Computational Parametric Analysis of Cellular Solids with the Miura-Ori Metamaterial Geometry under Quasistatic Compressive Loads

the SEA value of the model increase ﬁ rst and then decrease, and the SEA value is the largest when the value of b A is close to a A . The above conclusions provide a preliminary basis for future research on the practical engineering applications of the MMG cellular solids for energy absorption purposes. Future studies based on the-state-of-the-art fabrication methods such as metal 3D printing and glue bonding can be used to develop experimental models and perform compression tests to verify the simulation results.


Introduction
With the development of computer science, computational geometry, and graph theory, origami design and analysis techniques have developed rapidly over the past few decades. [1][2][3][4][5][6][7][8][9][10][11] Importantly, in recent years, origami techniques have been applied to a broad range of design problems in various fields of science and engineering. [12][13][14][15][16][17] In particular, researchers have discovered a range of desirable properties such as negative Poisson's ratio, [18][19][20] programmable morphology, [21][22][23][24][25][26][27] and energy absorption capacity [28][29][30][31][32][33][34][35] in some origami structures and have demonstrated them using various analytical, numerical, and experimental methods. [36] Miura-ori, as a classic fourfold origami tessellation, was first invented by K. Miura and applied to foldable solar panels. [24,37] Wang et al. [38] combined the re-entrant honeycomb concept with the Miura-ori pattern to create an origami metamaterial with programmable Poisson's ratio and multidirectional auxeticity. Yasuda et al. [39] explored reentrant 3D origami structures based on the Tachi-Miura polyhedron that exhibits both adjustable negative Poisson's ratio and structural bistability. Based on graph theory and group theory, Chen et al. [20][21][22] proposed a range of analytical and numerical methods for the design and analysis of origami structures. Schenk and Guest [40] proposed a metamaterial based on the Miura-ori and analyzed its geometric relationships, density, Poisson's ratio, and kinematic behavior. Wei et al. [41] explored the Poisson's ratio of the Miura-ori folded layer and established the geometric mechanics of the single-layer Miura-ori. Zhang et al. [42] revealed that the strength and densification strain of the Miura-ori metamaterials cannot be uniquely associated with their relative density. They concluded that the Miura-ori metamaterials had better energy absorption efficiency compared with honeycomb materials. Xiang et al. [43] introduced a gradient into the metamaterial structure and concluded that its energy absorption efficiency is better than that of a uniform metamaterial structure. Combining a large-displacement form-finding and dynamic characterization finite-element (FE) model, Sychterz et al. [44] successfully captured the kinematic properties of the motion of folded and rolled Miura-ori origami structures.

DOI: 10.1002/adem.202201762
Origami-based metamaterials have widespread application prospects in various industries including aerospace, automotive, flexible electronics, and civil engineering structures. Among the wide range of origami patterns, the fourfold tessellation known as Miura-ori is of particular attraction to engineers and designers. More specifically, researchers have proposed different 3D structures and metamaterials based on the geometric characteristics of this classic origami pattern. Herein, a computational modeling approach for the design and evaluation of 3D cellular solids with the Miura-ori metamaterial geometry which can be of zero or nonzero thicknesses is presented. To this end, first, a range of design alternatives generated based on a numerical parametric model is designed. Next, their mechanical properties and failure behavior under quasistatic axial compressive loads along three perpendicular directions are analyzed. Then, the effects of various geometric parameters on their energy absorption behavior under compression in the most appropriate direction are investigated. The findings of this study provide a basis for future experimental investigations and the potential application of such cellular solids for energy-absorbing purposes.
Much of the research on the Miura-ori metamaterials has been carried out through numerical methods. Heimbs [45] and Fischer [46] applied the Miura-ori pattern to a sandwich folded core and subjected it to bending, quasistatic compression, and low-and high-velocity impact tests. By comparing the experimental results with numerical simulations, they found that the two results were in satisfactory agreement. Their work demonstrated that numerical methods can be utilized to predict the mechanical behavior of the Miura-ori metamaterials. Zhang et al. [47] performed quasistatic in-plane compression tests on the Miuraori metamaterials and honeycomb structures. The results showed that the Miura-ori metamaterials had better energy absorption efficiency. In addition, Lv et al. [48] conducted quasistatic tests on the Miura-ori-patterned sheets and their corresponding sandwich panels. Considering the cell wall thickness, dihedral angle, and side length, they performed a FE parametric study. The results showed that smaller dihedral angles or thicker cell walls led to better energy absorption performance. Furthermore, smaller acute angles resulted in lower initial peak force, but higher average force.
Qiang et al. [49] modeled the quasistatic compressive response of the Miura-ori metamaterials in two principal directions. The results showed that the analytical results agreed well with experiments and FE simulations when the structure was subjected to out-of-plane compression. Besides, the analytical model could better predict the initial force in the in-plane compression. Xiang et al. [50] conducted numerical studies on the compressive behavior of nylon Miura-ori metamaterials under quasistatic and impact loads. The initial peak force under the impact load increased with the acute angle. The negative gradient model had better energy absorption ability.
Previous research has shown that gradient origami structures have great potential for energy absorption purposes. To further increase the energy absorption efficiency of Miura-ori-patterned sheets, Ma et al. [51] proposed a graded stiffness Miuraori-patterned structure in out-of-plane directions, the basic idea of which is to vary the geometric dimensions for each layer of the Miura-ori sheet. Their work pointed out that graded Miura-ori structures exhibited better energy absorption efficiency than uniform structures. Yuan et al. [52] proposed and analyzed a novel design based on the Miura-ori under quasistatic compression. They demonstrated that the new design of 2D and 3D gradient structures could produce periodic gradient stiffness and excellent energy absorption. Li et al. [53] investigated the dynamic crushing of a novel periodic origami-inspired cellular structure. The results showed that the gradient design effectively improved the energy absorption performance of such a structure.
In addition to the cell wall thickness, there are five other independent parameters that affect the geometry of the Miura-ori metamaterial cell, which subsequently influence the energy absorption behavior of the structure. Thereafter, the aim of this study is to gain an understanding of the effect of different parameters on the energy absorption behavior of the Miura-ori metamaterials. FE analysis using Abaqus is utilized to investigate the effects of wall thickness, sector angle of the first layer, sector angle of the second layer, dihedral angle of the first layer, and side length of the first layer on the energy absorption efficiency of the structures. Figure 1A shows a partially folded configuration of a 2 Â 2 cell of the Miura-ori, hereafter called "the cell," that consists of four identical parallelograms. The geometry of the cell can be described using the two sides of the parallelogram facet, with lengths a and b, along with the angle between them denoted by γ. Moreover, the dihedral angle θ between the parallelogram facet and the XY plane is used to quantify the degree of folding. [23,45] Using these variables, the geometry of the cell can be determined by the following parameters

Geometric Configuration of the Miura-Ori metamaterial
S ¼ ðb tan γ cos θÞð1 þ tan 2 γ cos 2 θÞ À0.5 www.advancedsciencenews.com www.aem-journal.com L ¼ a ð1 À sin 2 γ sin 2 θÞ 0.5 (4) where H is the height of the cell along the Z-direction, 2S is the length of the cell along the X-direction, and V þ 2L is the length of the cell along the Y-direction. As shown in Figure 1B, by repeating the cell M times in the Xand N times in the Y-directions, we can form an M Â N array which represents a finite Miura-ori sheet (in the depicted case, M = N = 5). Such a partially folded Miura-ori sheet can be regarded as a thin shell structure. According to the geometric configuration of the Miura-ori cell, the coupling of the cell expansion in the Xand Y-directions only depends on the angle between side b and the Y-axis. Therefore, Miura-ori sheets with different values of H can be stacked and bonded along the fold lines while maintaining rigid foldability. [40] A typical Miura-ori metamaterial is obtained by alternate stacking of the Miura-ori layers with patterns A and B, as depicted in Figure 1C. In order to ensure the geometric coordination of these layers during the folding and unfolding processes, they must satisfy the following requirements: [37] In other words, the geometric parameters of the B-layer sheet must satisfy Therefore, we obtain six parameters that determine the geometry of Miura-ori metamaterials, including the thickness h of the cell wall, the sector angle γ A of the A-layer sheet, the sector angle γ B of the B-layer sheet, the dihedral angle θ B (0 ≤ θ B ≤ π/2) of the A-layer sheet, the side length a A of the A-layer sheet, and the side length b A of the B-layer sheet.
In this article, we investigate the structural behavior of cellular solids with the Miura-ori metamaterial geometry, hereafter called the MMG cellular solids, which consist of multiple bonded layers of nonzero-thickness prefolded Miura-ori sheets. In particular, based on the abovementioned parameters, we perform an extensive study on how these parameters affect the quasistatic compression characteristics of the MMG cellular solids.

Parametric Modeling
Although there are several existing computational methods in the literature for establishing the 3D models of origami structures, they are often restricted to single-layer and zero-thickness origami models. [54][55][56] In general, such conventional modeling methods construct a model by offsetting the surface of the intermediate layer in the structural configuration. However, the Miura-ori metamaterial geometric model is composed of spatial facets with different dihedral angles; [57][58][59] consequently, if the facets are offset using the conventional methods, there will be blends or voids between adjacent facets.
To establish accurate models for the MMG cellular solids, which consist of multiple bonded layers of nonzero-thickness prefolded sheets, we introduce a computer-based modeling approach. To this end, we construct a 3D model by actively extruding the side sections of the structure along a specified path.
As illustrated in Figure 2, we first determine the cell parameters on the XZ plane and the parameters of the extrusion path. Then, a datum plane on the XZ plane and a path on the XY plane are generated by inputting M, N, O, and the wall thickness h. Finally, the datum plane is extruded along the path to obtain a solid model with nonzero thickness. The geometric relationship is established by where f A and f B are the one-sided offset lengths of a A and a B , respectively. It is worth noting that a zero-thickness model can also be obtained by setting h = 0.

FE Modeling
We use the FE package Abaqus/Explicit to simulate the quasistatic axial compression of the MMG cellular solids, as shown in Figure 3A. The model is placed between a fixed rigid plane and a downwardly moving rigid plane (all degrees of freedom of the fixed plane are constrained, and only the translation of the moving plane along the X-axis is unconstrained). The model itself is set to general contact, while the interfaces between the MMG solid model and the planes are set to point-to-surface contact. The maximum compressive distance is set to 85% of the length of the model in the compression direction. According to the mesh convergence test, the reduced-integration four-node shell elements S4R are used to mesh the model with an average mesh size of 2 mm. The two rigid planes are meshed with the R3D4 elements. The analysis time step is set to 0.02 s. To guarantee convergence in simulation, the smoothed analysis approach is adopted. In addition, two energy constraints should be satisfied when performing the simulation: 1) the ratio between kinetic energy and internal energy should be less than 5% to ignore dynamic effects and 2) the ratio of artificial energy to internal energy should be less than 6% to avoid the hourglass effect. The material of all models is the 6061-T6 aluminum alloy. In order to verify the accuracy of the computational model used in this study, we performed a numerical simulation based on the quasistatic experimental test carried out by Zhang et al. [42] The force-displacement curves of our numerical simulation are presented in Figure 3B along with those of the theoretical model and the experimental test. As can be seen from the figure, our numerical simulation results are in good agreement with the theoretical and experimental results.

Mechanical Performance Indices
The energy absorption capacity of the MMG cellular solid can be characterized by the total amount of energy absorbed E, which is calculated by www.advancedsciencenews.com www.aem-journal.com where W 1 is the effective compressive length, which is 70% of W f (the total compressive length of the model in this paper). F c (x) represents the compressive force corresponding to the compressive displacement x.
At the initial stage of compression, the structure undergoes buckling behavior, resulting in an initial peak force F max . The value of F max depends on the elastic-plastic buckling strength of the structure and material. If it is too high, the structure will be difficult to be crushed. As such, it should be controlled within a certain range. In addition, we introduce specific energy absorption (SEA) to assess the energy absorption capacity of the MMG cellular solids with different geometric parameters. Besides, SEA can characterize the light weight of the structure. It is defined as the energy absorbed per unit mass of the structure.
where m is the mass of the structure.

Identification of the Principal Compression Direction
In this section, we quantitatively assess the mechanical properties of a "base" MMG cellular solid model under quasistatic compression along the X-, Y-, and Z-direction. This aims to identify a principal loading direction along which the structure has the best energy absorption behavior. The lengths W 1 and W f of a base MMG cellular solid model in the three X-, Y-, and Z-directions are listed in Table 1. Figure 4 shows the deformation process of the model in these directions. When the X-direction compressive distance W X is 4.9 mm, the stress of the structure is below 200 N mm À2 . When W X = 67.0 mm, part regions of the structure reach a yield strength of 300 N mm À2 . The auxetic behavior of the Miura-ori metamaterial can be observed throughout the compression process. When the Y-direction compressive distance W Y is 4.5 mm, the stress of the structure is below 200 N mm À2 . Part regions of the structure reach a yield strength of 300 N mm À2 at W Y = 59.77 mm. When performing the Y-direction compression, the X-direction length of the model decreases and the Z-direction height increases. The stress of the model is below 200 N mm À2 at W Z = 6.7 mm. When W Z = 65.0 mm, more materials in the model reach yield. In the early and middle stages of compression, the middle part of the model tends to shrink inward, which is characteristic of auxetic materials. In the later stage of compression, the Xand Z-directions begin to expand outward as the material gradually densifies. www.advancedsciencenews.com www.aem-journal.com Figure 5 depicts the force-displacement curves of the MMG cellular solid under compressions along the X-, Y-, and Z-directions. It can be noticed that there is an initial peak force F max of 11.42 kN in the early stage of the X-direction compression. There is no initial peak force during the Yand Z-direction compressions. The corresponding compressive forces are also larger than that of the X-direction.
The SEA and the total absorbed energy of the model are listed in Table 1. It can be found that the SEA in the Z-direction compression is larger than those in the Xand Y-direction compressions. This is because the stiffness in the Z-direction is the largest, and the energy consumption mainly depends on the deformation of facets rather than plastic strains at the creases. According to the above results, we can conclude that the considered MMG cellular solid model exhibits the best energy absorption capacity along the X-direction.

Influence of h
In order to investigate the effect of the cell wall thicknesses h on F max and SEA for the MMG cellular solid, four sets of comparative test models are established based on the base model. The parameters of the models are shown in Table 2. Except for the thickness, the other geometric parameters are identical.
The force-displacement curves of five MMG cellular solid models are depicted in Figure 6A. It can be observed that the force-displacement curves of the five models show similar trends. In the initial stage of curves, the compression force F c shows a linear upward trend, reflecting the elastic mechanical response of the structure. After increasing to the initial peak force F max , the value of F c begins to decrease gradually. After that, F c remains almost unchanged with the increase of the compressive displacement, which means that the structure is in the energy consumption stage. After the compression reaches a certain level, the compression force begins to increase significantly until the limit displacement W f .
In Table 2, it can be seen that as the cell wall thickness increases, the mass and absorbed energy of the model increase. Besides, the thicker the cell, the larger the initial peak force F max , which is consistent with the experimental results by Zhang et al. [42] Compared with the base model MMG-1, the h, E, and F max of MMG-1-1 are increased by 16.67%, 45.56%, and 31.79%, respectively, whereas those of MMG-1-4 are decreased by 43.33%, 75.57%, and 62.52%, respectively. It can also be observed that the model with a larger wall thickness has a larger SEA. The SEA of MMG-1-1 and MMG-1-4 is 25.26% higher and 56.91% lower than that of MMG-1, respectively. However, increasing the thickness of the model results in an increase in the mass and relative density of the model. In other words, origami structures lose their lightweight advantage. Additionally, excessive initial peak force makes the model less prone to collapse. Therefore, we must be careful with the wall thickness of origami structures to ensure their lightweight and energy absorption efficiency.
The energy-displacement curves of MMG-1, MMG-1-1, and MMG-1-4 are listed in Figure 6B. Each set of curves is composed of an internal energy-displacement curve and a plastic dissipation energy-displacement curve of the model. They reflect the proportion of plastic dissipation energy to total internal energy in the compression process of the entire model. It is shown that the energy dissipated by plastic deformation accounts for the main part during compression.

Influence of Other Geometric Parameters of the Cell
The cell wall thickness does not change the overall size of the model, while the other five geometric parameters do. They are Figure 3. A) FE model of a typical MMG cellular solid. B) Force displacement curves obtained from the theoretical model, numerical simulation, and experimental test. Partially reproduced with permission from [42] Copyright 2023, Elsevier. www.advancedsciencenews.com www.aem-journal.com the sector angle γ A and γ B of the thin sheet of A and B layers, the dihedral angle θ A of the A-layer sheet, and the side lengths a A and b A of the A-layer sheet. To study the effects of these five parameters on the energy absorption efficiency of Miura-ori metamaterial structures, we designed five sets of comparative experimental models respectively. The thickness of each cell wall is taken as 0.3 mm.

Influence of a A
Four sets of comparative models are set up to investigate the effect of side length a A on energy absorption. The specific parameters of the models are listed in Table 3. The increase of a A increases the panel area, resulting in an increase in the mass of the model. According to the geometric model of the cell in Figure 1A, the a A side of the panel is in the YZ plane. Therefore, the change of a A does not affect the length of the X-direction of the model, which is also supported by the data in Table 3. It can be noticed from Figure 7A that the initial peak forces of the five models are relatively close, namely, 11.31, 11.25, 11.63, 12.52, and 13.18 kN. This indicates that the change of a A has little effect on the initial peak force of the model. When the a A of the MMG cellular solid is decreased and increased by 40%, its SEA is increased and decreased by 64.76% and 34.13%, respectively. It can be seen that the increase of a A not only increases the mass of the model, but also reduces its SEA. Apparently, part of the reason for this increase in energy absorption efficiency is the increase in relative density. In particular, based on the data in Figure 3B, we calculated the SEA value for the structure in ref. [42], in which a A = a B = 20 mm, to be a relatively low value of 0.57. Therefore, a reasonable selection of a A is required to  www.advancedsciencenews.com www.aem-journal.com design high-performance MMG structures. Figure 7B shows the corresponding energy-displacement curves of three MMG models with different values for parameter γ B .

Influence of γ B
Four sets of comparative experiments are designed to investigate the effect of sector angle γ B on energy absorption. The specific parameters are shown in Table 4. The increase of γ B does not affect the length of the model in the X-direction, but it will increase the mass of the model. It can be seen from Figure 8A that the ultimate compression force of MMG-9 is the largest, reaching about 370 kN. Moreover, the ultimate compression force of the other four models is below 250 kN. All five models have initial peak force F max with little difference. When the γ B of the MMG cellular solids is decreased and increased by 13.3%, its SEA is increased and decreased by 104.52% and 55.12%, respectively. It can be seen that the increase of γ B will lead to the decrease of SEA and the mass of the model. However, if γ B is relatively small, the selection range of γ A will become much smaller. Therefore, it is necessary to reasonably select γ B as the geometric parameter of the MMG cellular solid. It can be observed from Figure 8B that the plastic dissipation energy proportions of the three curves and the trends are similar. Changes in γ B have a negligible effect on the total energy absorbed by the model.

Influence of γ A
Four sets of comparative models are set up to investigate the effect of sector angle γ A on the energy absorption of the MMG cellular solid. The specific parameters of the models are listed in Table 5. It can be seen that the increase of γ A makes the X-direction length of the model increase, while the mass of the model decreases.
From the force-displacement curves in Figure 9A, it can be seen that the ultimate compression force of MMG-5 is the largest, reaching about 380 kN. When γ A = 70°, MMG-3 has a maximum initial peak force of 19.12 kN, which is much greater than that of the other models. Generally, when γ A is smaller than 60°, its variation has no effect on the initial peak force F max . The relative densities of MMG-4 and MMG-1 are 0.095 and 0.107, respectively. The reason for the change in the ultimate compressive force of the model is that a higher density produces a higher compressive force. [42] When the γ A of the MMG cellular solid is decreased and increased by 16.67%, its SEA is increased and decreased by 104.52% and 28.16%. It can be seen that as γ A increases, the SEA value of the model also increases. Figure 9B shows the energy curves of MMG-2, MMG-3, and MMG-5. It can be found that MMG-5 has the largest proportion of plastic dissipation energy to internal energy, and MMG-3 has the largest total internal energy.
In a word, increasing γ A can reduce the mass of the model and increase the total amount of energy absorption, significantly increasing the SEA value. This feature is well suited to our demand for both lightweight structure and high-energy absorption capacity. Table 6, four sets of contrasting models were established to investigate the effect of dihedral angle θ A on energy   absorption. The increase of θ A , corresponding to the increase of the dihedral angle of the cell, leads to the decline of the length of the model in the X-direction. Since only the inclination of the cell is changed, changes in θ A do not change the mass of the model. It can be seen from Figure 10A that the initial peak force of MMG-10 is the largest, reaching 36.54 kN, which is 223.08% greater than that of MMG-1. The initial peak forces of MMG-1, MMG-12, and MMG-11 are 11.31, 7.87, and 18.81 kN, respectively, while MMG-13 has no initial peak force. It can be seen that when θ A = 15°, the initial peak force is much larger than that of the other models. It can be seen from Figure 10B that the energy absorbed by MMG-13 is small. From the data in Table 6, it can be seen that the increase of θ A will lead to a decrease in the total absorbed energy and the SEA. Since the change of θ A does not affect the quality of the model, it is only necessary to consider its influence on the total energy absorption when choosing. Table 7 have been established to investigate the effect of side length b A on energy    absorption. Similar to a A , the increase of b A increases the cell wall area and the mass of the model. In Figure 11A, it can be noticed that the initial peak force of MMG-19 is the largest, reaching 15.62 kN, which is 38.11% larger than that of MMG-1. No effect of changes in b A on the initial peak force F max was found. As b A increases, the SEA of the model first increases and then decreases. When b A is close to a A , the SEA is the largest. Therefore, variations in the mass of the model and a A should be comprehensively considered when selecting b A in practical applications. The three curves in Figure 11B have little difference in the proportion of plastic dissipated energy. However, in terms of the total amount, the closer the b A is to a A , the more energy the structure will absorb.

Comparison and Validation of Energy Absorption Properties
In order to validate the numerical model utilized in this study, in this section, we use the model to simulate the quasistatic compression of the MMG cellular solid presented in ref. [42]. The geometric design configurations and force-displacement curves of the two structures are shown in Figure 12.
Based on the results of the parametric analyses presented in Section 4.1 and 4.2, the structure MMG-0 with excellent energy dissipation performance was selected to compare with the experimental structure of Zhang et al. [42] denoted by MMG exp . In this section, we have also simulated the quasistatic compression   Figure 10. Mechanical properties of models with different values for parameter θ A . A) Force-displacement curves. B) Energy-displacement curves. process of the experimental model, MMG exp , to verify our numerical model. The structure MMG-0 has a A = b A = 10 mm, θ A = 20°, γ A = 60°, γ B = 75°, and a wall thickness h = 0.171 mm. The geometric configurations and force-displacement curves of the two structures, that is, MMG-0 and MMG exp , are shown in Figure 12. The specifications and calculated data of the two structures are summarized in Table 8.
As shown in Table 8, the SEA of MMG-0 is 5.68 times that of the experimental structure MMG exp . From previous experimental results, [42] it can be found that, in general, the energy absorption efficiency of a single-layer Miura-ori sheet is better than that of the single-walled hexagonal honeycomb structure. Hence, MMG-0 is a metamaterial structure with excellent energy absorption efficiency when compared to its rivals.

Conclusion
Based on the geometric relationship of Miura-ori metamaterials, we developed a computational approach to modeling zero-and nonzero-thickness MMG cellular solids, which provides a base for follow-up numerical and experimental studies. After verifying the numerical model, and based on the FE simulation results and the requirements of thin-walled energy-absorbing structures, it was determined that the X-direction was the most appropriate compression direction. We examined 25 different models for which six geometric parameters were considered to determine the geometric configuration of the cellular solids. According to the parametric results, we can design MMG structures with better energy absorption performance than some existing origami-based energy-absorption metamaterials.
It is shown that when the wall thickness h of the cell increases by 16.7%, the mass increases in the same proportion. Furthermore, the SEA increases by 25.2%, and the initial peak force also increases. A 16.7% increase in γ A leads to a 104.5% increase in SEA, which has a great effect. A 13.3% increase in γ B not only increases the model quality, but also reduces the SEA by 55.1%. Nevertheless, too small γ B narrows the selection range of γ A . A 20% increase in θ A results in a 17.6% reduction in SEA; consequently, θ A should not be too large. For the side length of the cell, the increase of a A makes the quality of the model increase and the SEA value decrease. The increase of b A makes   www.advancedsciencenews.com www.aem-journal.com the SEA value of the model increase first and then decrease, and the SEA value is the largest when the value of b A is close to a A . The above conclusions provide a preliminary basis for future research on the practical engineering applications of the MMG cellular solids for energy absorption purposes. Future studies based on the-state-of-the-art fabrication methods such as metal 3D printing and glue bonding can be used to develop experimental models and perform compression tests to verify the simulation results.