# Analysis for Enhancing the Performance Characteristics of Honeycomb-Filled Tubes at Constant Mass

<figure><img src="image_1.png" /></figure>

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Abdennour Benhizia* ID, Abdelghani Khennab ID, Ilyas Bensalem ID

Mechanics of Structures and Materials Laboratory, University of Batna 2, Batna 05000, Algeria

Corresponding Author Email: a.benhizia@univ-batna2.dz

https://doi.org/10.18280/rcma.330307

Received: 9 January 2023

Accepted: 15 June 2023

**Keywords:**

compressive performance, energy absorption, filler material, honeycomb sandwich tubes, lightweight

## ABSTRACT

In this paper, assuming the lightweight design is the main requirement, an efficient design of honeycomb sandwich tubes and its quasi-static compressive properties improvement were presented. The structures are designed in SolidWorks software, consisting of two face sheets and a honeycomb core implemented in its in-plane position. The axial compression tests are performed using Abaqus software. Detailed deformation features and energy absorption characteristics during the crushing process were presented. The compressive properties of the improved structures were determined from the energy absorption efficiency curves. Additionally, mathematical formulas for predicting the quasi-static compressive properties are presented. Theoretical predictions and FEA findings were in good agreement. In comparison to the standard structure, the suggested method greatly increased the structure's strength without adding mass to the design.

## 1. INTRODUCTION

Improving the compressive performance of thin-walled tubes by changing the section shapes has become saturated due to the limitations of material forming processes [1]. Therefore, many efforts have been made to develop new designs, such as composite tubes that combine thin-walled metal tubes with other parts, which show many favorable properties [1]. The investigated components include lattice [2-5], foam [6-9], honeycomb [10-13], fold [14], ortho-grid [15, 16], circumferential [17], and longitudinal corrugated [18, 19] cores. It was demonstrated that the dual-bearing capacity of tube and foam improve the overall stability and mechanical performance of the combined structure [20].

Honeycomb-filled structures have also been suggested as a filler to benefit from the interaction between thin-walled tubes and honeycombs. Wang et al. [21] analyzed the mechanical characteristics of honeycomb-filled thin-walled tubes, using experimental and computational methods. Mechanical properties and energy absorption properties were determined for various HFST samples with different geometric shapes. A correlation was observed between the honeycomb core and the thin-walled metal structure.

The study [22] investigated numerically the mechanical response of fluted-core sandwich cylinders under quasi-static uniaxial compression load. The findings showed that sandwich cylinders with a low cell number were more susceptible to local buckling, which decreases the compression performance. This could be effectively improved by increasing the number of cells and the wall thickness.

The study [23] analyzes numerically the properties of single and bitubular polygonal tubes packed with honeycomb for energy absorption. The findings demonstrate that single tubes packed with honeycomb have greater energy absorption

properties than tubes with various geometrical layouts. The study [24] examines the lateral planar crushing and bending responses of an aluminum honeycomb-filled square carbon fiber reinforced plastic (CFRP) tube. As a result of lateral crushing, the filled tubes were able to absorb 6.56 and 4 times more energy than hollow tubes without fillings.

In most of the mentioned literature the properties of the combined structure increase with the increasing density of the filling material. However, an increase in density increases the structure weight, which is an unfavorable point in the lightweight design. Additionally, the honeycomb core is implemented in its out-of-plane position [25]. From a mechanical point of view, the out-of-plane position loses the main characteristic of cellular materials under compression, which is the progressive cell collapse, which controls significantly the deformation mechanism. Moreover, in most numerical modeling of honeycomb sandwich tubes under compression, the densification step is not addressed [22] due to difficulties encountered, such as instabilities and excessive distortion at large deformations. This remains the principal obstacle limiting the exploration of complex design material.

As observed in the above literature, achieving the improvement of the energy absorption performance of honeycomb-filled tubes is still challenging. Therefore, this work was aimed at studying the improvement of compressive performance under quasi-static compression of honeycomb sandwich tubes with two factors: at a constant mass and up to the densification range of deformation frequently employed in engineering applications of cellular materials.

The compressive properties and energy-absorbing capability of designed honeycomb sandwich tubes are investigated and compared. Finally, the improved typical compressive properties are expressed. The paper is structured as follows:
- The honeycomb sandwich tube structure modeling is presented in section 2.

- The numerical results of the quasi-static compression tests are given and analyzed in section 3.

- The conclusions are reported in section 4.

# 2. MATERIALS AND METHODS

## 2.1 Geometry

As shown in Figure 1, the 3D model of a honeycomb sandwich structure consisting of two face sheets and a honeycomb core implemented in its in-plane position is designed in SolidWorks software.

The face sheet has a thickness of 1mm and a size of 110.07×127.1mm², and the honeycomb core has 2mm of cell wall thickness and 10mm of cell lateral length.

To create a cylindrical honeycomb sandwich part, the Flex tool available in Solidworks is used to bend the designed honeycomb sandwich structure and then duplicated to get the closed model, as shown in Figure 2. The advantage of the proposed method is the directly obtained of a 3D model of honeycomb-filled double circular tubes.

As discussed in the introduction, the compression performance of the studied honeycomb sandwich tubes is improved at a constant density. To this end, the honeycomb cell size was manipulated to create new structures containing more cells, keeping the same dimension and density as in the original structure (named L), as shown in Figure 3.

<figure><img src="image_2.png" /><figcaption>**Figure 1.** Designed honeycomb sandwich panel structure</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>**Figure 2.** Schematic illustration of the created cylindrical honeycomb sandwich structure</figcaption></figure>

Two modifications are adopted in this study:

- Adding half of the overall honeycomb structure to the original one, as illustrated in Figure 3(a) (naming it 1.5L), and then scaling it with a scale factor of 0.667 to get the original dimensions (110.07×127.1mm²), as illustrated in Figure 3(b).

- Adding the total of the overall honeycomb structure to the original one in the two directions, as illustrated in Figure 3(a) (naming it 2L), and then scaling it with a scale factor of 0.5 to get the original dimensions (110.07×127.1mm²), as illustrated in Figure 3(b).

The measured relative density in the three structures: L, 1.5L, and 2L, respectively is 0.12, which eliminates the relative density effect.

Figure 4 and Figure 5 represent the designed honeycomb sandwich structures and the created cylindrical honeycomb sandwich.

<figure><img src="image_4.png" /><figcaption>**Figure 3.** New structures containing more cells, and the same dimension and density as in the original structure (a): before the scale and (b) after the scale</figcaption></figure>

<figure><img src="image_5.png" /><figcaption>**Figure 4.** Schematic illustration of honeycomb sandwich structures designed with an increased number of cells and constant dimensions</figcaption></figure>

<figure><img src="image_6.png" /><figcaption>**Figure 5.** Cylindrical honeycomb sandwich structures designed with an increased number of cells and constant dimensions</figcaption></figure>
## 2.2 Quasi-static axial compression loading

To evaluate the mechanical performance of the designed models, the in-plane quasi-static compression tests are performed up to the densification step using ABAQUS/Explicit code. As shown in Figure 6, the constructed model was loaded at a constant speed of 13.2m/s [26] by a rigid moving top plate while being maintained by a restrained rigid plate.

<figure><img src="image_7.png" /><figcaption>Figure 6. Illustration of the compression test configuration</figcaption></figure>

<figure><img src="image_8.png" /><figcaption>Figure 7. Illustration of 3D FE models</figcaption></figure>

<table><caption>Table 1. Material properties used in finite element simulation [27]</caption><tr><td>Density (kg/m³)</td><td>2710</td></tr><tr><td>Young's Modulus (GPa)</td><td>69</td></tr><tr><td>Yield Stress (MPa)</td><td>49.75</td></tr><tr><td>Poisson's Ratio</td><td>0.3</td></tr><tr><td>Stress (MPa)</td><td>Plastic strain</td></tr><tr><td>49.75</td><td>0</td></tr><tr><td>54.4</td><td>0.00539</td></tr><tr><td>63.69</td><td>0.0135</td></tr><tr><td>70.47</td><td>0.0216</td></tr><tr><td>76.53</td><td>0.0327</td></tr><tr><td>84</td><td>0.0529</td></tr><tr><td>90.39</td><td>0.0761</td></tr><tr><td>96.05</td><td>0.102</td></tr><tr><td>104.87</td><td>0.156</td></tr><tr><td>107.33</td><td>0.174</td></tr><tr><td>110.81</td><td>0.22</td></tr><tr><td>112.84</td><td>0.268</td></tr><tr><td>111.31</td><td>0.3</td></tr><tr><td>109.84</td><td>0.326</td></tr></table>

The geometric models have been discretized using tetrahedral elements with a size mesh of 1mm, as shown in Figure 7.

The Aluminum material was used for all components with the mechanical properties given in Table 1.

# 3. RESULTS AND DISCUSSIONS

## 3.1 Deformation patterns

The responses of the tested 3D models under compression test are shown below (Figures 8, 9, 10, 11, 12, and 13) with an illustration of the crushing pattern and Von Mises Stress distribution. The advantage of numerical modeling is that it can illustrate the detailed deformation process of inner parts, such as the honeycomb core and inner facesheet, which could not be captured during an experimental test.

<figure><img src="image_9.png" /><figcaption>Figure 8. Deformation pattern and von misses stress distribution in the original structure L during the compression test</figcaption></figure>

<figure><img src="image_10.png" /><figcaption>Figure 9. Captured deformation pattern in the internal geometry of the original structure L</figcaption></figure>

<figure><img src="image_11.png" /><figcaption>Figure 10. Deformation pattern and von misses stress distribution in the half-duplicated structure 1.5 L during the compression test</figcaption></figure>
<figure><img src="image_12.png" /><figcaption>Figure 11. Captured deformation pattern in the internal geometry of the half-duplicated structure 1.5L</figcaption></figure>

<figure><img src="image_13.png" /><figcaption>Figure 12. Deformation pattern and von misses stress distribution in the total-duplicated structure 2L during the compression test</figcaption></figure>

<figure><img src="image_14.png" /><figcaption>Figure 13. Captured deformation pattern in the internal geometry of the total-duplicated structure 2L</figcaption></figure>

Figures 8, 9, 10, 11, 12, and 13 show how the folds formed are directly related to the honeycomb cells when the honeycomb is added to the tube as a filler. The fold has appeared in the weak zone of the cell, which is the upper vertex of the hexagon. Consequently, the number of folds is influenced by the number of honeycomb cells, which is why the 2L structure has more folds compared to other structures.

As is clearly seen in these figures the collapse of the tubular structure is constrained by the deformation of the honeycomb cells.

The overall stability of the combined model under axial crushing is achieved by the continuous buckling mode of the cells of the honeycomb, this primarily makes the coupled structure achieve exceptional efficiency as energy absorbers.

## 3.2 Quasi-static characteristics

The resulting compression stress-strain curves for the three tested honeycomb-filled double circular tubes are displayed in Figure 14.

<figure><img src="image_15.png" /><figcaption>Figure 14. Resulting stress-strain compressive curves for the three tested honeycomb-filled double circular tubes</figcaption></figure>

The stress-strain curves of the examined sandwich cylinders under uniaxial compression load display the common stages of cellular materials e.g., namely, short elastic stage, followed by a prolonged plateau stage, and finished by a densification stage.

The comparison shows a remarkable difference between the levels of the curves. The level increases when increasing the number of cells. The increased level implies an improvement in compression performance.

## 3.3 Determination of compressive properties

To best explore the obtained results, the compressive mechanical properties are extracted from the obtained stress-strain curves. The energy absorption efficiency was used to calculate the densification strain and plateau stress [28] of the tested models as follows:

$$ \eta(\varepsilon_a) = \frac{\int_{0}^{\varepsilon_a} \sigma(\varepsilon) d\varepsilon}{\sigma_a}, \quad 0 \le \varepsilon_a \le 1 \quad (1) $$

The densification strain represents the highest peak in the energy absorption efficiency-strain curve given as:

$$ \left. \frac{d\eta(\varepsilon_a)}{d\varepsilon} \right|_{\varepsilon_a = \varepsilon_d} = 0, \quad 0 \le \varepsilon_d \le 1 \quad (2) $$

The plateau stress $\sigma_{pl}$ is calculated as:

$$ \sigma_{pl} = \frac{\int_{0}^{\varepsilon_d} \sigma(\varepsilon) d\varepsilon}{\varepsilon_d} \quad (3) $$

<figure><img src="image_16.png" /><figcaption>Figure 15. Efficiency-strain and stress-strain curves of original structure L</figcaption></figure>
<figure><img src="image_17.png" /><figcaption>**Figure 16.** Efficiency-strain and stress-strain curves of half-duplicated structure 1.5 L</figcaption></figure>

<figure><img src="image_18.png" /><figcaption>**Figure 17.** Efficiency-strain and stress-strain curves of total-duplicated structure 2L</figcaption></figure>

Table 2 compares the calculated values of quasi-static characteristics.

<table><caption>**Table 2.** Calculated quasi-static characteristics for different configurations</caption><thead><tr><th>Model</th><th>Collapse Stress (MPa)</th><th>Plateau Stress (MPa)</th><th>Densification Strain (%)</th></tr></thead><tbody><tr><td>L</td><td>13.05</td><td>10.45</td><td>0.56</td></tr><tr><td>1.5 L</td><td>15.41</td><td>12.65</td><td>0.58</td></tr><tr><td>2 L</td><td>17.48</td><td>14.28</td><td>0.6</td></tr></tbody></table>

Figures 15, 16, and 17 display the efficiency-strain and stress-strain curves for the three designed models.

To analytically express the observed compressive mechanical properties, the correlation between these properties and the repeated dimension n could be described as:

Power law function for initial crush stress and plateau stress as:

$$ \sigma = A(n)^B \qquad (4) $$

Simple first-degree polynomial equation for densification strain as:

$$ \varepsilon_D = \alpha + \beta(n) \qquad (5) $$

The fitting parameters values of A, B, α, and β used are given in Table 3.

<table><caption>**Table 3.** Fitted parameter values</caption><thead><tr><th colspan="2">Collapse Stress (MPa)</th><th colspan="2">Plateau Stress (MPa)</th><th colspan="2">Densification Strain (%)</th></tr><tr><th>A</th><th>B</th><th>A</th><th>B</th><th>α</th><th>β</th></tr></thead><tbody><tr><td>13.036</td><td>0.421</td><td>10.49</td><td>0.448</td><td>0.5145</td><td>0.043</td></tr></tbody></table>

<figure><img src="image_19.png" /><figcaption>**Figure 18.** Comparison between collapse stress of fitted and numerical results</figcaption></figure>

<figure><img src="image_20.png" /><figcaption>**Figure 19.** Comparison between plateau stress of fitted and numerical results</figcaption></figure>

<figure><img src="image_21.png" /><figcaption>**Figure 20.** Comparison between densification strain of fitted and numerical results</figcaption></figure>
Figures 18, 19, and 20 show the numerical findings along with the computed values using the suggested functions (Eq. (4) and Eq. (5)), respectively.

The numerical simulation results show that:

* The combined geometry interactions between the tubes and the honeycomb core led to an increase in crash resistance.

* The compressive strength increases with the increase of repeated dimension *n*.

* The predicted values using the proposed expressions showed good agreement with the FEA results.

## 4. CONCLUSIONS

In this study, honeycomb topology is suggested as a filler material to increase the compressive performance of tubular structures at constant density. 3D models of a cylindrical honeycomb sandwich structure are designed and investigated under quasi-static axial compression tests. Using Abaqus software, the axial compression tests are carried out. The obtained stress-strain compressive curves are used to determine the quasi-static compressive mechanical characteristics. The main conclusions were as follows:

- The honeycomb core structure changes the deformation mode of thin cylindrical tubes, giving them more stability and efficiency for energy absorption.

- Comparing the proposed strengthening approach to previous existing methods, it successfully enhanced the compressive performance without adding mass to the structure.

- The proposed analytical expressions linked the quasi-static compressive properties to the structural dimension, which can be used to adjust the design for a given application.

- Based on the numerical results, the honeycomb structure was demonstrated as the best impact-resistant lightweight structure.

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## NOMENCLATURE

A Fitting parameter

B Fitting parameter

E Young's Modulus, GPa

L Dimensionless length

n Repeated dimension

t Thickness, mm

## Greek symbols

σ Stress, MPa

ε Strain

η Energy absorption efficiency

ρ Density, kg/m³

σc Collapse stress, MPa

σpl Plateau stress, MPa

εd Densification strain, %

α Fitting parameter

β Fitting parameter