviour of the concentric infill pattern group changes from elastoplastic at 20% infill to elastomeric at 30% infill, though the values in Figure 6–10 suggest that a 30% infill may be too strong for comfort applications.
Post hoc Tukey HSD tests indicated that infill percentage did not have a statistically significant effect on Ei or hc values (Tables 3 and 5, respectively). Its effect on the other three material characteristics tends to be a combination interaction with the infill pattern.
3.2 Effect of infill pattern
The results in Figures 6–10 suggest that the infill pattern affects all material characteristics defined from the stress-strain data. Figure 6 shows that the cross infill exhibited the highest linear elastic region stiffness (Ei) with the post hoc Tukey HSD test (Table 5) indicating a statistically significant difference between the cross infill pattern groups’ Ei and those of the other testing groups. The highest collapse stress (σc) of the flexible sample groups was exhibited by the cross infill pattern groups as seen in Figure 8, with the post hoc Tukey HSD test in Table 4 indicating cross infill’s statistically significant different collapse stress from most other groups, somewhat dependent on infill percentage. Figure 8 shows the average hysteresis loss values for all testing groups at their collapse strains. Table 5 summarising the post hoc Tukey’s HSD test indicates that the hysteresis loss differed significantly between the 2D infill pattern groups (concentric and cross) and the 3D infill pattern groups (cross3D and gyroid and VPF with a stochastic, 3D cellular structure). Average hysteresis values were lower in the 3D infill pattern groups, suggesting a 3D infill pattern in flexible TPU dissipates less energy due to internal friction in compression than 2D infill patterns.
The cross3D infill pattern groups exhibited the highest plateau region stiffnesses (Epl), as shown in Figure 9 but the post hoc Tukey HSD test (Table 6) indicated that the effect of the infill pattern on this value varied depending on infill percentage. For the low-infill testing groups, the average plateau stiffness for the cross3D infill pattern differed significantly from that of gyroid infill. For the high infill groups, the average plateau stiffness for the cross3D infill pattern was significantly different from all other different patterns at a low infill but only significantly different from gyroid at high infill.
Figure 10 shows the average densification stresses (σd) for each testing group. The post hoc Tukey’s HSD test (Table 7) indicated that the effect of infill pattern on σd varied from low- to high-infill percentage. Most low-infill patterns did not behave significantly differently from one another for this material character, except for gyroid and cross3D. For the high-infill percentage groups, the average densification stresses for the cross and gyroid infill patterns were not significantly different from each other and the cross3D infill pattern exhibited average densification stress that was statistically significantly different and higher than all other infill patterns, regardless of infill percentage.
Figure 12 displays the average stress-strain curves for all testing groups including foam in compression at a strain rate of 3.33 × 10−3 s−1. Figures 11 and 12 further suggest that the infill pattern affects the behaviour of the TPU samples in compression. Concentric and cross infills at low infill percentages exhibit elastoplastic behaviour in compression, such as that shown in Figure 5, while the other infill patterns exhibit behaviour in compression such as that shown in Figure 4 for elastic materials. Elastomeric behaviour is better suited for comfort applications, as an elastoplastic response indicates sudden buckling of the cell structure that may be uncomfortable for the user, translating high levels of vibration or impact to the user. The current results indicate that the internal structure of the 3D printed sample heavily influences its propensity to exhibit either elastomeric (Figure 4) or elastoplastic (Figure 5) response in compression and supports the concept that cell wall structures can be modelled, with simplifications, with Euler column theory, as suggested in related literature on cellular polymers (Gibson and Ashby, 1997; de Vries, 2009).
3.3 Three-dimensional printed thermoplastic polyurethane compared to viscoelastic polyurethane foam
Results in Figure 6–10 and the statistical analyses in Tables 3–7 suggest that as a lower infill percentage in a 3D printed TPU sample exhibits a higher strength in compression than VPF, 3D printed infills above 20% would not be required in comfort applications. It is possible that a lower infill percentage would exhibit stiffness, collapse stress and densification stress closer to VPF, but further investigation is needed to determine the optimum infill percentage range. Printing a TPU material with such a low infill that its stiffness, collapse stress and densification stress are below those of VPF may not be possible, nor advisable due to the possibility of “bottoming-out” or the deformation of a support surface to the extent that pressure redistribution benefits of that would prevent pressure injury development are lost (Ferguson-Pell, 1990; Wang and Dal Nevo, 2016; European Pressure Ulcer Advisory Panel, National Pressure Injury Advisory Panel and Pan Pacific Pressure Injury Alliance, 2019).
Figure 12 suggests that the concentric 20% infill is the nearest to VPF’s performance in compression, but the further investigation should be undertaken at a larger scale as Ultimaker Cura slicing software does not have a feature yet for users to define multiple locations from which the concentric pattern grows. The centre is always the point from which the concentric pattern spreads out from, so the pattern concentrates material in the middle of the sliced object. This may not be optimal for VPF comfort applications where pressure redistribution is a key reason for material or manufacturing method choice (Gefen, 2014; Mohanty and Mahapatra, 2014).
The next closest infill pattern in compression behaviour to VPF is gyroid at 5% infill. As can be seen in Figure 11d, its response is also elastomeric in nature, such as VPF (Briody, 2012). The authors believe this infill pattern would be an effective alternative to VPF in comfort applications due to its 3D structure. The cells in the gyroid samples cause the sample to exhibit stiffness and collapse stress nearer to VPF than the other TPU infill patterns. The gyroid samples have an ordered pattern of cells, while VPF typically exhibits a stochastic structure of different-sized microscopic cells (Briody, 2012). To have a 3D printed support surface behave such as VPF in compression, the authors suggest based on the results of this study that a low-density, 3D infill pattern should be used.
3.4 Further implications for manufacturing decisions
The results of this study indicate that a 3D printed flexible polymer such as the TPU used does not necessarily exhibit similar behaviour to VPF in comfort applications. However, a 3D printed TPU may be a suitable alternative to VPF for products tailored to a specific user, e.g. pilot ejection seats, Formula One car seats, custom wheelchair seating. In the case of custom wheelchair seating, the advantages and disadvantages of producing a custom VPF wheelchair cushion through computer numerically controlled (CNC) milling is compared to those of manufacturing the same cushion in TPU using FFF have been considered in recent literature (Nace et al., 2019). The review concludes that 3D printing may offer a better manufacturing method than CNC milling VPF for custom wheelchair cushions, as 3D printing enables the creation of complex internal structures in the cushion that help to lower skin temperature and local humidity while keeping manufacturing costs and times similar to those related to CNC milling. These effects, coupled with lowered support pressures resulting from surface contouring in several settings (Tuck et al., 2008; Brienza et al., 2010; Akins et al., 2011; Hosking, 2017), can lower the risk of pressure injury development according to the relevant literature (Gefen, 2011; Jan et al., 2013; Kottner et al., 2018; Tzen et al., 2019).
3.5 Limitations
This study used samples sized below 10% of the volume needed in most support surfaces such as mattresses and seat cushions. Results for larger 3D printed specimens may differ from the samples used in this study and should be investigated in the future. The stress-distribution of a seated model or person is often used to compare the efficacy of different support surfaces (Apatsidis et al., 2002; Akins et al., 2011; McDonald et al., 2015; Bui et al., 2017); the stress distribution on a larger 3D printed support surface should thus be investigated beyond the planar compression investigation conducted here to inform future design and manufacturing decisions. The thermal investigation should also be prioritised to address whether a 3D printed support surface can lower peak pressures while maintaining appropriate temperature and humidity levels to decrease pressure injury risk in the user.
4. Conclusion
This study found that both infill percentage and infill pattern have significant effects on the behaviour of 3D printed TPU in compression. As infill percentage increases, the strength and stiffness of the 3D printed object tend to increase. The effect of the infill pattern is more complex, with different behaviours seen in the infill patterns tested here, regardless of material or infill percentage. Results indicate that of the samples tested, TPU 3D printed at 20% infill in a concentric pattern behaves most closely to VPF in compression. However, due to concerns related to stress distribution and elastic collapse of infill patterns, the authors recommend a 3D infill pattern such as gyroid for future development of 3D printed alternatives to VPF in comfort applications. In the current data set, the gyroid pattern printed at 5% infill shows promising results. There are numerous different infill patterns available to manufacturers and 3D printing hobbyists on various slicing programs. This study investigated only four of these patterns in one slicing program, which may not include the optimal infill pattern for comfort applications where VPF is used. The results here are a useful start for further investigation of how different infill patterns affect the behaviour of 3D printed products which are designed for compliance and pressure injury prevention and contributing knowledge to how important infill pattern and density choices are in the design process of any 3D printed part.
Figures
The basic printing parameters used for all thermoplastic polyurethane (TPU) samples
| Printing Parameters | |||||||
|---|---|---|---|---|---|---|---|
| Layer height | Top/bottom thickness | Wall thickness | Print speed | Sample shape | Sample height | Sample width and length | |
| TPU | 0.2 mm | 0.8 mm | 0 mm | 30 mm/s | cuboid | 25 mm | 50 mm |
TPU samples were tested against ISO 3866-1 standard for compressive characteristic of cellular flexible materials. A cuboid sample with the given dimensions was modelled in Autodesk Inventor Professional 2020 CAD software. Printing parameters were set in the slicing software Ultimaker Cura version 4.5. A 0mm external wall thickness was set for specimens so that the internal structure was visible during testing, as suggested by the ISO standard 3866-1
Material properties for the thermoplastic polyurethane (TPU) and viscoelastic polyurethane foam (VPF) tested in this study
| Material | Density (kg/m3) | Ultimate tensile strength (MPa) | Young's modulus (MPa) | Elongation at break (%) | Hardness (Shore A) |
|---|---|---|---|---|---|
| TPU | 1235 | 42 | 9.8 | 500 | 93 |
| VPF | 80 | 0.131 | 0.122-0.139 | 137-202 | – |
The TPU material is SpoolWorks FlexD green 2.85 mm diameter filament (E3D-Online, United Kingdom). The VPF is soft fire-retardant grade SunMate foam (Dynamic Systems, Inc., United States). Properties were attained from the respective manufacturers of each material
Summary of results of a two-way ANOVA of the linear elastic stiffnesses recorded for sample testing groups, i.e. infill pattern and percentage, in compression at a strain rate of 3.33x10−3 s−1
| Linear elastic stiffness (Ei) | Concentric 20% | Concentric 30% | Cross 20% | Cross 30% | Cross3D 20% | Cross3D 30% | Gyroid 5% | Gyroid 8% | VPF |
|---|---|---|---|---|---|---|---|---|---|
| Concentric 20% | * | * | |||||||
| Concentric 30% | * | * | |||||||
| Cross 20% | * | * | * | * | * | * | * | ||
| Cross 30% | * | * | * | * | * | * | * | ||
| Cross3D 20% | * | * | |||||||
| Cross3D 30% | * | * | |||||||
| Gyroid 5% | * | * | |||||||
| Gyroid 8% | * | * | |||||||
| VPF | * | * |
An asterisk indicates statistically significant difference (p < 0.01)
Summary of results of a two-way ANOVA of the collapse stresses recorded for sample testing groups, i.e. infill pattern and percentage, in compression at a strain rate of 3.33x10−3 s−1
| Collapse stress (σc) | Concentric 20% | Concentric 30% | Cross 20% | Cross 30% | Cross3D 20% | Cross3D 30% | Gyroid 5% | Gyroid 8% | VPF |
|---|---|---|---|---|---|---|---|---|---|
| Concentric 20% | * | * | * | * | |||||
| Concentric 30% | * | * | * | * | |||||
| Cross 20% | * | * | * | * | * | ||||
| Cross 30% | * | * | * | * | * | * | * | ||
| Cross3D 20% | * | * | * | ||||||
| Cross3D 30% | * | * | * | * | * | ||||
| Gyroid 5% | * | * | * | * | |||||
| Gyroid 8% | * | * | * | * | * | ||||
| VPF | * | * | * | * | * |
An asterisk indicates statistically significant difference (p < 0.01)
Summary of results of a two-way ANOVA of the hysteresis loss values recorded for sample testing groups, i.e. infill pattern and percentage, in compression at a strain rate of 3.33x10−3 s−1
| Hysteresis loss (hc) | Concentric 20% | Concentric 30% | Cross 20% | Cross 30% | Cross3D 20% | Cross3D 30% | Gyroid 5% | Gyroid 8% | VPF |
|---|---|---|---|---|---|---|---|---|---|
| Concentric 20% | * | * | * | * | * | ||||
| Concentric 30% | * | * | * | * | * | ||||
| Cross 20% | * | * | * | * | * | ||||
| Cross 30% | * | * | * | * | * | ||||
| Cross3D 20% | * | * | * | * | |||||
| Cross3D 30% | * | * | * | * | |||||
| Gyroid 5% | * | * | * | * | |||||
| Gyroid 8% | * | * | * | * | |||||
| VPF | * | * | * | * |
An asterisk indicates statistically significant difference (p < 0.01)
Summary of results of a two-way ANOVA of the plateau stiffnesses recorded for sample testing groups, i.e. infill pattern and percentage, in compression at a strain rate of 3.33x10−3 s−1
| Plateau stiffness (Epl) | Concentric 20% | Concentric 30% | Cross 20% | Cross 30% | Cross3D 20% | Cross3D 30% | Gyroid 5% | Gyroid 8% | VPF |
|---|---|---|---|---|---|---|---|---|---|
| Concentric 20% | * | * | |||||||
| Concentric 30% | * | * | |||||||
| Cross 20% | * | ||||||||
| Cross 30% | |||||||||
| Cross3D 20% | * | ||||||||
| Cross3D 30% | * | * | * | * | * | ||||
| Gyroid 5% | * | * | * | ||||||
| Gyroid 8% | * | ||||||||
| VPF | * |
An asterisk indicates statistically significant difference (p < 0.01)
Summary of results of a two-way ANOVA of the densification stresses recorded for sample testing groups, i.e. infill pattern and percentage, in compression at a strain rate of 3.33x10−3 s−1
| Densification stress (σd) | Concentric 20% | Concentric 30% | Cross 20% | Cross 30% | Cross3D 20% | Cross3D 30% | Gyroid 5% | Gyroid 8% | VPF |
|---|---|---|---|---|---|---|---|---|---|
| Concentric 20% | * | * | * | ||||||
| Concentric 30% | * | * | * | * | |||||
| Cross 20% | * | * | * | * | |||||
| Cross 30% | * | * | * | * | * | * | |||
| Cross3D 20% | * | * | * | * | |||||
| Cross3D 30% | * | * | * | * | * | * | * | * | |
| Gyroid 5% | * | * | * | * | |||||
| Gyroid 8% | * | * | * | * | * | * | * | ||
| VPF | * | * | * | * | * | * |
An asterisk indicates statistically significant difference (p < 0.01)
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Acknowledgements
This work has been funded by the Irish Research Council and Enable Ireland through the Employment Based Postgraduate Programme (grant number EBP/2017/498) and University College Dublin’s School of Mechanical and Materials Engineering.
Conflict of interest statement: The authors have no conflict of interest in the research to declare.