Compressive response and energy absorption of foam-filled aluminum honeycomb composite: experiments and simulation

In this study, the effect of foam-filling pattern on the compressive response and energy absorption capacity of the aluminum honeycomb composite has been investigated. An aluminum honeycomb core and a polyurethane foam were used to produce foam-filled honeycomb panels in three patterns with the same volume fraction of the foam. Experimental quasi-static compression tests were performed in the in-plane direction. Numerical analysis based on the conducted tests was also performed by ABAQUS finite element software in similar laboratory conditions to verify the accuracy of the experiments. The results show that the polyurethane-filling pattern is effective in the compressive behavior of the honeycomb core due to the creation and change of the shear bands, the length of the path deflection, and compressive force distribution. At an angle of 30°–35°, the honeycomb materials deform in the in-plane direction, forming shear bands with a greater strain. However, by using the optimized foam pattern—alternating pattern—in addition to enhancing the honeycomb's compressive strength and energy absorption capacity by 490% and 800%, respectively, the foam usage rate can be reduced up to 35% compared to the full foam mode, resulting in lower cost.


Introduction
When a high stiffness-to-weight ratio is required, cellular materials are employed in various aerospace, automobile, and wind energy structural components.One of these materials' advantages is their high energy absorption capability [1][2][3].Because of its better crushing strength, hexagonal honeycomb cores are increasingly being used in cellular materials.The mechanical reaction of honeycomb cores is a key factor in optimizing the design of lightweight engineering structures.The elastic modulus, yield strength, and plateau stress in the plastic deformation regime are the most relevant parameters with regard to the application [4][5][6][7].
In some applications, such as the energy absorption layer of an aircraft against a bird or foreign object collision, crushing can occur along any direction of the honeycomb [8].Therefore, in addition to the out-of-plane behavior, it is also necessary to know the in-plane honeycomb crushing behavior.Honeycomb cores can crush and failure under these conditions because in-plane loads are unavoidable in these structures [9][10][11].
According to research on the effects of cell geometry on compressive strength and absorbed energy in the in-plane direction for different cellular structures, the diamondshaped cell structure had the lowest absorbed energy and the Kagome structure had the highest absorbed energy.Some calculated profiles, in contrast to the square cell structure investigated so far, indicate the absence of a distinct peak stress that initiates structural collapse.Furthermore, simulations for shapes such as squares, bias without compression, diamond 90°, and others reveal up to 75% deformation degrees.According to the determined results, the Kagome profile has the highest forces in the in-plane load direction.This partly confirms the theory derived from the literature that structures such as Kagome geometry with a tensile-dominated deformation mechanism are superior to those occupied by bending [12,13].
The effect of thickness variation on the energy-absorbing behavior under quasi-static loading in various parts of a certain structure was examined in another study by Kazemi et al. [14].The specific energy absorption of the optimal sample was improved by about 272%, according to the results.
Reinforcement of the honeycomb core is important to avoid premature failure.The usefulness of honeycombs in airplane crashes has recently been reported.The effects of strain in the low strain rate domain on the out-of-plane compressive mechanical behavior of bare and polyurethane foam-filled honeycomb structures were examined by Alavinia and Sadeghi [15].They discovered that the strain rate is more responsive to bare panels than to foam-filled panels.The increase in plateau stress caused by raising the strain rate is substantially greater in bare panels than in foam-filled panels.Mozafari et al. [16] studied the out-ofplane crushing and local stiffness of foam-filled sandwich panels proposed for Korean tilting trains.Khan et al. [17] studied the honeycomb core's in-plane and out-of-plane crushing capabilities.They discovered that the deformation originated in the sample's shear band at 45° and was restricted to the shear bands' boundaries.
A study conducted by Cricr et al. [18] revealed that crushing in the Y direction propagates via horizontal paths.They deduced that the stress along the Y direction causes the buckling phenomenon since the deformed honeycomb often has horizontal (orthogonal to the direction of load) crushed rows that are localized around the mid side of the honeycomb.Furthermore, Liu et al. [19] discovered X-shaped shear bands in the structure by crushing the honeycomb.Also, Carlson et al. [20] studied the behavior of the honeycomb under in plane compression.They found that the uniaxial compressive stress is required to initiate and propagate an inclined shear band, first across the specimen and then by band-broadening.Goodarzi et al. [21] investigated the shear band propagation in honeycomb and concluded that there are three consecutive stages of shear band propagation-shear band consolidation, shear band expansion and shear band deformation.Liu et al. [22] investigated the compressive strength of honeycomb using a plastic reinforced carbon fiber framework and found that the effect of honeycomb filling played a more significant role in the lateral crushing compared to lateral bending.Some researchers have used a digital image correlation technique (DIC) to study more closely the deformation behavior of cellular materials.Djemaoune et al. [23] observed the formation of X-shear band in the in-plane compression test of aluminum honeycomb.Jin et al. [24] utilized DIC to investigate the crushing reaction of foams, and Lamb [25] used DIC to investigate the failure mechanisms of pre-deformed Al honeycomb cores.
When the purpose of the product is to protect the human body or a sensitive part from damage caused by impact loads, the in-plane loading of the honeycomb structure becomes important.The main purpose of the research is to study the effect of polyurethane filling patterns on the compressive behavior of aluminum honeycomb core in the in-plane direction.Also, the simulation of the experiment is performed by ABAQUS finite element software under similar conditions to compare the results with the experimental tests.

Materials
A commercially available aluminum honeycomb core made of AA1060H12 with a yield strength of 65 MPa, was used Page 3 of 10 562 for the sample.The specifications of the honeycomb sample are as follows: 0.06 mm foil thickness (t c ), 8 mm cell size (s), and 53.6 kg/m 3 apparent density of the core ( c ) based on the following equation: [26] where Al is the density of aluminum.The apparent density of polyurethane foam selected to fill the honeycomb core was 25 kg/m 3 .A sample of 70 × 70 mm 2 with a thickness of 25.4 mm was provided according to ASTM D1621 [27] to obtain the compressive stress-strain curve of the foam.The sample was exposed to a compressed load routed at a speed of 1 mm/s.
Polyurethane foam spray was used to fill the honeycomb cells.Besides the "bare honeycomb (BH)", the specimens were filled in three patterns consisting of "diagonal (HD), sinusoidal (HS) and alternate (HA)" with the same volume fraction of 65% (Fig. 1).

Tests and evaluations
To evaluate the in-plane compressive behavior, all honeycombs and foam-filled honeycombs were prepared and subjected to a displacement-controlled quasi-static compressive load at a constant rate of 1 mm/s.For each pattern, three tests were carried out with the SANTAM (STM-20) machine and the average values of compression strength were considered in this study.A digital image correlation (DIC) system was also performed to examine the deformation behavior of specimens under load.Stress-strain curves acquired from the test machine have been used to adjust the DIC results.The test machine curves and DIC data were combined to provide a complete picture of the honeycomb cells' deformation behavior at any given time.
To ensure that the experimental results are accurate, the compression test on the in-plane direction for different patterns similar to the experimental test conditions was simulated by ABAQUS finite element software.A three-dimensional finite element (FE) model of foam, bare, and foam-filled honeycombs was developed using the ABAQUS software package [28].The FE models (1) c = Al × 8t c 3s comprised three parts.Core (bare or filled with foam) and jaws of the device.For the jaws of the device, two rigid plates are modeled, one of which is movable and the other is fixed (the upper one).To model the aluminum honeycomb, it is considered to be a homogeneous shell.The honeycomb sample consisted of 6 cells in the X direction and 7 cells in the Y direction.In addition, the geometry of the cells was completely hexagonal, and the junction of the cells was considered to be fully adherent.The linear elastic-perfectly plastic material model is applied to the honeycomb of the finite element model.The compressible foam mechanical model was used to model the PU foam.The foam elastic modulus (E) and Poisson's ratio ( ) were selected as 3.5 MPa and zero, respectively.Poisson's ratio of plastics (ϑp), which is the ratio between the horizontal plastic deformation and the longitudinal plastic deformation under uniaxial compression, for a variety of low-density foams is assumed to be near zero [29].The density of the filled foam in all cells was assumed to be the same.The solution method in finite element software is based on the grid.A 4-node S4R shell element was used for honeycomb meshing, and a 6-node C3D8R element was used for foam meshing, and the size of the elements was considered to be 1.5 mm.
The model of honeycomb filled with foam consisted of 53,236 S4R shell elements for bare honeycomb, 1088 R3D4 quadrilateral elements for the rigid plates, and 13,179 C3D8R solid elements for the foam.Figure 2 shows the finite element models of the foam-filled honeycomb with different patterns.
To eliminate any penetration between the cell walls, the overall surface-to-surface contact was defined on the unfilled honeycomb model.In the case of a foam-filled honeycomb, tie constraint is used to stick the foam cell faces to the adjacent honeycomb cell walls.In the definition of the boundary conditions, the moving plate is constrained to only move in the Y direction with a constant velocity to compress the honeycomb core under quasistatic conditions [30], and the fixed plate is restricted by its degrees of freedom.Then, analyses are performed and, by considering the effective contact area and initial distance, stress-strain curves are obtained.

Results and discussion
Based on the conducted tests, the deformation behavior of the specimens with the different patterns was studied under the compression load.In this section, the deformation mode and the stress-strain curves of the specimens were discussed.Also, mean compression strength and energy absorption were determined.Finally, the experimental and finite element results were compared together.Figure 3 shows the experimental compression test and finite element results on the polyurethane foam.It can be seen that the compression stress-strain curve obtained from the test machine has three regions, which is in accordance with the literature [31,32].
The first one is the elastic region and the stress-strain increases linearly, then the second, the stress reaches a yield point at the mark 1 corresponding to 0.08 strain in 32 kPa stress (yield stress), and the strain increases without any changes in the stress.In this area, the stress is almost constant (plateau) and slightly oscillating and continues to the densification region.Finally, the third region is the densification mode at mark 2 corresponding to 0.5 strain, the stress increases sharply.As shown in Fig. 3, the polyurethane foam exhibits elastic-perfectly plastic behavior [30].Also, the stress-strain curve obtained from the finite element model showed a similar behavior, but there was a slight difference in the stress level as well as the strain on the starting regions.
The deformation mode of the bare honeycomb in the Y direction is shown in Fig. 4. Figure 5 shows the experimental and finite element compression stress-strain curves of the bare honeycomb in the Y direction.As shown in the Fig. 5, at first the stress increases linearly to 2 kPa in 0.02 strain, which is the elastic region.It can be seen that most of the specimen volume was not involved in the crushing process nor contributed in the global strain, especially in the initial stages of the plastic deformation.Then, the stress remains relatively constant to the mark 1 corresponding to 0.1 strain.In this region, which is also shown in Fig. 4, the shear band is formed and expanded at an angle of approximately 30°.As a result, it merges with other shear marks in the sign 2 related to the strain of 0.23.According to the studies conducted in this field [19,23,33], the X-shaped shear band is formed in this stage.
The deformation mechanism of the honeycomb under uniaxial pressure is the formation of shear bands.This was investigated by Carlson et al. [20], who confirmed that honeycombs are deformed by shear bands that form and propagate at about 45° angles.They also stated that the infinitesimal shear mode, including the rotation of the vertical walls of the honeycomb at an angle of 90°, propagates under almost constant stress.The deformation mode is dominant in the bending shear band and has two hexagonal wavelengths (Fig. 6).
The type of deformation of a cell is dependent on the position of the cell in the sample.The cells in the shear band regime are deformed initially in the crushing process while the cells outside the regime of the shear band are deformed in the later stages of the test.After that, the stress increases with the strain, proportionally.The deformed cells have transferred subsequent loading to the neighboring cells once the critical limit of the load is achieved.These shear bands cause progressive folding to the densification region at the mark 3 corresponding to 0.89 strain.The deformation is limited to the regions within the shear band.Other studies by Khan and Cricri have made similar claims [17,18].
Three samples of each pattern were compressed in the Y direction.The deformation mode of HD, HS, and HA samples under uniaxial compression test are shown in Figs. 7,  8, and 9, respectively.The deformation mechanism of these samples is carried out by the formation of the shear bands as previously described and reported by Khan et al. [17,19,20].In fact, the most important result obtained from the deformation mode of the specimens is the influence of the foam-filling pattern on the shear band formation pattern.In the sinusoidal (HS) and diagonal (HD) patterns, the specimens move toward the foaming path where the sample with alternate pattern (HA) is folded without any deflection.Indeed, changing the foam-filling pattern affects the progression of the shear bands.Figure 10 shows the length of the path deflection and force distribution in the different patterns.
The experimental stress-strain curves of the specimens are shown in Fig. 11a.Accordingly, the highest compressive strength and energy absorption are for the alternate pattern (HA) due to the length of the foam pattern deflection path, which is the smallest one (Fig. 10).Thus, in HA sample, the compressive load applied by the upper jaw is transferred to the lower jaw with less deflection.So, the HA sample is loading faster than the other two patterns.
In other words, in the stress-strain curve for the HA sample, increasing stress is conducted in small strain.Also, due to less deflection of pattern in the HA sample, the level of stress is further than the other patterns in the same strain.Based on Fig. 10, the sample with a sinusoidal pattern has a similar mechanism to the alternating pattern, but due to the long path deflection of the pattern, it has less compressive strength than HA.The diagonal pattern, in addition to larger path deflection, has a 9.5° angle deviation to the perpendicular direction, which means that the total vector of the compressive force has the same deviation angle (Fig. 7) and it makes the sample compress easily and to possess a less compressive strength.In fact, the deviation of the force path from the vertical direction has reduced the compressive strength of the diagonal pattern.To obtain the mean compressive strength in the finite element model, the stress-strain curve was obtained by dividing the load change by the effective contact area and the displacement by the initial distance.Next, the average compressive strength according to Eq. 2 [30]: which m is the mean compressive strength and d is the densification strain.The amount of absorbed energy can be calculated from the area under the stress-strain curve.The  E V ) is obtained by inte- grating the stress-strain response according to Eq. 3 [34]: The finite element results showed that the deformation of the modeled samples is similar to the deformation of the experimental specimens.The formation of shear bands is also observed in the simulated samples [31].In the diagonal one, a deviation to one side was noticed during compression.Figure 11b shows the results of the simulated compression tests.As can be seen, the curves are slightly different from the experimental curves.In the first elastic region, the slope of the curves and yield strength are higher than the experimental curves.Also, the plateau region in simulation results is longer and it continues to approximately 0.3 strain.On the other hand, the stress level in the finite element curves is higher than the experimental curves.
Table 1 lists the mean compressive strength and energy absorption values of all samples, which are compared to the FE results.Also, the improvement amount of the mean compressive strength and energy absorption for three patterns relative to the bare honeycomb is shown in Fig. 12.As shown in the figure, the highest amount of increase in mean compressive strength and adsorbed energy is related to the HA sample.
The in-plane compressive strength of the HA sample has increased by 490% compared to the empty honeycomb.This happened while only two-thirds of the volume of the honeycomb was filled with foam, and about a 34% reduction in the use of polyurethane foam compared to the full-filled sample.The reason as discussed earlier, is less deflection of the foam path than the other two models.Also, the HS sample has the highest strength, which is due to the similarity of the HS pattern with the HA but with a longer path length.

Conclusion
In this research, the effect of polyurethane foam-filling pattern on the compressive behavior and energy absorption capacity of the aluminum honeycomb composite has been investigated.The quasi-static uniaxial compression test was performed on samples with different patterns.The finite element ABAQUS software was also utilized to validate the accuracy of the experimental data.The  tern-in addition to increasing the compressive strength and the energy absorption capacity of the empty honeycomb up to 490% and 800%, respectively, the foam utilization rate can be reduced up to 35% comparing to the full foam mode, resulting in lower cost.
Funding No funds, grants, or other support was received from any organization for the submitted work.

Data availability
The raw/processed data required to reproduce these findings cannot be shared at this time as the data also form part of an ongoing study and can be shared if only part of the research data is required to reproduce these findings.

Fig. 2 Fig. 3
Fig. 2 Finite element models of the foam-filled honeycomb with different patterns, a HS, b HA and c HD

Fig. 4 Fig. 5 Fig. 6
Fig. 4 Deformation of BH sample under compression test in the Y direction unit volume (

Fig. 7 Fig. 8
Fig. 7 Deformation of HD sample under in-plane compression test in the Y direction

Fig. 9
Fig. 9 Deformation of HA sample under in-plane compression test and predicted by the FE simulation

Fig. 10
Fig. 10 Schematic path deflection in the foam-filled honeycomb with a HA, b HD and c HS patterns

Fig. 11 a
Fig. 11 a Experimental and b simulation result curves of the compression tests

Fig. 12
Fig. 12 Improvement amount of the mean compressive strength and the absorption energy for different patterns

Table 1
Results of the experimental and FEM evaluations