Research on a cushioning structure for the midsoles of sports shoes based on the three-dimensional pore structure of loofahs

A study based on the three-dimensional structural properties of loofahs was carried out to model and analyse the vibration damping characteristics of reinforced composite loofah materials and structures. The structural model was tested for Young's modulus compression by using �nite element techniques. Based on the results of the study, a lightweight cushioning structure based on a reinforced composite loofah with polygonal pores was developed and used as a midsole cushioning module for running shoes. The structure was then subjected to dynamic shock vibrations, compression, vibration damping and loss factor, fatigue testing and compression testing. The results of the tests showed that the midsole achieved an ideal balance of weight and mechanical performance and was an excellent cushioning structure with high durability.


Introduction
In industrial design engineering, lightweight or ultralightweight cushioning materials and structures are favoured material candidates for products for structural engineers and materials engineers due to their high damping and high strength.High damping is one of the most important indicators of material performance in the design of many product structures, especially in the design of sports equipment.Over the past few years, a number of synthetic cushioning foams and porelike cushioning materials have been developed.These materials, with their light weights, high speci c compressive strengths, low moisture absorption and high impact resistance, combined with their excellent damping properties, are being progressively used in industrial product development.For example, in 2015, HRL Laboratories, a subsidiary of Boeing, conducted extensive research on microlattice damping materials and, in the same year, demonstrated the potential of a material's unique 3D printed microlattice structure, which it considered to be the lightest in the world.The material is a crystal array structure of interconnected hollow tubes with walls only 100 nanometres thick, one thousandth the thickness of a hair, and a density of just 0.9 mg/CC, making it lighter than plastic.This special structure makes the material extremely resistant to compression and results in a high absorption capacity [1].The formerly widely used viscoelastic damping materials absorb energy through stresses that are transferred across polymer chains.However, the effects of viscoelastic polymers are very sensitive to temperature changes, as they exhibit only high damping coe cients over a small temperature range and poor performance at extreme temperatures.By exploiting the energy absorption mechanism of the bending of hollow tubes, the results from HRL Laboratories can facilitate high damping performance, especially in the elds of acoustics, vibrations or shocks.In addition, Zhao L, Zhao L, et  In addition to the synthetic cushioning foam materials mentioned above, many types of biological materials exist in nature, such as wood, bamboo, palm, coconut shell and loofah, which all have the potential to produce lightweight cushioning materials or the possibility of structural mimicry.In general, the effective properties of low-density porous materials depend on their macrostructures, microstructures and the properties of their solid composition.Among the materials mentioned above, loofah has a unique spatial pore bre structure at the macroscopic scale and has excellent properties, such as being ultralightweight and having a high elasticity and excellent absorption, as shown in Figure 1.
However, in the eld of materials science research, there is still no in-depth material mechanics and structural mechanics analysis study on the damping performance of loofah.
In the eld of running shoe design, cushioning technology is an important indicator of the quality of the product.Synthetic cushioning materials are being used in the design of running shoe midsoles.The midsole, which is the sandwich between the sole and the shoe, is the core structure that comprises the cushioning technology and acts as a cushion against ground vibrations during exercise.In recent years, the number of runners has increased signi cantly.
However, the poor cushioning of running shoes has led to a parallel increase in the proportion of knee and ankle injuries.Experimental studies have proven that the impact of the ground on the body when running is eight times greater than when walking, so it is important whether the midsole of a pair of running shoes is good or bad.Without a midsole, the vibrations and friction generated during running or other sport-related activities will constantly damage the body, especially the bones, knees, soles, ankles, tops of the feet, thighs and calves, which will be injured by the vibrations spanning throughout the whole leg.In lateral movements, such as lateral stops, the user is prone to a torsion-like deformation of the running shoe due to excessive speed or impact.The purpose of the midsole support plate is to prevent such movements from causing accidents, such as a broken foot or even joint fractures.The poor cushioning performance of many running shoes is partly related to the petroleum-based materials that are now widely used to design midsoles.On the other hand, it is also closely related to the structural design of the midsoles of running shoes.Therefore, it is essential to design a running shoe with a reasonable structure and good cushioning function.
Common midsoles are divided into several categories: foam, cushioning rubber, physical deformation cushioning, air cushioning and Boost.Foam has superior rebound and cushioning properties.They can change shape over time and are susceptible to weather conditions.Cushioning rubbers are often found in professional running shoes and provide extreme cushioning.Boost is patented by ADIDAS, who uses Boost technology to create a midsole that absorbs impact the moment the foot is stepped on and bounces back to provide support when the foot is lifted.It provides not just cushioning but also energy storage, keeping the knee and foot out of the way.ADIDAS also developed new sneakers with regular lattice structure as the midsole cushioning structure.It is made of TPU material through 3D printing technology.Each of the above commonly used materials and technologies has its own advantages and disadvantages.Overall, the materials considered in the design of a running shoe midsole should be structurally sound, with excellent performance and a high damping factor.Loofah has properties such as low density, good mechanical strength and better cushioning characteristics and can be an important design reference source.Therefore, the aim of this study is to improve the damping characteristics of the midsoles of running shoes using a reinforced composite loofah bre structure to minimise the injuries that often occur during running.

Preparation Of Loofah Experimental Samples
The loofah used in this study was purchased from Zhuhai of Guangdong Province in China.

Extraction of bres
Naturally, ripe loofahs have a multidirectional, pore-like brous structure in the dried fruit called loofah.The loofah has a complex geometric structure, as shown in Figure 2. The spatial con guration of loofah has a number of distinctive features.First, loofah is divided into two parts, an inner brous core and an outer cylindrical core, connected by three radial walls.Second, each layer has a large number of open pores, a feature that results in a low relative density.Third, each layer has a different pore pattern.In the outermost layer, the pores are distributed axially, whereas in the inner layer, the distribution of pores is circular.Because of its unique brous microstructure and macroscopic pore structure, including uniformly distributed voids and rmly connected spatial structures, loofah has unique structural properties, such as a low density and high elasticity.

Chemical treatment
First, loofah bres were treated with distilled water.The loofah material was soaked, washed and rinsed in distilled water for one hour until it became soft.The samples were dried well at room temperature.Next, the loofah bres were soaked in a solution of sodium hydroxide at a molar concentration of 1 mol/L for 2 h.They were then removed from the solution and dried at room temperature.

Preparation of experimental samples
The loofah used for the experiment is shown in Figure 3(a).
A. Limited by the thickness between the outer wall of the loofah and the inner cavity, the loofah sponge bres were cut into 65 mm x 50 mm x 10 mm squares, as shown in Figure 3(b).
B. The bres on the bre blocks were aligned in parallel directions, and the three blocks were stacked top-to-bottom to make a 65 mm x 50 mm x 30 mm rectangular sample.
C. Thermoplastic resin DY250 was mixed with curing agent TH7103 at a ratio of 2:1, and this mixed solution was evenly applied to the sample.The coating was cured to obtain a loofah composite with a reinforced structure.This is shown in Figure 3(c) below.
The properties of thermoplastic resin-reinforced loofahs are shown in Table 1.

Determination of material properties
The thermoplastic resin-reinforced loofah exhibits the properties of both a viscous and elastic material.It is therefore classi ed as a viscoelastic material.In general, viscoelastic materials are mainly used as damping layers.Their main characteristics are temperature-and frequency dependent.They are materials in which both elastic and viscous deformation mechanisms exist simultaneously under the action of external forces.Resin-reinforced loofah composites consist of long, exible bres and are viscoelastic in nature.

Vibration damping tests and determination of loss factors
To test the vibration damping data of a sample and the frequency response function of its structure, an excitation must be applied to the structure.The common excitation methods are force hammer excitation and the excitation of the shaker.The advantages of force hammer excitation are that it is fast, easy and suitable for eld measurements.Therefore, this experiment uses force hammer excitation for testing.The loss factor in vibration damping tests is an important data indicator.The loss factor is the tangent of the phase angle difference between stress and strain (called the loss angle) and is usually used as a measure of the damping of a system subjected to forced vibration.It can also be thought of as the ratio of the modulus of loss (or loss exibility) to the modulus of energy storage (or energy storage exibility) measured under tension, shear force, compression and longitudinal compression.The loss coe cients of thermoplastic resin-reinforced loofah samples were determined using an ENDEVCO 2302 modal force hammer.This modal force hammer excites the sample with a constant impact force over a range of frequencies.The excitation response for the selected frequencies was measured and recorded as shown in Table 2.In the experiments, Young's modulus was evaluated using the known resonant frequencies of the samples.The experimental results are shown in Table 2, where the moduli were evaluated and recorded.The experiments were conducted using ASTME606-04 strain-controlled fatigue test equipment, which was calibrated as a standard for straincontrolled low-and high-cycle fatigue testing.To accurately simulate the condition of an athletic shoe during use, the machine was loaded with samples that were heated to 33°C and subjected to a dynamic impact force of 80 kg.The relative humidity was regulated at 85%.Low and high strain rates and relaxation times were measured and recorded.The machine repeated a certain number of cycles automatically.Test data were obtained at the end of the experiment, as shown in Table 3.
Table 3 Fatigue tests

Compression tests
Using statistical data analysis, it was assumed that the weight of a typical athlete 80 kg and that the typical exercise duration is 2.5 h.Based on the above data, the test sample was loaded on the compressor, and a compressive force of 80 kg was applied for approximately 2.5 h.The low level was measured and recorded.The load was released, and the high level was recorded at 2 second intervals until the sample reached its original height.The compression analysis test curve is shown in Fig. 4.
The mechanical properties of the reinforced loofah were mathematically modelled by using the Kelvin-Voigt model.After analysing thicknesses of 0.023 m, 0.033 m, 0.043 m, 0.053 m and 0.066 m, an optimum thickness of 43 mm was derived for the midsoles of sports shoes, as shown in Fig. 5(c).Other results are shown as (a), (b), (d) and (e) in Fig. 5.

Setting of the midsole height
The height of the midsole of an athletic shoe is a crucial indicator of its cushioning properties [4].It affects the point of contact between the shoe and the ground and the impact force [5,6], and the impact force determines the vibration dynamics within the cushioning system.It varies proportionally with the distance between the midsole contact point and the ground.As shown in Fig. 5, Cases (a) to (e) show that the damping characteristics of the midsole approach a steady state as the midsole thickness increases.For reducing damped vibrations, the time for the damping system to reach progressive stability is of paramount importance.As shown in Case (e) in Fig. 5, the system reaches a progressive steady state in the shortest possible time when the thickness is 43 mm.Therefore, an athlete weight of 80 kg and a midsole thickness of 43 mm can be assumed as design criteria.A detailed description is shown in Table 3.The damping e ciency of the system is a function of the design factor of the midsole.The design factor depends on the thickness of the midsole, which also affects the athlete's running speed.If a high midsole is used, the potential energy of the athlete will be high and converted into a high kinetic energy and momentum during running.The potential energy of the system is therefore proportional to the thickness of the midsole.The thickness also provides an effective damping mechanism during running.

Analysis of vibration damping mechanisms
The midsole is designed to e ciently convert vibration energy into thermal energy while reducing the strain rate over time.In addition, the midsole retains marginal energy for continuous vibration during low or high cyclic loads.This marginal energy allows the vibration energy to be superimposed and thus resonate, providing a comfortable experience for the user.During movement, the rate of energy dissipation increases proportionally with time for each compression-relaxation cycle.This process converts the vibration energy into heat, which radiates to the surrounding area, thereby reducing the strain amplitude to a steady state.As a result, progressive stability is achieved in the shortest possible time, as shown in Case (c) in Fig. 5.The use of sports shoes with poor vibration damping mechanisms during running can lead to knee and ankle injuries.Such shoes do not dampen the rise and fall of strain amplitudes caused by prolonged vibration.The newly designed vibration damping system, on the other hand, achieves progressive stability in the shortest possible time.The damping characteristics of the midsole are described as underdamping.This is a function of control factors such as the loss factor, Young's modulus and design factor.The midsole is designed to ensure a balance among the loss factor, Young's modulus and design factor to ensure comfort and high damping e ciency during running.

Fatigue strength
The material chosen for the design has an important in uence on the durability and effectiveness of the midsole.As shown in Fig. 6, the experimental data show that the strength of the design decreases with decreasing impact force rates and strain rates.The fatigue life of a vibrationally damped structure is in the range of 0-1,200,000 cycles, roughly equivalent to a distance of 1720 km.Beyond this range, fatigue occurs.This design is suitable for long-and shortdistance running exercises as well as for low-and high-speed running exercises.The results of the fatigue test are shown in Fig. 6, where the strain amplitude rate decreases as the impact rate increases.This indicates that the strength of the midsole decreases with each increase in load.

Resilient behaviour
The exibility of the midsole is an important design indicator.The midsole relaxes quickly under prolonged compression.The loofah three-dimensional network structure and the thermoplastic matrix work together to achieve the elastic properties of the midsole.The loofah structure has spring-like properties, while the matrix enhances the strength and durability of the material.As a result, the reinforced composite loofah midsole exhibits excellent elasticity characteristics.
The design factor was rounded to the nearest hundred, and the average thickness was evaluated for the runner's weight range.The surface area of the midsole can be calculated using the formula.This is because the surface area of the midsole varies over the weight range.

Structural design
The previous section obtained basic data from material and structural mechanics experiments on loofah composite reinforced samples, providing a structural model for the development of vibration damping materials based on the results of the experimental analysis.However, the loofah prototype has a very complex three-dimensional spatial structure with a complex pore distribution, shape and size, making it very di cult to build a realistic loofah structure for numerical simulation.This is shown in Fig. 7.
Therefore, to facilitate the modelling, a simulated scaled-up bionic two-layer structural damping model with more complex polygonal pores was designed.The pore structure of the loofah was assumed to be a two-layer open-cell foam structure with porous shell walls in each layer.These two layers were connected by three porous radial plates.The damping structure obtained by structural simpli cation had the advantages of low density and high elasticity.In the bionic damping model, the polygonal pores formed different patterns representing the difference between the inner and outer layers of the loofah.

Overall axial Young's modulus nite element analysis
To accurately obtain the overall compressive performance of the cushioned structure, a simpli ed llet was designed as a cylindrical cushioned structure model with a radius of 42 mm and a height of 43 mm.In the nite element analysis, the structure was assumed to be homogeneous, isotropic and linearly elastic.The material was assumed to be a thermoplastic synthetic resin.Finite element analysis was carried out by the commercial software ABAQUS to calculate the effective material properties of the pore and solid models, as shown in Fig. 8.The pore model shown in Fig. 8(a) was meshed using the free mesh strategy in ABAQUS.
The model was calculated to have 212,392 C3D10 elements (see Fig. 9), and the solid model was divided into 61800 C3D20R elements using the sweep technique.The total number of nodes that determined the scale of the FEA calculation was 326407 for the pore model and 203505 for the solid elements.In the FEA, different axial pressure loads, i.e.,10 N, 20 N, 30 N, 40 N, 50 N, 60 N, 70 N, 80 N, 90 N and 100 N, were applied to the two end faces of the pore and solid models to investigate their linear elastic compression behaviours.The corresponding relationships between the mean axial stress and mean axial strain are shown in Fig. 9(a) and Fig. 9(b), respectively.The approximately linear relationship between the axial stress and axial strain can be seen in these two plots.The Young's modulus for the pore and solid models were 69.058GPa and 68.9 GPa, respectively.
The above experimental analysis shows that the damping model based on the loofah 3D mesh structure has a very good damping effect.
4.3.Finite element analysis of Young's modulus of the lattice structure compared with the regular lattice structure of the midsole The experiments are based on the well-known explicit nite element analysis tool Ansys LS-DYNA.Because the regular lattice structure of 3D printing is widely used as the cushioning structure of the midsole of sports shoes by sports brands today, we designed a model with regular lattice structure for comparative tests.This is shown in Fig. 10.
The main objective of this experiment is to determine the elastic deformation and resilience of the bottom of the latticelike structure and the regular lattice structure under the same impact conditions.Impact specimen A was a regular lattice model, and impact specimen B was a loofah model.The material used for the specimens was TPU, a widely used material for sports shoe midsoles [7].The TPU material properties are shown in Table 4.Both models have a radius of 42 mm, a height of 43 mm and a mass of 40 g.The parameters of the two specimens were entered into LS-DYNA to simulate the impact motion, observe the deformation and rebound effect during impact and analyse the structural properties of the two specimens.The top 8 athletes from the 30th Olympic Games were used to study the height, weight and Kettlebell Index of track and eld athletes.The results showed that the highest average weight of male track and eld athletes in each region was 102 kg for South American athletes, 99 kg for Asian athletes ranked second, 97.2 kg for European athletes ranked third, and 97 kg, 83 kg and 75 kg for North America, Oceania and Africa ranked fourth, fth and sixth, respectively [8].Based on the above data, the impact force used in this experiment was chosen as the median value, simulating an athlete with a body weight of 80 kg and a proposed contact area of 60 mm in diameter between the arch and the heel.The two structures were each impacted with 80 kg at 0.5 m/s (see Fig. 11).The results of the experiments are shown in Figs. 12, 13, 14, 15, 16 and 17.The regular lattice structure bounced back within 0.065 seconds with a compression of 19.025 mm, and the loofah structure bounced back within 0.028 seconds with a compression of 7.044 mm; the regular lattice structure had a large deformation, while the loofah structure model had a small deformation.
The above experimental results show that the loofah structure is more supportive and resilient when the same material, thickness, diameter and weight are used.Therefore, the loofah structure is more material-e cient and has better properties than the regular lattice structure.

Conclusion
This study addresses the overall factors that ensure safety and comfort during running.Available statistics show that the frequency of ankle and knee injuries among runners during running is increasing.The impact forces during running cause strains that are transmitted through the feet and ankles in the form of vertical sine waves to the more important parts of the body.Most of the time, the impact force is greater than the kinetic energy attenuation capacity of the foot and leg muscles, resulting in injury.In this paper, a lightweight three-dimensional pore structure was developed by experimenting with the material and three-dimensional spatial structure of loofahs.Numerical experiments were conducted to assess the effective axial Young's modulus of a pore model through nite element simulations.The equivalent density of the pore material was also evaluated.The numerical results show that the elastic modulus of the pore material is similar to that of the solid model, while it shows a lower equivalent density than the solid material and a higher speci c stiffness than the solid material.The experimental data and analysis show that the reinforced composite loofah sponge is an ideal mechanical improvement material for the midsoles of running shoes, as it can effectively suppress vibrations due to impact during running.The ultralight porous material is suitable for absorbing transient impact energy.By carefully considering the pore space con guration of loofahs, a preliminary bionic design for a lightweight material was provided.Future research will focus on the fabrication of lightweight three-dimensional pore structures and their axial compressive properties.The sandwich composite with the developed lightweight 3D pore material as the core material will then be tested with the aim of investigating its mechanical properties under various loads, such as impact loading.A more accurate numerical study of this lightweight structure will be carried out in the future by advanced numerical methods, such as the hybrid nite element method.

Declarations Figures
Page 10/ al. of the University of Science and Technology of China investigated layered composite pores (HCH) with woven fabric sandwich walls.The quasistatic uniaxial compression behaviour of a block cushioning foam made of 405 unblemished steel hollow spheres sintered by Lin TJ et al. at Georgia Tech was investigated experimentally [2].Krishnan S, Garimella S V, Murthy J Y. Simulation of thermal transport in open-cell cushioning foams with different periodic units [3].All the above studies provided excellent results of recent material science research and can offer a broad technical basis for the development of high-performance cushioning materials. 18

Figure 1 Internal
Figure 1

Figure 5 Effect
Figure 5

Figure 10 The
Figure 10 Figure 12

Table 1
Properties of thermoplastic resin-reinforced loofahs

Table 4
The TPU material properties are as follows