Applied Science and Innovative Research ISSN 2474-4972 (Print) ISSN 2474-4980 (Online) Vol. 9, No. 1, 2025 www.scholink.org/ojs/index.php/asir 24 Original Paper Modeling and Statics Analysis of Outsole Structure of Men's Shoes Based on Finite Element Method Pengbo Wan1, Yu Wu1* & Xue Tian2 1 College of Art and Design, Shaanxi University of Science & Technology, Xi’an 710021, China 2 Xi’an Medical University, Xi’an 710021, China * Corresponding author: Yu Wu, E-mail: 2795561526@qq.com Received: November 9, 2024 Accepted: December 18, 2024 Online Published: December 24, 2024 doi:10.22158/asir.v9n1p24 URL: http://doi.org/10.22158/asir.v9n1p24 Abstract In order to explore the influence of the heel structure of men's shoes on the deformation of the outsole, and simulate the stress distribution and deformation of the outsole in different human states, taking the existing leisure men's shoes outsole as the research object, the "sole-ground" coupling finite element model was established through reverse engineering, and the instantaneous stress of the sole was simulated and statically analyzed. The stress and strain areas of the model under different working conditions are consistent with those under the real test, mainly in the area where the transverse stiffener at the heel meets the inner edge. This paper applies finite element analysis to the static analysis of soles, which can provide new ideas for the design of regional structure of outsole heel of men's shoes, and improve the utilization rate of sole materials and sole performance. Keywords sole structure, reverse engineering, finite element analysis, static analysis 1. Introduction As the terminal link of lower limbs, the foot has the functions of supporting stability, buffering shock and absorbing energy. Sole is the carrier of human feet contacting with the ground, which is composed of insole, midsole and outsole, in which outsole usually refers to the bottom of shoes contacting with the ground, which can effectively reduce the ground reaction force and is an important part in the research and development of shoes and boots. At present, the research and design of sole structure in footwear manufacturing industry mostly relies on traditional design experience and subjective comfort feedback of the wearer, lacking scientific theoretical basis. Moreover, in the sole mold opening and production process, the adjustment of mold www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 9, No. 1, 2025 25 Published by SCHOLINK INC. parameters will change the function and comfort of shoes and boots, which is prone to the problems of high research and development cost and long development cycle. In the performance testing stage of sole structure, physical experiments or sports biomechanics methods are usually relied on, and the sole data can’t be adjusted and updated in time, which will lead to problems such as relatively lagging optimization of sole structure. In recent years, Finite Element Analysis (FEA), as an important means of simulation in modern engineering field, has been widely used in architecture, medical treatment, design and many other fields, which can provide support for human biomechanics and sole structure analysis. Ling Jingxiu et al. designed two kinds of sole schemes with rhombus and regular hexagon structure on the basis of existing soles, and analyzed the static performance of different soles by finite element method, and finally obtained the optimal sole structure scheme. Zhou Qixuan et al. established three kinds of foot contact simulation models by combining foot biomechanics and finite element method, designed the structure of running shoe midsole, and provided research ideas for the optimization of running shoe midsole structure. The finite element analysis method is applied to the sole structure analysis, and the sole structure is divided into finite and regular continuous unit combinations. By establishing mathematical equilibrium equations and analyzing the mechanical properties of each unit, the approximate solution of the overall sole structure analysis can be obtained, which can provide guidance and reference for researchers, and cooperate with sports biomechanics research to analyze the sole structure, which can effectively supplement the sole R&D design method. In this paper, the outsole of men's shoes is taken as the research object. Through reverse engineering and finite element analysis, the existing outsole structure of men's shoes is modeled and statically analyzed, and the stress distribution and stress deformation changes of the outsole in different human motion States are simulated, so as to explore the feasibility of finite element analysis in the structural design optimization of men's shoes. 2. Materials and Methods 2.1 Research materials The product number of this shoe is A2202AM1, and the outsole is made of rubber, with a shoe size of 42, as shown in Figure 1. Figure 1. Outsole for Testing www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 9, No. 1, 2025 26 Published by SCHOLINK INC. 2.2 Finite Element Model Reconstruction In this study, reverse engineering (RE) was used to reconstruct the sole model. Reverse engineering is a reverse implementation of traditional forward engineering. By measuring the three-dimensional dimensions of existing product entities, using computer-aided design to model and digitally reproduce them, product redesign, innovation and manufacturing can be realized. The measurement principle of reverse engineering includes contact and non-contact. In this paper, the non-contact scanning method is used, and the outsole is scanned by MetraSCAN 3D scanning equipment to obtain the data information of the outsole of men's shoes. Combined with the supporting VXelements 3D scanning software, the collected point cloud data is viewed. The point cloud data of the outsole is imported into Geomagic Wrap software, and the point cloud data of the outsole is deleted and noise points are filtered, and the outsole data is transformed into triangular patches, and the unsealed area of the outsole is filled and repaired, and the data of the front and back sides of the sole are merged to generate a closed surface. The repaired sole surface is exported to STL format, which is imported into UG 3D modeling software. The basic coordinates of the outsole surface are adjusted and the benchmark is checked, and the missing details of the outsole model are repaired during 3D scanning. The midsole with a thickness of 1.5mm is drawn based on the edge of the inner surface of the sole, and the midsole is divided into 99 separate areas according to the distribution of 99 sensors of the sole pressure insole, so that the stress on the outsole is more in line with the actual situation. The model is exported to STP format. At the same time, a cuboid with a length of 40cm, a width of 20cm and a height of 1cm is drawn as a ground model. The solid models of ground, outsole and midsole are assembled into a three-dimensional coupling model, which is derived in STP format for subsequent finite element analysis. The coupling model of "sole-ground" is shown in Figure 2. Figure 2. "Sole-Ground" Coupling Model Finite element modeling and mesh generation are carried out by HyperMesh software. The outsole of men's shoes is meshed with tetrahedral elements. In order to ensure the accuracy of the analysis, the mesh size of the midsole is set to 1.5mm according to the thickness of the midsole. The outsole structure is complex, and the grid size is set to 3 mm; The grid size of the ground has little influence on the simulation accuracy, and the size is set to 10 mm. Four indexes, such as Jacobian, Aspect Ratio, Warpage and Skew angle, are selected to compare the grid quality. Setting the Jacobian value above 0.7, www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 9, No. 1, 2025 27 Published by SCHOLINK INC. the length-width ratio value less than 5, the warping degree less than 5 and the torsion degree less than 60 meets the requirements. Finally, the "sole-ground" coupling finite element model has 50,842 nodes and 136,026 elements. The size and quantity of each unit are shown in Table 1. Table 1. Dimensions and Quantity of Components and Units Components Unit Type Unit Size (mm) Number of Units (unit) Middle bottom plate Two-dimensional S4 1.5 15247 Outsole Three-dimensional C3D4 3 116271 Ground Three-dimensional C3D4 10 3934 2.3 Finite Element Model Material Properties The density, elastic modulus and Poisson's ratio of sole materials were measured by precision electronic analytical balance, universal testing machine and static strain gauge respectively. The material parameters of the sole and ground are shown in Table 2. Table 2. Sole Material Parameters Sole Material Parameters Material Type Density (g/cm3) Elastic Modulus (MPa) Poisson's Ratio Outsole Rubber 1.149 1.47.26 0.454 Middle bottom plate Cork 0.647 1100.00 0.339 Ground Wood Composite Floor 0.733 1000.00 0.352 2.4 Finite Element Model Loading and Boundary Conditions The research subject is a male college student (age 24, height 180cm, weight 73.6kg, shoe size 42), whose main stress foot is his right foot, with the habit of running and fitness every week. His arches are healthy, and there is no foot disease or related injury. The informed consent form was signed before the test. FootScan flat sole pressure system was used to measure the data of sole pressure when the subjects were standing still with shoes on, and Novel Pedar insole sole pressure testing system was used to measure the stress on the feet of the subjects in four movements: standing still, walking at a constant speed of 1.2 m/s, jogging at a speed of 2.4 m/s and actively jumping at a height of 40 cm. The test frequency is set to 100 Hz. The finite element model of "sole-ground" is imported into Abaqus software and the boundary conditions are set. The midsole and the outsole are binding constraints, and the ground and the outsole are ordinary friction, so the ground is fixed constraints. According to the plantar pressure data when the subject stands still, they are respectively applied to the middle sole plate, and the direction is vertical downward, as shown in Figure 3. www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 9, No. 1, 2025 28 Published by SCHOLINK INC. (a) Distribution and data of sole pressure under standing condition (b) Plantar pressure loading Figure 3. Distribution and Loading of Plantar Pressure under Static Standing Condition 2.5 Finite Element Model Verification The measured pressure distribution values of the sole and sole of the subjects standing in static state are compared with the pressure nephogram obtained by finite element simulation, which verifies the effectiveness of the above-mentioned "sole-ground" coupling finite element model. Among them, the information of sole structure, sole material parameters, human load and constraint conditions are consistent with the actual situation, and the consistency of static standing conditions is maintained. The ground reaction force and contact area parameters are selected to calculate the average pressure between the outsole of men's shoes and the ground. 2.6 Static Simulation In order to explore the stress difference and distribution of soles under different motion postures, this study selected three human motion conditions, namely, uniform walking, jogging and active jumping. Based on the above settings of loading constraints on the model under static standing conditions, Abaqus software was used to analyze the stress magnitude and distribution of soles under different working conditions. The dynamic equation of the system for linear statics analysis can be expressed by Formula 1. （1） Where: m-mass matrix; C-damping matrix; K-system stiffness matrix; F-external force; , , represent the system acceleration, velocity and displacement. According to the definition of linear statics, the load is constant and the speed and acceleration of the system are both zero, so based on Hooke's law, the static analysis equation can be expressed by Formula 2. www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 9, No. 1, 2025 29 Published by SCHOLINK INC. （2） Where: k-material properties, model size and constraints, etc. F-external force; X-displacement; 3. Research Result 3.1 Model Verification Results The stress and strain between the outsole of men's shoes and the ground are shown in Figures 4-a and 4-b, that is, the stress distribution of the sole is relatively uniform under the static standing condition, and the maximum stress value is 5.783 Mpa. The largest deformation area is the forefoot area of the outsole, and the maximum deformation is 10.26 mm from the front tip to the back, the stress and deformation gradually decrease. As can be seen from Figure 4-c, the contact area between the outsole and the ground is mainly from the forefoot to the heel area, with a contact area of 83.6 cm2 and a ground reaction force of 386.2 N. As can be seen from Figure 4-d, the peak pressure of the outsole is the red area in the center of the heel, and the maximum peak pressure is 2.680 Mpa. （a）Stress distribution of outsole (b) Strain diagram of outsole www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 9, No. 1, 2025 30 Published by SCHOLINK INC. (c) The contact area between the outsole and the ground (d) The peak pressure of the outsole Figure 4. Simulation Results under Static Standing Condition Comparing the data measured by FootScan with the finite element simulation results of the outsole model, the results are consistent, the error is less than 10%, and the model is effective, as shown in Table 3. Table 3. Comparison of Simulation and Actual Measurement Results Index Simulation Actual Measurement Error (%) Ground reaction force (N) 386.2 379.2 1.8 Average pressure (N/cm2) 4.6 4.2 9 3.2 Static Simulation Analysis Results (1) Walking Condition After solving the uniform walking condition of 1.2 m/s by Abaqus, the instantaneous calculation result of sole touching the ground is shown in Figure 5. (a) Stress distribution of middle bottom plate (b) Deformation of bottom plate www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 9, No. 1, 2025 31 Published by SCHOLINK INC. (c) Stress distribution of outsole (d) Contact area between outsole and ground Figure 5. Simulation Results under Walking Conditions From the simulation results, it can be seen that the stress of the midsole is mainly distributed in the forefoot region and the heel region of the outsole, and the stress in the region contacting with the reinforcing ribs of the outsole groove is obviously small, and the maximum stress value is 20.45 Mpa, which occurs in the forefoot region. The maximum deformation of the middle bottom plate is 19.58 mm, which appears in the front tip area. The stress of the outsole is mainly distributed in the edge area of the inner side of the outsole. The closer to the middle area of the outsole, the smaller the stress is, and the maximum stress value is 7.437 Mpa, which occurs in the area where the heel rib meets the inner side edge. The stress and deformation of the outsole of men's shoes are basically consistent with the distribution of the midsole, and the maximum deformation is 19.58 mm. (2) Jogging Condition The jogging condition of 2.4m/s at a constant speed is solved by Abaqus, and the instantaneous calculation result of the sole touching the ground is shown in Figure 6. (a) Stress distribution of middle bottom plate (b) Deformation of bottom plate www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 9, No. 1, 2025 32 Published by SCHOLINK INC. (c) Stress distribution of outsole (d) Contact area between outsole and ground Figure 6. Simulation Results under Jogging Conditions From the analysis results, it can be seen that the stress and strain distribution areas and forms of uniform jogging and walking tend to be consistent, and the maximum stress and deformation of the middle floor are 23.60 Mpa and 22.01 mm respectively. The maximum stress of the outsole is 8.509 Mpa and the maximum deformation is 21.43 mm. (3) Active Jump Condition After Abaqus solves the active jumping condition with a height of 40 cm, the instantaneous calculation result of the sole touching the ground is shown in Figure 7. (a) Stress distribution of middle bottom plate (b) Deformation of bottom plate www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 9, No. 1, 2025 33 Published by SCHOLINK INC. (c) Stress distribution of outsole (d) Contact area between outsole and ground Figure 7. Simulation Results under Jumping Conditions From the analysis results, it can be seen that the stress and strain distribution areas and forms of uniform jogging and walking tend to be consistent, and the maximum stress and deformation of the middle floor are 35.19 Mpa and 23.01 mm respectively. The maximum stress of the outsole is 12.18 Mpa and the maximum deformation is 22.36 mm. According to the test of the validity of the finite element model under static standing conditions and the static analysis under three characteristic conditions, the stress and strain analysis results of the middle floor and the outsole are shown in Table 4 and Table 5 respectively. Table 4. Stress and Strain Results of Bottom Plate under Different Working Conditions Index Maximum stress (MPa) Maximum deformation (mm) Maximum stress area Stand still 0.74 10.26 Middle area of forefoot Walking at a constant speed of 1.2m/s 20.45 19.58 Medial margin of forefoot Jogging at a constant speed of 1.2m/s 23.60 22.01 Medial margin of forefoot 40cm active jump 35.19 23.01 Middle heel area Table 5. Strain and Stress Results of Outsole under Different Working Conditions Index Maximum stress (MPa) Maximum deformation (mm) Maximum stress area Stand still 5.783 10.26 Middle heel area Walking at a constant speed of 1.2m/s 7.437 19.58 Edge of medial heel rib Jogging at a constant speed of 1.2m/s 8.509 21.46 Edge of medial heel rib 40cm active jump 12.470 22.36 Edge of medial heel rib www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 9, No. 1, 2025 34 Published by SCHOLINK INC. According to the stress nephogram, maximum stress and strain results of the outsole of men's shoes under four different conditions, it can be seen that the maximum stress area in each condition is mainly concentrated in the heel area, and most of them are related to the position of the transverse stiffener, and the stress value in the rest of the heel area is relatively small. 4. Discussion and Analysis In the study of sports shoes, every optimization of sole structure is inseparable from the study of sports biomechanics. The establishment of sole-ground finite element analysis model can effectively help to analyze the interaction between shoes and ground under various working conditions, and provide scientific basis for the performance test of sole materials, the optimization of sole structure and the production design of soles. Ke Sicheng et al. established the finite element simulation model of foot-sole-ground, simulated the stress of the foot in the state of shoes during landing, and predicted the shock absorption performance of the sole. Yu et al. established a three-dimensional coupled finite element model of foot-ankle-shoe, simulated the wearing contact process and walking process of foot and shoe by interface contact simulation method, studied the plantar pressure when walking in high heels, and proved the versatility and potential of the calculation method in biomechanical evaluation and optimization in virtual environment. Tian et al. established a three-dimensional finite element model of foot-boot coupling, and simulated and studied the biomechanical changes of paratroopers' foot contact with the ground during parachute landing and falling. Dimitris et al. established a dynamic finite element model of running shoes, taking into account the time-varying plantar pressure distribution and boundary conditions, and put forward suggestions for improving the material distribution of midsole. Based on the existing traditional outsole of men's shoes, this study established a finite element model of sole-ground coupling, combined with biomechanical tests to explore the stress and strain size and distribution of soles, and provided guidance and suggestions for the optimization of outsole of men's shoes, especially the lightweight design of sole ribs. Model verification is one of the most important steps after the model is established. By comparing the simulated calculation value with the actual test value, the consistency of the two methods is analyzed, so as to realize the simulation as close as possible to the real motion characteristics. In this study, there is a difference between the simulation results of the finite element model of men's shoe outsole and the biomechanical test results, and the relative error is less than 10%, which may be caused by the reverse modeling of the sole or the accuracy of sensor acquisition during actual measurement. Although the simulation analysis results are not exactly the same as the actual measured values, the measured results show that the validity of the finite element model meets the expected requirements and can be used for subsequent analysis and guidance in the early stage of shoe design and development. By comparing the stress and strain analysis of each area of the outsole of men's shoes under three working conditions, it is found that the area where the outsole of men's shoes has the largest deformation is the forefoot under the static standing condition. This is because in the actual production of shoes and boots, the front tip of www.scholink.org/ojs/index.php/asir Applied Science and Innovative Research Vol. 9, No. 1, 2025 35 Published by SCHOLINK INC. the shoes will be designed with a certain degree of warping, which is generally called front stilts to meet the requirements of human comfort. The stress distribution area of the outsole of men's shoes is mainly in the edge area of the inner side of the outsole, and the closer it is to the middle area of the outsole, the smaller the stress is, because the midsole needs to be bonded with the inner edge of the outsole, and the inner edge of the outsole will be stressed more. 5. Conclusion Based on an existing casual men's shoe outsole, this study constructs a "sole-ground" coupling finite element model by combining reverse and forward modeling methods, and the model is verified to be effective and reliable. By measuring the sole load under three common human movements, namely walking, jogging and active jumping, the stress, strain and distribution of the outsole of men's shoes under different working conditions are solved, and it is concluded that the stress and strain of the outsole of men's shoes are in the front stilt part of the shoes and the area where the lateral rib of the heel meets the inner edge, which can provide research ideas and data support for the structural design of the outsole of men's shoes. References Davia-Aracil, M., Jimeno-Morenilla, A., & Salas, F. (2016). A new methodological approach for shoe sole design and validation. The International Journal of Advanced Manufacturing Technology, 86(9-12), 3495-3516. https://doi.org/10.1007/s00170-016-8427-5 Dimitris, D., Evagelos, K., & Maria, P. (2018). Gait-Specific Optimization of Composite Footwear Midsole Systems, Facilitated through Dynamic Finite Element Modelling. 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