Design optimization of pangolin inspired composites for enhanced energy absorption

Abstract

The demand for lightweight, high energy absorbing materials has increased, especially for high risk applications such as aerospace, transport and nuclear. This study aims at analyzing the design and behavior of biomimicking composite structures for structural applications based on the dermal armor system of pangolin under quasi-static loads. We consider two plant-based fibers, luffa and linen, as environmentally friendly substitutes for glass fibers. Using Taguchi, we quantitatively investigated the effects of five factors: fiber type, curvature radius, number of composite plies, trapezoidal scale Y1, and trapezoidal scale Y2 on TAE and SAE. Lateral compressive loads were applied to composite specimens prepared using unsaturated isophthalic polyester resin. It was observed that luffa fibers possess higher TAE and linen fibers possess higher SAE. The Taguchi method set the optimal values for the parameter levels for the prediction of TAE of 11.2431 J and SAE of 2.3677 J/g, while the actual experimental result brought the percentage of error to 5.76% for TAE and 3.94% for SAE. From the theoretical analysis of the RPP and Hollomon models, we gain insights into the energy dissipation process, such as curvature reduction and plastic hinge formation. It is hoped that this work will help to open up a wider field of bio-inspired designs for high-performance sustainable materials; in particular, the proposed framework provides clear ways of predicting the energy absorption characteristics of such structures.

Introduction

The replication of natural materials for engineering new lightweight structures with high energy absorption capability has attracted much attention in the engineering literature. This interest arises from the outstanding mechanical performance of biological structures, which have evolved through natural selection over millions of years. This and other bio-inspired strategies present exciting opportunities for the development of new materials and structures with specific properties like light weight and high energy absorption capacity, which are often necessary in aerospace, automotive, nuclear power plant, and civil engineering industries. In the area of material science and engineering, composite materials have been greatly developed because of their light weight and very high mechanical strength. These composites are preferred in many industries today because they have unique characteristics that can be modified to suit certain application requirements. At the same time, the use of biological concepts in industry, known as biomimetics and bioinspiration, has begun to develop. Biological materials are attractive because they are cheap, have a low impact on the environment, are renewable, and possess inherent structural benefits^1–3. Significant work has been done to investigate and improve the energy dissipation mechanisms in composite structures. For example, Song et al.⁴ studied the axial fracture behavior and energy absorption capability of glass/epoxy composites wound around metal tubes and pointed out the role of composite structure and metal characteristics. In the same vein, Tarlochan et al.⁵ investigated the quasistatic compressive behavior of composite sandwich structures with tubular reinforcement and the corresponding criteria of peak load and energy absorption efficiency. Zhou et al.⁶ and Xu et al.⁷ described the energy absorption capacities of composite foams and carbon fiber reinforced pipes under static and dynamic loading, respectively. Subsequent works by Meng et al.⁸ and Hu et al.⁹ demonstrated the enhanced mechanical characteristics of bamboo and advanced composite tubes, as well as by Othman et al.¹⁰ and Zhu et al.¹¹ on the crashworthiness enhancement through internal materials such as polyurethane foam and composite frames. The latest studies focused on the improvement of bio-inspired designs and optimization procedures to improve the energy absorption of composite materials. Liu et al.¹² and Wu et al.¹³ employed biomimetic structures; honeycomb-patterned and muscle-like structures were incorporated and therefore the load distribution and energy absorption capabilities were improved. In addition, different studies have highlighted some works on the development of improved material design and structure using enhanced optimization methods together with biomimicry^14–16. Therefore, there are still challenges to the general understanding and full use of bio-inspired composite structures, especially when using plant fibers other than traditional reinforcement materials. Previous research has primarily focused on synthetic fabrics or comparatively limited natural fabrics, leaving unnoticed other possible sustainable materials that can provide superior energy capacity as well as being environmentally friendly^17–23. Moreover, the integration of systematic optimization techniques together with theoretical modeling for predicting and improving energy absorption characteristics using the Taguchi technique is scarce in the literature^24–27. To fill these gaps, this paper provides a comprehensive description and analysis of bio-inspired composite quasi-scale specimens under quasi-static loading. Using the Taguchi method of experimental design, we examined luffa and linen fibers as sustainable alternatives to glass fibers. The objectives of this study are to confirm the accuracy of the Taguchi method in energy-absorption predictions, to determine potential energy-absorption mechanisms, and to define functional relationships with material and geometrical characteristics. This research combines Rigid Perfectly Plastic (RPP) and Hollomon material models to enhance the prediction of the energy absorption of bio-inspired composites. The main findings of this work are in the framework of the systematic optimization process of fiber-reinforced composites that mimic natural dermal armor and provide a better understanding of material design for high-performance, environmentally friendly structural applications.

Materials and methods

Bio-inspired design

The pangolin, a unique anteater adorned with keratin scales, is the sole mammalian example of such dermal armor. Spanning lengths of 30 to 152 cm and weighing up to 33 kg, these creatures exemplify lightweight, compact design. A distinctive defense mechanism involves curling into an impervious ball to thwart predators, as depicted in Fig. 1.

Fig. 1.

(a) Natural pangolin anteater (https://commons.wikimedia.org/wiki/File:Manis_temminckii_MHNT_PHOL_1.jpg). (b) Posture and defensive formation (https://supercurioso.com/que-es-un-pangolin/pangolin-enrollado/), (c) Pangolin scales under a pressure load by hunter (https://tswalu.com/wildlife-journal-spring-2020/cats-outsmarted-by-a-ground-pangolin/).

The geometry of pangolin scales and their arrangement is such that their impermeability is increased. It can be found that each scale is in proper overlap with six other neighboring scales by carefully observing the arrangement of the scales, in such a way that its outer surface is in contact with the inner surfaces of the three adjacent upper scales and its inner surface covers the outer surfaces of the three lower adjacent scales as illustrated in Fig. 1a, more information can be found in Ref²⁸. Therefore, the pangolin cover acts like an energy absorber, which is subjected to pressure loading process by the predator’s jaws and penetrated by its teeth as shown in Fig. 1c by imitating their geometry and arrangement, energy absorbers such as sandwich panel and suitable armor can be made and tested under the crushing or penetration process.

Nature’s recurring patterns, observable in fish scales, pine cones, wheat heads, and palm tree trunks, strikingly resemble the pangolin’s scale arrangement (Fig. 2), underscoring the universality of efficient design strategies across species.

Fig. 2.

Recurrence of pangolin-inspired scale patterns in natural phenomena: (a) Fish scales (https://pikbest.com/png-images/qianku-animal-surface-fish-scales_2389963.html), (b) Palm tree trunks (https://fa.m.wikipedia.org/wiki/%D9%BE%D8%B1%D9%88%D9%86%D8%AF%D9%87:Kabkab-date.jpg), (c) Wheat heads (https://www.anyrgb.com/en-clipart-svbnt), (d) Pine cones (https://mega-sad.ru/yel-obyknovennaya/).

To initiate the experimental design for crush testing, we drew inspiration from the Chinese pangolin (Manis pentadactyla), a South Asian species. Its scales, measuring approximately 1 to 3 cm in height, 2 to 4 cm at the base, and 0.4 to 3 mm in thickness (as depicted in Fig. 3, where Y1, Y2, and L denote the smaller base, larger base, and height of the trapezoidal scale, respectively), served as a blueprint for composite quasi-scale prototypes²⁸.

Fig. 3.

(a) Natural dimensions of pangolin scales ²⁸ and (b) trapezoidal configuration of composite analogs.

Considering fabrication practicality and facilitating the examination of multiple variables, the composite quasi-scales were upscaled to 1.5 times the actual pangolin scale dimensions.

Taguchi methodology

In the Taguchi method, orthogonal arrays are used to design experiments. When some tests are repeated and their results are quantitatively measured, Taguchi recommends a signal-to-noise ratio. The signal-to-noise ratio indicates the sensitivity of the main factors in a cost function. To determine the signal-to-noise ratio (SNR), three functions can be used, consisting of “the smallest is the best”, “the largest is the best”, and “nominal value is the best”; and based on some relations, the signal-to-noise ratio is determined. The following mathematical expressions are used in the Taguchi’s method^29,30. For minimizing the performance of a system and achieving the function “the smallest is the best”, the SNR is calculated as follows²⁹:

1

where y, subscript i, and N indicate the performance indicator, experiment number, and number of replicates of the experiment “i”. To maximize the performance of a system and achieve the function “the largest is the best”, the SNR is calculated as follows²⁹:

2

To achieve a predetermined nominal value and the function of "nominal is the best," the SNR is calculated as follows¹⁸:

3

where, value of is calculated as follows:

4

In the above equation, indicates number of designed experiments based on the Taguchi method. The value of S is obtained as follows²⁹:

5

For all conditions, a higher SNR value indicates a better quality characteristic. By calculating the SNR value of each experiment from Eq. (2), the mean SNR was obtained based on the following general relation:

6

The summation of squares, that is indicated by δ is calculated as follows³⁰:

7

The summation of squares due to differences in the mean SNR for the ith process parameter is indicated by δ_i and calculated as²⁹:

8

Finally, the share percentage of each factor on the objective function is obtained as follows:

9

Further explanations of the Taguchi method can be found in Ref³¹. In this investigation design of experiments (DOE) and analysis of data by the Taguchi method, we used Minitab Statistical Software (version 16, https://www.minitab.com/en-us/products/minitab/free-trial/) package to determine the effects of each parameter on the objective function.

After the software was installed on the PC, for using the Taguchi method from the DOE menu, should be refer to the Stat toolbar of software and one of DOE methods should be choise and Taguchi method was selected and clicked on Create Taguchi Design option then the number of factors and the test level of this study that are 6 and 3 respectively were selected and clicked on Design option and one of Taguchi’s test designs was choosed that is L27 in this study i.e. 27 experiments are introduced in this investigation and their levels of each factor are determined based on the arrays that provided by Taguchi method. The obtained data was entered into the software after whole specimens were fabricated and their tests were done, Then, as in the previous steps, stat/DOE/Taguchi should be selected and clicked on the Analyze Taguchi Design option, and after the necessary settings were done and Larger is better option (for present study) was selected, the results will be extracted.

For this purpose, the total absorbed energy (TAE) and specific absorbed energy (SAE) were considered as the main goals to be maximized.

To increase efficiency of statistical properties with the goal of optimization, results of designed experiments were presented, based on signal-to-noise ratios (SNR), using the logarithmic relationships. Generally, in energy absorbers, the maximum value of TAE and SAE were desirable; so, TAE and SAE were defined as “the largest is the best” characteristic and expressed by Eq. (2). The described analysis was performed to optimize the geometric configuration³².

In this investigation, the effects of six factors, including fiber type, R, n, L, Y₂ and Y₁ were studied on TAE and SAE, in this study, R and n are the radius of curvature of specimen and number of composite plies, respectively.

In practice (Level^Factor), 729 specimens should be fabricated and tested by assigning three levels for each factor. These experimental tests are expensive and time-consuming, but by using the design of experiments based on the Taguchi method, the number of experimental tests can be reduced to 27.

Therefore, orthogonal array L₂₇ was selected as the DOE. Table 1 shows the effective factors and levels in the experimental design. The design of the Taguchi experiments and the SAEs, TAEs, and their SNRs of each experiment are given in Table 2.

Table 1.

Effective factors and DOE levels in the crushing of pangolin quasi-scale specimens.

Level	Fiber	R (mm)	n	L (mm)	Y2 (mm)	Y1 (mm)
Level1	Fiber glass	20	3	45	60	40
Level2	Luffa fiber	25	4	40	50	25
Level3	Linen fiber	30	5	35	40	10

Table 2.

DOE results obtained from experimental tests based on Taguchi method.

Trial no	Sample code	Fiber	R (mm)	n	L (mm)	Y2 (mm)	Y1 (mm)	TAE (J)	TAE SNR	SAE (J/g)	SAE SNR
1	PG01	Glass	20	3	45	60	40	1.6088	4.1300	1.2370	1.8474
2	PG02	Glass	20	3	45	50	25	1.1507	1.2192	1.1507	1.2192
3	PG03	Glass	20	3	45	40	10	0.9338	− 0.6024	1.3300	2.4770
4	PG04	Glass	25	4	40	60	40	1.23	1.7981	0.5125	− 5.8061
5	PG05	Glass	25	4	40	50	25	0.796	− 1.9817	0.7960	− 1.9817
6	PG06	Glass	25	4	40	40	10	0.7707	− 2.2623	0.9600	− 0.3546
7	PG07	Glass	30	5	35	60	40	1.5975	4.0688	0.9397	− 0.5402
8	PG08	Glass	30	5	35	50	25	0.9681	− 0.2816	0.8067	− 1.8658
9	PG09	Glass	30	5	35	40	10	0.8635	− 1.2748	1.0700	0.5877
10	PG10	Luffa	20	4	35	60	25	11.176	20.9655	1.007	0.0589
11	PG11	Luffa	20	4	35	50	10	9.723	19.7560	1.3140	2.3719
12	PG12	Luffa	20	4	35	40	40	6.86	16.7265	0.5600	− 5.0362
13	PG13	Luffa	25	5	45	60	25	8.2454	18.3242	0.7705	− 2.2645
14	PG14	Luffa	25	5	45	50	10	7.7926	17.8336	1.0670	0.5633
15	PG15	Luffa	25	5	45	40	40	4.8129	13.6481	0.5460	− 5.2561
16	PG16	Luffa	30	3	40	60	25	3.0149	9.5424	0.3200	− 9.8970
17	PG17	Luffa	30	3	40	50	10	2.17	6.7292	0.3800	− 8.4043
18	PG18	Luffa	30	3	40	40	40	1.9168	5.6515	0.2330	− 12.653
19	PG19	Linen	20	5	40	60	10	9.4062	19.4682	2.7665	8.8386
20	PG20	Linen	20	5	40	50	40	8.7779	18.8678	1.8700	5.4368
21	PG21	Linen	20	5	40	40	25	5.6683	15.0691	1.7700	4.9595
22	PG22	Linen	25	3	35	60	10	1.465	3.3168	0.7700	− 2.2702
23	PG23	Linen	25	3	35	50	40	1.39	2.8603	0.5800	− 4.7314
24	PG24	Linen	25	3	35	40	25	1.038	0.3239	0.5800	− 4.7314
25	PG25	Linen	30	4	45	60	10	3.818	11.6367	1.1900	1.5109
26	PG26	Linen	30	4	45	50	40	2.17	6.7292	0.5400	− 5.3521
27	PG27	Linen	30	4	45	40	25	2.0761	6.3450	0.6500	− 3.7417

Experimental study

Experimental setup

In this study, the construction of composite specimens can be divided into three steps. In brief, the construction of quasi-scale composite specimens is presented in the flowchart shown in Fig. 4.

Fig. 4.

Flowchart of composite quasi-scale specimens’ fabrication.

In the first step, wooden waved molds, which are economically produced, were employed, waxed, and then placed at room temperature for at least half an hour. The use of wax allows the composite specimens to be easily separated from the mold and prevents damage to the mold and the manufactured specimens. Figure 5 shows the waxed mold used for specimen construction.

Fig. 5.

Waxed mold for fabricating composite quasi-scale specimens.

Trapezoidal prototypes with certain dimensions, which were proposed based on the experimental design, were cut from glass fibers, linen plant fabric, and luffa plant fibers, as shown in Fig. 6.

Fig. 6.

(a) Dacron fabric and trapezoid prototypes made of: (b) Glass fibers, (c) Linen plant fabric, (d) Luffa plant fibers.

An unsaturated isophthalic polyester resin (MUO-040) procured from Rozitan Company served as the matrix.

Preparation of the resin mixture entailed adding cobalt and peroxide at concentrations of 0.2% and 1% of the resin weight, respectively, to ensure proper curing either before or during the resin gelation phase. The fabrication process for composite specimens was meticulously executed, with each type of fiber requiring specific handling.

The second step of the composite specimen construction differs according to the type of the trapezoid prototype; a manual lay-up method was employed for prototypes made of glass fibers and linen plant fibers.

For this purpose, the lower waxed wooden mold is coated with resin using a brush, and then a layer of Dacron fabric is placed on it. The resin then came from under the Dacron layer to its face by hitting with a brush, and this process was continued throughout the entire Dacron fabric.

Then, it is covered again with resin trapezoidal fabrics made of linen fabric or glass fibers are placed on the waved mold after Dacron is completely impregnated with resin. The resin spreads from Dacron fibers to linen fibers or glass fibers by brush hitting then it is smeared with resin by brush again, and the next trapezoidal layer of linen fibers or glass fibers is placed on the previous layer. This process is repeated for several layers of linen fibers or glass fibers as many layers as provided in the design of experiment as shown in Fig. 7a at the end of this step, the Dacron layer is placed on several layers of linen or glass fibers impregnated with resin, as illustrated in Fig. 7b.

Fig. 7.

Fabrication steps of composite quasi-scale specimens of glass fibers or linen plant fabric using the hand lay-up method: (a) placing the first Dacron fabric, glass fibers, or linen fibers on the lower wooden mold, (b) placing the second Dacron fabric on them.

The resins of the fibers spread to Dacron fibers, and additional resins are absorbed by the brush, leaving a polished surface for quasi-scale composite specimens with minimal resin absorption.

In the second stage of the construction of the composite quasi-scale specimen, luffa trapezoid prototypes were used. For this purpose, trapezoid prototypes with specifications provided from the experimental design were immersed in resin, as shown in Fig. 8.

Fig. 8.

(a) Luffa fibers and resin before immersion, (b) Immersion of luffa fibers in resin for fabrication of quasi-scale composite specimens.

The immersed trapezoidal prototypes were then placed on top of the lower waxed wooden mold, as illustrated in Fig. 9.

Fig. 9.

The luffa trapezoid prototypes impregnated with resin were placed on the wooden mold.

In the third step, the upper wooden mold puts on the lower one and weights were used to exert the necessary compaction force. Application of 20 kg weights during the fabrication process ensures adequate consolidation. Quasi-scale composite specimens are constructed by taking out the additional resin, as depicted in Fig. 10.

Fig. 10.

Trapezoidal prototype under loading to remove excess resin.

The fabricated composite quasi-scale specimens comprised of (a) glass fibers, (b) linen fibers, and (c) luffa fibers are presented in Fig. 11.

Fig. 11.

Composite quasi-scale specimens fabricated from (a) Glass fibers, (b) Linen fibers, (c) Luffa fibers.

The energy absorption characteristics of these specimens, guided by the designed experiments, were systematically investigated under quasi-static lateral compressive loading. Using a DMG model 7166 simple tensile test machine (depicted in Fig. 12), force–displacement data were recorded. The total absorbed energy (TAE) was inferred from the area beneath the force–displacement curve, with the specific absorbed energy (SAE) calculated by dividing the TAE by the specimen’s mass.

Fig. 12.

DMG model 7166 simple tensile test machine and a composite quasi-scale specimen during testing.

In adherence to the Taguchi method, a comprehensive array of 27 experiments was systematically designed, encompassing 6 influential factors across 3 distinct levels. Each experiment’s performance was assessed using the "larger is better" SNR calculation (Eq. 2), as detailed in Table 2. The overarching objective of the quasi-static crushing assessments was to augment TAE while concurrently reducing specimen mass, thereby necessitating a thorough examination of both TAE and SAE.

Materials properties

“Effect of the stacking sequence of the composite laminate on the SAE” section delved into the stacking sequence of composite laminates, observing negligible influence on the crushing process, thus justifying the quasi-isotropic approximation of the composite quasi-scale specimens. Following ASTM D3039-17 standards³³, composite samples fabricated from linen and glass fibers were fabricated and tested. Conversely, luffa fiber specimens were adhered to ASTM D638 for tensile testing preparations³⁴. The mechanical properties of these composites are summarized in Table 3.

Table 3.

Mechanical properties of composite specimens fabricated using luffa, linen, and glass fibers.

Fiber	Sy (MPa)	Su (MPa)	E (GPa)	m	k (MPa)	σ0 (MPa)
Glass	154.0531	154.0531	4.48	0.9543	3849.2	110.19
Linen	34.2909	18.24	0.47	0.5507	86.5108	20.083
Luffa	8.65	12.9686	0.185	0.8992	138.3269	7.68

Theoretical analysis

To elucidate the governing mechanisms of the crushing process and to inform the experimental design, the energy absorption behaviors of the composite quasi-scales were theoretically modeled. The process involved the transformation of the specimen curvature into a flattened configuration alongside plastic hinge formations. Molded with a wave-like pattern to mimic the quasi-scale geometry (Fig. 3), specimens were fabricated by arranging trapezoidal sections of luffa, linen, and glass fibers onto semi-cylindrical molds, as depicted schematically in Fig. 13.

Fig. 13.

(a) Schematic of the trapezoidal geometry and (b) the geometry of the manufactured quasi-scale specimens.

The parameters defining the trapezoidal geometry are described in Eqs. (10) to (11), with variables as illustrated in Fig. 13.

10

11

12

The variables in relations (10) to (11) are presented in Fig. 13. By dividing the trapezoidal geometry into simpler geometries, the total absorbed energy resulting from the transformation of the curvature of the quasi-scale specimen into a flat plane (E_Curvature) in the quasi-static crushing process will be as the following:

13

In relation (13), the stress, strain, and volume of the quasi-scale elements shown in Fig. 14 are σ, ε and dv, respectively.

Fig. 14.

The volumetric element used to calculate the TAE of the specimen.

The TAE in the crushing process can be calculated for the areas of (I) and (II), and the relations (14) to (15) can be extracted by the necessary calculations. The considered material model in these relations is the rigid perfect plastic (RPP).

14

15

The flow stress () is obtained as follows³⁵:

16

In the relation (14) to (15), S_u, S_y, m, t, θ₁, θ₂, L are ultimate strength, yield strength, strain hardening exponent, thickness, created small and large arcs, and height of the quasi-scale specimens, as shown in Fig. 13.

The TAE of the transformation of the curvature of the quasi-scale specimens into a flat plane can be obtained by substituting relations (14) to (15) into relations (13) as follows:

17

Relation (17) can be rewritten as a more tangible relation as follows:

18

Y₁, Y₂ and R are the small and large bases of the trapezoid and the radius of curvature of the manufactured quasi-scale specimens, respectively, as shown in Fig. 13. This part of the absorbed energy was caused by the normal stresses created along the thickness of the quasi-scale specimens, which turned the curvature of the specimens into a smooth and flat plane.

Another mechanism of energy absorption that occurs in the crushing process of quasi-scale specimens is the formation of a plastic hinge called an E_Hinge.

E_Hinge is caused by the created moment along the longitudinal line (L) of the specimens and the angle of rotation (θ _Hinge) that obtained by Eq. (22).

In most quasi-scale specimens, the number of plastic hinge formations during the crushing process is three, as illustrated in Fig. 15, and the absorbed energy is calculated by Eq. (19) for the RPP material model.

Fig. 15.

(a) Schematic of the steps of plastic hinge formation in the quasi-scale specimens, (b) Schematic of the formed quasi-scale specimen, (c) The formed quasi-scale specimens.

The TAE of the quasi-scale specimens was obtained by subsiding the Eqs. (19) and (17) into the Eq. (20), which is called E_Total.

19

20

21

22

θ_Hinge will be proved in the next sections.

Hollomon’s Eq. (23) was used to obtain the general theoretical equation for predicting the TAE of the quasi-scale specimens.

23

In Eq. (23), σ, k, ε, m are the stress, strength coefficient, strain, strain, and hardening exponent, respectively.

The Eqs. (26) and (27) were derived by instituting Eqs. (24) and (25) into (13) and considering the mechanism of converting the curvature of the specimens into a flat and smooth surface using the Hollomon material model.

24

25

26

27

The Eq. (28) are obtained by considering the plastic hinge formation mechanism.

28

The Eq. (29) shows the TAE of the quasi-scale specimens in the crushing process obtained by replacing the Eq. (27) and (28) into (20) and using the Hollomon material model.

29

θ_Hinge is replaced in Eq. (29), which is proved. For this purpose, the geometry of the quarter circle was considered, as shown in Fig. 16.

Fig. 16.

Schematic of the geometric relationship between the DMG jaw advance, the quasiscale specimen radius, and the plastic hinge angle.

From Fig. 16, we derive the following:

30

31

32

In Eqs. (30) to (31), δ, R, θ and θ _Hinge are DMG jaw advance, the radius of curvature of the specimen, the semi-rotation angle of the plastic hinge, and the rotation angle of the plastic hinge during the crushing process. The range of δ in Eqs. (30) and (31) is obtained from relation (33) according to Fig. 16. The maximum angle of the plastic hinge is calculated by placing the upper limit in the crushing process for the semicircle, as well as, it is derived for a sector of a circle by putting the upper limit of relation (34).

33

34

35

In this equation, Y₂ and γ are the sectors of the quasi-scale specimen and its opposite arc, respectively, as illustrated in Fig. 17.

Fig. 17.

Circular sector formation of base Y₂ and its opposite arc in the quasi-scales specimen.

As illustrated in Fig. 18, the quasi-scale specimen is controlled by side Y₂ during the crushing process when the plastic hinge forms.

Fig. 18.

The effect of the base Y₂ in the plastic hinge formation in the quasi-scales specimen.

Results and discussion

Experimental results

The main effects plots of TAE and SAE are shown in Fig. 19a,b, respectively, demonstrating the effect of each control factor on TAE and SAE.

Fig. 19.

The effects of control factors on (a) TAE and (b) SAE of the fabricated quasi-scale specimen.

Figure 19a shows the influence of various parameters, including geometric factors (Y1, Y2, L, t, R) and material properties (σ₀), on the total absorption energy (TAE) during the crushing process. The experimental results indicate that luffa plant fibers exhibit a higher energy absorption capacity than linen plant fibers and synthetic glass fibers. Additionally, an increase in the curvature radius of the specimens was observed to inversely correlate with the TAE, as anticipated by theoretical Eq. (21). This equation also predicts that the TAE should increase with increasing number of composite layers, height, and both the large and small bases of the specimens. However, the experimental trend, as analyzed by the Taguchi method, aligns with the theoretical predictions for all parameters except for the small base of the specimen, which exhibits minimal variation and contradicts theoretical expectations. This discrepancy necessitates further experimental investigation into the effect of the small base on TAE, under the assumption of constant values for other parameters, given that the Taguchi method may not adequately predict its impact because of its statistically insignificant effect on TAE in practical scenarios.

The SAE is a critical metric that warrants investigation, as specimens exhibiting higher SAE values are preferred for their enhanced performance. Figure 19b illustrates the main effects of the signal-to-noise ratio on the SAE of the specimens, providing insights into the parameter levels that contribute most significantly to this important property.

Figure 19b shows the impact of various parameters, including geometric factors (Y1, Y2, L, t, R) and material properties (σ₀), on the SAE during the crushing process. The experimental results demonstrate that linen plant fibers achieve a higher mean SNR than luffa plant fibers and synthetic glass fibers. The figure visually represents the SNR values at each level of the effective factors for SAE, enabling determination of their respective ranks.

Optimization

The optimal performance of the specimens, as determined by the Taguchi method, was predicted by selecting the highest level values for each factor, as illustrated in Fig. 19a,b. To verify these results, an optimal specimen should be fabricated and compared with the predictions made by the Taguchi method. The optimal performance of the process can be estimated using the following general formula:

36

In Eq. (36), Y_TAE is the optimal value or the maximum predicted value of quasi-scale specimens in the investigated domain. indicate the average experimental TAE results for all investigated specimens. Also Fiber^TAE, R^TAE, n^TAE, L^TAE, Y₂^TAE and Y₁^TAE are the average values of the TAE of the specimens at the optimal level of the parameters Fiber, R, n, L, Y₂ and Y₁ respectively as shown in Fig. 19a.

The most optimal set of parameters according to the objective of the DOE by the Taguchi method “the more TAE is better” are as follows: luffa fibers, radius of curvature 20 mm, number of layers 5, height 45 mm, large base 60 mm, and small base 10 mm.

According to Eq. (36), the predicted TAE for the optimal specimen is 11.2431 J. To verify the Taguchi method prediction, the optimal specimen was fabricated and subjected to experimental testing in the crushing process, yielding a TAE of 11.93 J. This result indicates a maximum error percentage of 5.76% for the optimal specimen, which is within the acceptable range.

Similarly, the optimal value of the specific absorption energy (SAE) can be determined using Eq. (36) for the crushing process of the quasi-scale specimens. Higher SAE values are more desirable, indicating superior performance. The maximum SAE was predicted by selecting the effective factors at their optimal levels, as illustrated in Fig. 19b. Based on the Taguchi method, we obtain.

The most optimal set of parameters for the purpose of “the more SAE is better” are as follows: linen fiber material, curvature radius 20 mm, number of layers 5, height 45 mm, large base 60 mm, and small base 10 mm.

The SAE of the optimal specimen was calculated as 2.3677 J/g. Experimental testing of the fabricated optimal specimen resulted in an SAE of 2.465 J/g, with an error percentage of approximately 3.94%, which is considered acceptable.

Effect of the stacking sequence of the composite laminate on the SAE

The specimen with code PG03 was considered to consist of two-dimensional woven glass fibers and was prepared by hand layup in three plies with the same direction of 0°, 30°, and 60° with codes of PG03D00, PG03D30, and PG03D60, respectively. It was found that the stacking sequence composite laminate did not significantly affect the SAE of the specimen, as shown in Fig. 20a.

Fig. 20.

Comparison of the SAE for the specimens with codes of PG03, PG11, and PG19 included of (a) Three plies glass fibers, (b) Three plies luffa fibers, and (c) Three plies linen fibers with same directions of 0⁰, 30⁰, and 60⁰ for each specimen.

Similarly, this result can be obtained for a specimen consisting of luffa and linen plant fibers, as illustrated in Fig. 20b,c, respectively.

Therefore, the stacking-sequence composite laminate is not an effective factor in the DOE by Taguchi method.

Investigation of contribution percentage of effective factors to the experimental results

The TAE and SAE are the performance criteria in the crushing process, and it is necessary to investigate the effects of the control factors. The various types of control factors have different effects on the TAE and SAE in the crushing process; therefore, it is essential to determine the percentage contribution of the control factors, as shown in Fig. 21a,b. For this purpose, the Eq. (9) was used.

Fig. 21.

Percentage contribution of different factors on (a) TAE and (b) The SAE.

The dependence of the TAE and SAE on the effective factors is different, as shown in Fig. 21a,b. and are the comparison of percentage contribution for various factors to the TAE and SAE, respectively. The percentage contribution of the factors to the TAE is expressed as follows:

Fiber type is 40%, the radius of the curvature is 27.799%, the number of composite plies is 22.53%, the large base and small base are 5.31% and 0.827%, respectively, and the height of the specimen is 0.1162%. In addition, these are for the SAE as follows:

The radius of the curvature is 42.737%, the number of composite plies is 20.602%, the fiber type is 14.868%, the height of the specimen is 2.852%, the large base and small base are 2.388% and 11.721%, respectively.

Validation of the experimental and theoretical results of the crushing process

It is necessary to carry out extra tests in addition to the DOE by Taguchi method presented in Table 4 to compare the influence of the effective factors in the crushing process on the theoretical and experimental results. For this purpose, fiber glass was used because it is easy to construct and access.

Table 4.

The experimental and theoretical results of supplementary tests other than the DOE were obtained using the Taguchi method.

Sample code	Weight (gr)	R (mm)	n	L (mm)	Y2 (mm)	Y1 (mm)	Experimental TAE Results (J)	Theatrical TAE Results (J)	Error%
PG28	2	20	4	40	60	40	1.8692	1.9670	5.232185
PG29	2.2	27.5	4	40	60	40	1.0733	1.0653	0.745365
PG30	2.2	30	4	40	60	40	1.0370	0.9235	10.94503
PG31	1.8	35	4	40	60	40	0.6930	0.7222	4.213564
PG32	2.2	25	4	45	60	40	1.287	1.4093	9.50272
PG33	3.2	25	5	40	60	40	2.2383	2.4391	8.971094
PG34	2.3	25	3	40	60	40	1.079	0.9275	14.04078
PG35	2.1	25	4	35	60	40	1.069	1.0961	2.53508
PG36	2.2	25	4	40	60	25	1.129	1.1916	5.54473
PG37	1.6	25	4	40	60	10	1.033	1.1305	9.438529
PG38	2.1	25	4	40	50	40	0.860	0.9506	10.53488
PG39	1.5	25	4	40	40	40	0.618	0.7027	13.7055

The experimental results based on the DOE by Taguchi method and the theoretical results obtained from Eqs. (21) and (29) are presented in Fig. 22a.

Fig. 22.

(a) Comparison of experimental results based on the DOE by Taguchi method and theoretical results; (b) Comparison of error percentages.

The rigid perfectly plastic material model was used to predict the behavior of specimens consisting of glass fibers and linen plant fibers, and the Hollomon material model was applied to the specimens consisting of luffa plant fibers.

The error percentage obtained from the theoretical results is calculated by Eq. (37) and presented in Fig. 22b.

37

In Eq. (37) Re_Experimenal and Re_Theoretical are the experimental and theoretical results, respectively.

Discrepancies between theoretical predictions and experimental outcomes can be categorized into two principal groups. The first cluster of errors arises from the fabrication of composite specimens, which is an inherently imperfect procedure when employing the manual hand-layup technique. Factors such as ambient temperature fluctuations, humidity variations, and inconsistent resin compaction pressures during specimen construction can contribute to this uncertainty. Despite diligent efforts to minimize these extraneous variables, their complete eradication is unfeasible, thereby introducing an inherent margin of error.

The second genre of discrepancies arises from the theoretical framework’s exclusion of alternative energy absorption mechanisms. The mathematical models employed do not comprehensively account for every real-world energy dissipation process that may occur during testing, thereby giving rise to a secondary source of discrepancy between theoretical calculations and empirical observations.

Percentage of energy absorption in the mechanisms of the crushing process in theoretical results

Two significant mechanisms of energy absorption are observed in the crushing process of quasi-scale composite specimens: the mechanism of converting the curvature of the specimens into a smooth plane (E_Curvature) and another is the formation of the plastic hinge (E_Hinge).

Equations (21) and (29) were used to calculate the value of each mechanism, as shown in Fig. 23.

Fig. 23.

Comparison of the energy absorption percentage in the mechanisms of the crushing process for different fiber types in composite specimens.

According to Fig. 23, the maximum energy absorption occurs in the plastic hinge formation mechanism, and this occurs in the composite specimens containing linen plant fibers.

Confidence interval of experimental results

Because the population parameter is usually unknown in statistical analysis, samples’ data are used to estimate it. For this purpose, a confidence interval is considered as the percentage of confidence (confidence level) that the population’s mean lies within its range.

In the present study, to obtain the population’s mean parameter, such as the SAE and TAE, Student’s t-distribution was used due to the unknown variance of the population.

The variance of the samples is used to estimate the population’s mean, provided that the statistical distribution of the population is normal or the sample’s size is more than 30 based on the central limit theorem.

In this study, the upper and lower limits of the confidence interval were obtained for estimating the population’s mean parameter of samples with 39 sizes using the following equation:

38

and are samples’ mean and margin of error, respectively, and obtained by the following equation:

39

40

, , and are critical value, the variance of the samples, sample size and of sample respectively that critical value is calculated by t table or software such as excel software by command that and are significance level and degree of freedom of samples, respectively, which they are calculated by following equation, respectively:

41

42

is confidence level and is calculated using the following equation:

43

is called standard of deviation of samples.

The confidence intervals obtained for population’s mean parameter such as TAE and SAE, are presented in Tables 5 and 6.

Table 5.

Confidence interval of population’s mean of TAE.

Confidence level	90%	95%	99%
Critical value	1.686	2.024	2.712
Variance of samples	9.238	9.238	9.238
Error margin	0.821	0.985	1.32
Samples’ mean	2.96	2.96	2.96
Confidence interval	(2.139, 3.78)	(1.974, 3.945)	(1.64, 4.279)

Table 6.

Confidence interval of population’s mean of SAE.

Confidence level	90%	95%	99%
Critical value	1.686	2.024	2.712
Variance of samples	0.246	0.246	0.246
Error margin	0.134	0.161	0.215
Samples’ mean	0.827	0.827	0.827
Confidence interval	(0.693, 0.961)	(0.666, 0.987)	(0.611, 1.042)

Effective factors in the theoretical and experimental results in the crushing process of the quasi-scale composite specimens

Investigation of the R effect (radius of curvature factor) on the quasi-scale composite specimens

From the derivations in Eqs. (21) and (29), it is evident that an escalation in the radius of curvature leads to a decrease in the total absorption energy (TAE) of the fabricated specimens. To rigorously validate this theoretical proposition against the empirical findings from the Design of Experiments (DOE) utilizing the Taguchi method, supplementary tests were imperative. In these additional assessments, all variables other than the radius of curvature were held constant. Specifically, specimens labeled PG04, PG28, PG29, PG30, and PG31 were selected for investigation.

The detailed characteristics of these specimens and the outcomes of their crushing tests are meticulously documented in Tables 2 and 4. To facilitate a visual comparison of the experimental results and to underscore the correlation between the radius of curvature and TAE, Fig. 24a presents a graphical summary, thereby consolidating the understanding of this pivotal relationship and affirming the synergy between theoretical propositions and empirical evidence.

Fig. 24.

(a) Effect of curvature on the TAE of the manufactured specimens, (b) Variation in the TAE with respect to the radius of curvature of the specimens and its comparison with the experimental results.

Augmentation in the radius of curvature is inversely associated with a decline in the total absorbance energy (TAE) of the specimens, as clearly demonstrated in Fig. 24a. This observed trend is corroborated by both the theoretical predictions and the outcomes derived from the Design of Experiments (DOE) employing the Taguchi methodology, as depicted in Fig. 24b. These converging lines of evidence emphasize the reliability of the theoretical framework and the effectiveness of the Taguchi method in anticipating the influence of the radius of curvature’s influence on energy absorption characteristics.

As illustrated in Fig. 24b, a notable correspondence exists between the empirical outcomes and their theoretical counterparts, which confirms the validity of the analytical framework.

To physically rationalize the connection between the radius of curvature and the total absorption energy (TAE) of specimens, Eq. (44) serves as a pivotal tool, where (M), (EI), and (K) denote the bending moment, flexural strength, and curvature, respectively.

44

The underlying principle involves envisioning the transformation of a planar surface into one with a specified curvature radius, thereby engendering a bending moment. A diminution in the radius of curvature amplify the curvature of the surface, thereby escalating the bending moment. Given that the TAE is directly proportional to the bending moment, as posited by Eq. (19), a decrease in the curvature radius intuitively leads to an enhancement in the energy absorption capability. Conversely, an enlargement in the radius of curvature diminishes the curvature, rendering the specimens flatter and less proficient at energy absorption.

Investigation of the t effect (thickness factor) on the quasi-scale composite specimens

The TAE exhibits a quadratic relationship with the thickness of the fabricated specimens, a finding consistently supported by Eqs. (21) and (29). Notably, this theoretical prediction aligns closely with the empirical evidence garnered from the application of the DOE utilizing the Taguchi methodology and additional experimental investigations, as vividly illustrated in Fig. 25a. This concurrence signifies a robust correlation, reinforcing the validity and predictive power of the theoretical models in the context of understanding the thickness-dependent energy absorption dynamics.

Fig. 25.

Variation of the TAE with respect to: (a) The thickness of the specimens and (b) The height of the specimens and their comparison with the experimental results.

An increase in specimen thickness directly influences the overall dimensions of the fabricated samples, consequently exerting a direct impact on the total absorption energy (TAE), a consequence that is both intuitive and anticipated. To delve deeper into this phenomenon, reference to Eq. (44) provides a rigorous basis for exploring the effect of thickness on energy absorption.

Specifically, when the thickness of a specimen is increased while maintaining constant values for the radius of curvature and flexural strength, the required bending moment for the specimen increases. In accordance with Eq. (19), this leads to a subsequent increase in TAE, underscoring the direct influence of the thickness on the energy absorption capability.

To further elaborate, consider a sheet with dimensions (t) (thickness) and (L) (length). The stress within this sheet can be quantified using Eq. (45), thereby emphasizing the fundamental mechanics at play. The sheet transitions into the plastic deformation regime as the crushing process advances. Adopting the Rigid Perfectly Plastic (RPP) material model, it is postulated that the normal stress remains constant throughout this plastic region. Consequently, an increase in specimen thickness necessitates a proportional increase in the bending moment, which is in line with the RPP assumption. Ultimately, this heightened bending moment, as per Eq. (19), translates into a marked elevation in the total absorption energy, affirming the pivotal role of thickness in dictating the energy absorption dynamics.

45

Investigation of the L effect (height factor) on the quasi-scale composite specimens

According to the formulations presented in Eqs. (21) and (29), a direct correlation was established between the height of the specimen and its total absorption energy (TAE). This finding is corroborated by the outcomes derived from the Design of Experiments (DOE) employing Taguchi methodology, which further validates the existence of this positive relationship. Notably, the theoretical predictions concerning the height-TAE relationship showed a high degree of concordance with the empirical observations, highlighting the reliability and predictive power of the theoretical models in aligning with the actual experimental results.

As depicted in Fig. 25b, the total absorbance energy (TAE) exhibits a linear correlation with the height of the specimens. This observation finds its physical rationale echoed in Eqs. (44) and (45), which mathematically substantiate the direct relationship between the TAE and the height, akin to the interpretation of thickness in energy absorption mechanics. Thus, the elevation in specimen height, which is akin to an increase in thickness, logically contributes to a proportionate rise in energy absorption capacity, reinforcing the significance of geometric dimensions in determining the energy absorption performance.

Investigation of Y₁ and Y₂ effects (small base and large base factor) on quasi-scale composite specimens

The total absorption energy (TAE) demonstrates a direct proportional relationship with the small base dimension, conforming to a linear pattern, and conversely, its relationship with the large base is characterized by a nonlinear yet positive correlation, as elaborated in Eqs. (21) and (29). Notably, the theoretical predictions concerning TAE’s dependency on the large base dimension align favorably with the supplementary experimental outcomes and the empirical data garnered from the Design of Experiments (DOE) employing the Taguchi methodology, as evidenced in Fig. 26a. This congruence fortifies the reliability of the theoretical frameworks and underscores the robustness of the empirical findings in capturing complex energy-absorption dynamics.

Fig. 26.

Variation of the TAE with respect to: (a) large base of the specimens and (b) small base of the specimens and their comparison with the experimental results.

Supplementary experimental investigations and complementary theoretical analyses, as depicted in Fig. 26b, revealed an ascending trend in total absorption energy (TAE) concomitant with an increase in the small base dimension of the specimens. This observation intriguingly contrasts with the outcomes derived from the Design of Experiments (DOE) utilizing the Taguchi method, which suggested a largely consistent, or invariant, relationship between TAE and the small base, as evidenced in Fig. 19a. The aforementioned discrepancy prompts further exploration and reconciliation of these findings to attain a more nuanced understanding of the contributing factors to energy absorption dynamics.

Notably, an expansion in both the small and large base dimensions of the specimens inherently increases their volume, subsequently elevating the total absorption energy (TAE) during the crushing process.

The emergence of plastic hinges, pivotal to energy absorption, is governed predominantly by the large base dimension of the quasi-scales, introducing a nonlinear relationship between TAE and the large base, as depicted in Fig. 26a. To elaborate, envisioning the large base (Y2) as a beam with a rolling support of fixed width enduring only the lateral force (F) offers insight into this nonlinearity.

Advances in the crushing process transform the arc length (Y2) into a flattened configuration, necessitating the calculation of the applied moment via Eq. (46), which underscores how an increase in arc length, while keeping other variables constant, amplifies the moment arm and consequently the applied moment. In accordance with Eq. (19), this boosts the TAE. The parallel rationale applies to the arc length (Y1).

46

The veracity of Eq. (46) is further supported upon examining the effect of increasing the curvature radius (R): under constant other parameters, a decrease in applied moment ensues, thereby reducing TAE, aligning seamlessly with the conclusions of the preceding sections. Referring to Fig. 26b and ancillary experimental outcomes, the marginal difference of 0.197 between the maximum and minimum values, coupled with a slope of approximately 0.0065 near zero from the line of best fit through experimental data, underscores a minimal variation with respect to changes in the small base. This observation agrees with the DOE-Taguchi findings, reinforcing the notion that the small base’s influence on TAE is effectively consistent, thereby validating the study’s statistical approach. A bio-inspired sandwich panel with a pangolin quasi-scales core is shown in Fig. 27.

Fig. 27.

Bioinspired sandwich panel with pangolin quasi-scales core.

The findings of other researchers who studied energy absorbers consisting of sandwich panels are shown in Table 7 various geometries, materials, and arrangements have been used in their construction. Natural materials such as flax, coconut mesocarp, and synthetic materials including glass fibers, carbon fiber, and foam filler for increasing energy absorption, and also metals were used. According to the table, SAE, which is an effective factor for the evaluation and selection of energy absorbers, was presented. Therefore, the mentioned table can be used to compare the SAE of composite quasi-scale specimens of natural materials with those of other studies.

Table 7.

Comparison of the results of the present study with those of other researchers.

Type of structure	Material	SAE(J/g)	References
Sandwich panel with corrugated core	Glass fiber with Ecofoam GP330 insertion	0.6	36
	Carbon fiber with Ecofoam GP330 insertion	0.82
	Glass and carbon (50:50) with the Ecofoam GP330 inserted	0.65
Sandwich panel with a square single-wall core	Flax/PLA	0.48	37
The sandwich panel with cubic core	Coconut mesocarp core with reinforced glass-fiber plastic	1	2
	Coconut mesocarp core with reinforced carbon fiber plastic	0.91
The sandwich panel with square core	Flax/PLA	0.90	38
	PP/Flax	3
The sandwich panel with triangular core	Flax/PLA	0.8
	PP/Flax	2.7
Two-layered sandwich panel with a Trapezoidal corrugated core	Aluminum alloy core, face sheets, and interlayer sheet with regular arrangement	1.1112	39
	Aluminum alloy core, face sheets, and interlayer sheet with symmetrical arrangement	4.1774
Composite quasi-scale specimen	Linen fibers/polyester resin	2.76	Present work
	Luffa fibers/polyethylene resin	1.31

The composite quasi-scale specimens can be used for energy absorption instead of synthetic materials that are not recyclable to nature and have equal or lower SAE than composite quasi-scale specimens provided that there are no special considerations. Therefore, the results of the specific absorbed energy obtained from the quasi-static crushing process in the present study were compared with the research works conducted by other researchers and are presented in Table 7.

Conclusion

This study focused on the fabrication, optimization, and characterization of bio-inspired composites quasi-scale specimens inspired by the skin structure of pangolin. The DOE and Taguchi methods were applied to select the best specimen, which yielded an 11.2431 J of TAE and 2.3677 J/gr of SAE, created from luffa and linen plant fibers. The experimental results showed that TAE is highly dependent on the thickness, height, small base, and large base, but less so on the radius of curvature. The experimental values for linen and glass fibers using the rigid perfectly plastic (RPP) model and for luffa fibers using the Hollomon model agreed well with the theoretical values. Analysis of theoretical data indicated that TAE increases in direct proportion to height and base dimensions but increases nonlinearly with the base and thickness. However, TAE had a negative correlation that varied nonlinear with the radius of curvature. Surprisingly, the DOE-Taguchi analysis revealed that the radius of curvature had the largest effect on SAE, and the ply count, fiber type, large base, small base, and height had the second largest effect on SAE. The analysis for TAE showed that fiber type was the most influential factor, with the radius of curvature, ply count, large base, small base, and height also being important. The findings also supported the proposition that the SAE was almost unaffected by the stacking sequence, as assumed under the quasi-isotropic condition in these composite systems when crushed. The energy dissipation modes were found to be curvature transformation to a planar configuration and plastic hinge formation, where the latter was found to be more dominant in the linen-fiber-reinforced specimens. Hence, an ideal sandwich panel design was recommended using the high-thermal-assisted machining (HTAM) quasi-scale composite specimens. The SAE observed during the crushing process was higher in panels constructed with linen plant fibers than in panels made from industrial glass fibers. The objective of this work is to investigate the possibility of using linen and luffa, which are natural materials, as more environmentally friendly alternatives to synthetic and damaging materials in sandwich panel structures. This work is beneficial as it transforms materials into biobased materials and increases their recyclability. It also advances sustainable energy-absorbing composites for future use. These results imply that it is necessary to encourage the use of sustainable materials in industries to promote environmental protection in the future.

Author contributions

IKF performed the study’s conception, design, and data collection and analysis. AN and HZZ supervised the study, analyzed the data, and prepared the manuscript. All authors have reviewed and approved the final manuscript.

Data availability

All data generated or analysed during this study are included in this published article.

Declarations

Competing interests

The authors declare no competing interests.