Numerical Analysis of Out-of-Plane Crushing of Reinforced Honeycomb Core and Effect of Cell Parameters on its Properties

The non-linear finite element code LS-DYNA has been used in this work to conduct the crushing examination of both normal and reinforced honeycomb cores. The honeycomb-like cores are provided with out-of-plane quasi-static conditions of stress via an explicit dynamic approach. We have parametrically investigated the effects of cell properties on crushed behaviour as well as the absorption of energy, including the size of the cell, wall thickness, height, along with cell wall tilted position. Regular honeycomb (R0-HC), reinforced every other ribbon (R1-HC), and reinforced every ribbon (R2-HC) are three different varieties of honeycomb. The findings of the numerical analysis of these three types of honeycomb are compared to understand how reinforcing affects energy absorption and crushing parameters. The sheet material AA3003-H18 was chosen to make the honeycomb core. In comparison to ordinary honeycombs, the reinforced honeycombs demonstrated superior crushing behavior and energy absorption. In comparison to the others, reinforced every ribbon (R2-HC) type honeycombs exhibited the greatest values for crushing characteristics and energy absorption. The crushing characteristics and energy absorption of reinforced every other ribbon (R1-HC) honeycombs were higher than those of ordinary honeycombs (R0-HCThe crushing force, average plateau force, and energy absorption values decrease as the cell size, height, and wall angle are increased, however, all these crushing characteristics increase as the cell wall thickness is increased.


Introduction
With remarkable energy absorption capabilities and extremely high strength-to-weight ratio, honeycomb structures have long been a focus of research.They have a huge variety of uses, including in high-end automobiles, corporate and aviation jets, and military activities.High strength-to-weight ratios and high energy absorption capacities are fundamental requirements across a range of sectors, including high-end automotive applications, railway the field of engineering, military usage, and the aerospace industry.All these fundamental needs are met by honeycomb structures, which are also simple to fabricate and manufacture.Since honeycomb structures are the best on weight criterion, they should be employed in industries in which there exists a skin buckling issue.Both inside the plane as well as out-of-plane orientations, honeycomb structures offer outstanding durability along with excellent energy absorption levels.In comparison to their in-plane counterparts, honeycombs are stronger and can absorb more energy in the out-of-plane direction.Reinforced honeycombs have the potential to be employed in various situations where a high-impact load or strength requirement is necessary [1][2].Wierzbicki (1983) created a theoretical method founded on the minimal concept of plasticity with considerations of energy to estimate honeycomb cells crushing strength.The equation Pm= 8.61yt5/3 l1/3 can be used to calculate the crushed force, where Pm stands for the mean crushed force, l for the cell's side length, t for the wall thickness, and y for the material's yield stress.A hexagonal honeycomb that has some double-thickness walls has a dynamic crushing strength that is roughly 1.3 times greater than a hexagonal the honeycomb with double-thickness walls [3][4].Cell expansion angle, lamina thickness, and cellular dimensions have a significant impact on the parameters of crush force efficiency, overall energy absorption, and overall energy absorbent effectiveness [5].
Sandwiched panels having unreinforced cores are shown to exhibit higher modal damping coefficients over sandwich structures.With fibre-reinforced cores, suggesting that the viscoelastic characteristics of the matrix material are going to have the biggest impact over damping.Mechanical properties are improved by more than 100% and damping is reduced by 40% with fiber-reinforced cores [6].The aluminium-honeycomb core, the aluminium-plate ortho-grid core, and the aluminium-plate ortho-grid core filled with aluminium-honeycomb blocks were all subjected to three-point bending tests.Investigations showed that for thin-walled designed structures, the honeycomb-filled ortho-grid cores sandwiched with carbon fibre faced sheets gave outstanding structural properties [7].When compared with a single core, the grid-reinforced honeycomb had a better damage tolerance.The interface areas of contact and interface toughness of the aluminium honeycomb were considerably increased by the fillet reinforcement.On the other hand, the dense grid generated a significant moment of inertia in order to avoid local buckling.As a consequence, the honeycomb along with the grid combo inhibited regional core instability and interface de-bonding [8].
By incorporating CFRP tubes within the honeycomb, the core's capacity to absorb energy was greatly enhanced.SEA values from dynamic studies on tube-reinforced honeycombs were greater than those from quasi-static measurements [9].The best crash-proof combination was found to be square aluminium tubes packed with a combination of polyurethane foam plus aluminum honeycomb [10].It was determined that the Wierzbicki model for crushing force proved best suitable for a honeycomb core built of the Al-1100 H12 alloy.According to research, the reinforced honeycomb construction has a relative density that is 50% higher than that of the traditional honeycomb, thus enhancing its crushing strength [11].Square honeycombs with hollow lattices outperformed square honeycombs and hollowed lattices in terms of crush force efficiency as well as specific energy absorption.Microtopological hybrid designs can close gaps in mechanical characteristics charts and increase energy absorption as well as crushing protection structures [12].The early and final deformation phases are significantly influenced by the honeycomb structure's shape.The amount of force needed to crush the core rose with cell wall thickness but decreased with cell size [13].Sandwiches made of aluminum IOP Publishing doi:10.1088/1755-1315/1285/1/0120273 honeycomb with glass-epoxy reinforcement have better energy absorption and weight carrying capabilities [14].An approximately linear association between the load level and the reduction in fatigue life was observed.With static and significant amplitude fatigue loads, face yielding produces failure, whereas de-lamination near the core while skin interface causes failure with moderate fatigue loading [15].The maximal crushing force and energy absorption are significantly influenced by the thickness of the ordinary and reinforced honeycomb cell walls.In contrast to increasing cell size, which had the opposite impact, increased cell wall thickness boosted the structure's crushing strength and energy absorption capacity [16].The impact strength and hardness of honeycomb composed of natural fibers (9 wt%) reinforced honeycomb were higher compared to that of other composite materials.More filler reduces the impact and hardness properties [17].
The bending strength of the honeycomb is significantly influenced by its orientation.The combined structure maintains structural integrity and a minimal amount of bearing capacity, and the specimen failure is ductile.Natural frequencies rose and converged as face sheet thickness grew.Deformation and corresponding Von-Mises stresses were observed to decrease as the face sheet's thickness increased [18].When it comes to crash reliability, hexagon honeycomb works effectively; however, the corresponding standards are a little lower than those of conventional hexagonal honeycomb.While hexagonal honeycomb displays an undesirable "X"-shaped localization band, the deformation mechanism of octagon honeycomb was more durable under in-plane compression as well, keeping the cells substantially unaffected [19].Compared between the OTH and DTH, the SHTH exhibited a higher collision intensity magnitude and improved energy absorption.A higher relative density and more combinations increase the SHTH's reliability in crashes [20].The layer-by-layer collapse of the honeycomb cells in the loading direction reveals the confined band that is formed during the failure process of the 3D-printed CFRCHSs.In terms of compressive strength and specific energy absorption, the 3D-printed CFRCHSs outperform a number of competing cellular topologies.According to shape recovery research, 3D-printed CFRCHSs could play a significant role in lightweight intelligent systems and tunable energy absorbers [21].In comparison to an empty honeycomb sandwich structure, the metallic tube-reinforced structure quickly absorbed impact energy, and tube reinforcement greatly decreased front face-sheet deformation [22][23].
Alomarah et al. 2020 [24] investigated the out-of-plane along with in-plane characteristics of a recently suggested auxetic framework, re-entrant chiral auxetic (RCA), within quasi-static uniaxial compression using a combination of both experimental and numerical methods.When evaluating energy absorption efficiency, the hexagonal honeycomb demonstrated the maximum energy absorbent efficiency of 65%, compared to 44% and 52% for the re-entrant and suggested RCA structures, respectively.For in-plane the compression process, the proposed structure has a negative Poisson ratio exhibiting anisotropy mechanical properties.Using experimental quasi-static testing, Nadkarni et al.(2020) investigated the crushing behavior of an aluminum honeycomb composite under out-of-plane compressive stresses.It may be inferred that the aluminum honeycomb structure offers an excellent balance between strength and weight and a steady crush force having predictable properties, consequently making it a preferred choice for many energy-absorbing operations [25][26].Qiu et al. (2020) investigated three distinct kinds of cores: rectangular in shape, hexagonal, and triangular.The periodicity and the supposition that the out-of-plane shifting remains zero at the points of intersection simplify the equations after invoking the Bloch wave depiction form.Few researchers demonstrated the low-energy shock behavior of woven carbon fiber reinforced plastic (CFRP) sandwich panels made of composite material with thermoplastic honeycomb and reentrant cores through both numerical and experimental methods under 3 distinct impact energy levels (20 J, 40 J, and 70 J).In an experiment of out-of-plane crushing, the researchers Zhai et al. 2022 studied critically the energyabsorption properties of an origami-designed honeycomb [27][28].The findings revealed that origamidesigned honeycombs possess a more robust folding mechanism than traditional honeycombs.Using the super-folding method, the energy-absorption properties of origami designs honeycombs were theoretically determined.The accuracy of the proposed model was confirmed by the error between the numerical simulations and theoretical results, which ranged from -8.55% to 6.50% [29][30][31].In this regard, the current research explored with the influences of cell parameters of honeycomb core reinforced using numerical analysis especially for out-of-plane structures.

Method and Materials
The numerical modelling program ABACUS was used in this investigation endeavor to simulate all three distinct kinds of honeycomb core models having various cell layouts.In order to produce honeycomb models with reinforced each subsequent ribbon (R1-HC), a ribbon was added to every other cell.Ribbon reinforcement was added to every cell to form the reinforced everyribbon honeycomb (R2-HC) model.In order to compare the outcomes with the reinforced honeycomb models, regular honeycomb models were also created.Three distinct cell sizes like 6 mm, 8 mm, and 10 mm were used to produce each of these models.The panel had 50 mm broad and 50 mm long dimensions.A 5mm step was used to adjust the node length (cell height) between 10mm and 20mm.The cell wall thickness was adjusted in 0.02mm steps between 0.06mm and 0.10mm.The cell wall angles of 30°, 45°, and 60° were chosen.All of the models displayed in Fig. 1 adhered to these fundamental parameters.

Material Characterization
AA-3003-H18 sheet was utilized for the normal and reinforced honeycomb versions, and structural steel was used for the stiff plate.Table 1 lists the mechanical characteristics of several materials.In the current work, a hard plate was employed to crush the models.There is only one direction (the negative-z direction) in which this rigid plate may move.This plate was moved at a rate of 2 mm per minute in the negative-z direction.The models were broken along the z-axis.In order to maintain the model fixed in one place, the bottom nodal points of the models were fixed in every possible direction.The rigid plate and model were connected by an automatic node to surface contact, and the honeycomb model was connected via an automatic single surface contact to prevent the cell walls from folding in on them.For the meshing core and crusher, respectively, the Belytschko-Tsay 4-node shell element and solid element are used.There are five integration sites in the thickness and one in the element plane for the four-node Belytschko-Tsay shell element.Mesh size has an impact on calculation time and simulation results.After reviewing the mesh convergence test, a mesh size of 0.6mm x 0.6mm was decided upon for the current investigation.In LS-DYNA (MAT-03) plastic kinematic was applied.Both the elastic and plastic characteristics of the material were well-represented by this material model.For the numerical evaluation of honeycomb plates, the loading setup is shown in Fig. 2.

Fig. 2 loading setup for numerical analysis
On normal and reinforced hexagon honeycomb models, a quasi-static out-of-plane crushing was conducted.It takes a long time to perform a quasi-static process in numerical analysis.In order to reduce computing time, mass-scaling was carried out using the Santosa et al [23].

Energy absorbed (EA)
It can be calculated as the area beneath the force vs. displacement plot up to the point of densification.It can be represented as Energy absorbed () = ∫ .  0 Where F is the crushing force, and d is the axial crushing distance (from d=0 to the start of the densification phase).

Average plateau force (Fpav)
The energy absorbed per unit of deformation for the crushing process during the plateau region is called the average plateau force.It can be evaluated by dividing the energy absorbed by deformation.
=   Where Fpav is the average plateau force,  is the axial crushing distance (from 0 to the start of the densification phase).

Specific energy absorbed (SEA)
Specific energy absorbed can be defined as the energy absorbed per unit mass.It can be evaluated as

Specific energy absorbed =
Energy absorbed by structure up to densification point mass of cellular structure

Deformation analysis
In the study, the cores of the traditional honeycomb (R0-HC), reinforced each individual ribbon (R1-HC), and reinforced each ribbon (R2-HC) honeycomb were crushed out of the plane in a quasi-static manner.According to Fig. 2, the rigid top plate was assigned a rate of displacement of 2 millimeters per minute and was only permitted to move in that direction.The results' force vs. displacement curve provides details on the typical out-of-plane crushing procedure.By looking at the force vs. displacement graph, the following conclusions can be drawn.A typical crushing reaction to out-ofplane force is shown in Fig. 3.There are three steps or areas in the out-of-plane crushing.Within the elastic limit, also known as the linear or elastic area, the cells first begin to flex elastically.The critical force, which caused the cells to collapse at greater amounts of force near the end of the elastic zone, is what causes this.Following the first collapse, cells begin to fold with reduced forces, and the progressive creation of folds is seen.Till the densification phase begins, this progressive folding continues.The plateau region is where progressive folding takes place.The densification point, also known as the beginning of the growth phase, encompasses all the extra height or volume beyond the area known as the plateau.The force needed to crush the core grows quickly throughout the densification phase, as indicated by the force vs. displacement curve's steepening slope.The entirely integrated BT shell completed the meshing of the reinforced honeycomb core.To reduce the impact of the hourglass, use an element with a greater degree of precision.Various mesh sizes, including 0.5, 0.6, 0.75, and 0.8 mm, were taken into consideration for the reinforced honeycomb cores.The outcomes of out-of-plane crushed about a honeycomb structure featuring cells that were 10mm in diameter, 10mm in height, and 0.06mm thick are shown in Table 3.
The successful convergence results demonstrate (Table 2) that a mesh size of 0.6 x 0.6 provides high accuracy while requiring little CPU time.The ordinary honeycomb model's forms of deformation are displayed in Fig. 4. A designation method was made available to help people recognize the different models.R0 stands for standard honeycomb, R1 for reinforced each additional ribbon honeycomb and R2 for reinforced every ribbons type honeycomb.R2_10_20_0.06, for instance, stands for a reinforced ribbons honeycomb having cells that are 10 mm in diameter, 20 mm in height, and 0.06 mm thick with a 30 o wall angle.Lists of every single honeycomb model's attributes may be found in Table 3.

Effect of cell size on crushing parameters
After studies of the ordinary honeycomb model's cell sizes, it was found that each model had size variances of up to 2mm. Figure 5 shows a schematic of the typical honeycomb cell sizes.In Fig. 6, the force vs. displacement graphs for the regular honeycomb R2-H, R1-HC, and CR0-HC with 10mm, 8mm, and 6mm cell sizes are shown.
. For honeycomb models in general, the data table below contains a list of all the crushing factors for out-of-plane loads.The standard deviation of the plateau force was greater for the designs with 6mm cells than it was for the models with both of the two cell sizes.For 6mm cell size, results for crushed energy and force absorption remained similarly higher.For honeycomb types with three distinct cell sizes of out-of-plane R0, R1, and R2 Models, Table 4 shows the crushing variables.

Effect of reinforcement on crushing parameters with three different cell sizes
The data for R0-HC, R1-HC, along with R2-HC's crushing force as well as the energy absorbed are shown in Fig. 7(a-b).According to the findings, ordinary honeycomb's crushing toughness and energy absorption capacities are increased by adding reinforcement.R2-HC, whose cell size was 6 mm, absorbed the most energy.R2-HCs absorbed 104.95% greater amounts of energy than R0-HCs for a 6 mm cell size, while R1-HCs absorbed 38.08% more.

Effect of cell wall thickness on crushing parameters
To determine the impact of cellular wall thickness on crushed variables, honeycomb models having three distinct cell wall thicknesses-0.06,0.08, and 0.10mm were crushed in an out-of-plane direction.
The cell size remained 8mm for all versions, and all other parameters remained consistent.With the aid of LS-DYNA, the forces vs. displacement profiles for each model were obtained.The forces vs. displacement graphs for R0-HC, R1-HC, and R2-HCs are displayed in Fig. 8(a-c).It was found that raising the thickness significantly increases the degree of crushing parameters for every one of the varieties of honeycombs.Maximum crushed force along with average stagnation force was maximum for 0.10 millimeters thick materials.The energy absorbing values for R0-HC, R1-HC, and R2-HC with various cell thicknesses of walls are shown in Fig. 9(b).R2-HCs absorbed 85%, 85.1%, and 96.3% greater amounts of energy than R0-HC at the same thicknesses of 0.10mm, 0.08mm, and 0.06mm, respectively.Whenever the cell wall thicknesses were raised to 0.10 mm, the amount of energy absorption data for R2-HCs was significantly enhanced.It demonstrates that R2-HCs can be utilized to increase thickness and improve energy source absorption.

Effect of cell height on crushing parameters
Nine prototypes were chosen and quasi-statically crushed to examine the impact of cell height.Curves of force versus displacement were obtained.All cell parameters were held constant during building the models, with the exception of cell height, which was changed in steps of 5mm.The effects of three distinct cell heights-10 mm, 15 mm, and 20 mm were studied.The chosen cell size was 10 mm, and the thickness of the cell wall was 0.006 mm.The force vs. displacement graphs for R0-HC, R1-HC, and R2-HC are shown in Fig. 10

Effect of cell wall angle on crushing parameters of reinforced honeycombs
Three models referred to as R1-HC and R2-HC with cellular wall angles of 30°, 45°, and 60° each were chosen to determine the impact of cell wall angle with regard to the reinforced honeycomb core.All of the models featured cells that were 6 mm in diameter, 10 mm in height, and 0.06 mm thick.Figures 12(a) and 12(b) exhibit the force versus.The displacement graphs for R1-HC and R2-HC having cellular wall angles of 30°, 45°, and 60°.The force vs. displacement curve for cell wall angles of 60° and 45° was found to be lower than that for cell wall angles of 30°.Table 8 shows that the peak crushing values are highest at a cell wall angle of 30°, and the plateau force was additionally higher in the present study.Table 8 lists the characteristics of R1-HC and R2-HC's out-of-plane crushing at various cell wall inclinations.Table 5 shows that the maximum crushing values are highest at a cell wall angle of 30°, whereas the plateau of force was significantly higher in this instance.The crushing force falls by 23.55% and 34.27%, respectively, when the cell wall angle in R1-HCs is increased from 30o to 45o and 60o.For 45o and 60o cell wall angles, the energy absorbed values drop by 18.83% and 44.6%, respectively.The out-of-plane crushed characteristics for R1-HC decrease as cell wall thickness increases.The crushing force in R2-HC decreased by 23% and 46.5%, respectively, as the cell wall angle was increased from 30o to 45o and 60o.The amount of energy absorbed likewise fell by 29.75% and 54.8%, respectively, as the cell wall angle increased.The findings show that for R1-HC and R2-HC, decreasing the cell wall angle reduces the out-of-plane crushing characteristics.

Fig. 9
Fig.9 (a) Crushing force values (b) Energy absorption values of R0, R1 and R2-HC with three different cell wall thicknesses.

Table 1
Material properties of Al 3003-H18

Table 4
Out-of-plane crushing parameters for honeycomb models with three different cell sizes

Table 5 .
Out-of-plane crushing parameters of R1-HC and R2-HC with different cell wall angles