Contact Force Distribution Research Articles

ABSTRACTThe geosynthetics can improve the shear performance of ordinary stone columns (OSCs) to resist the lateral force caused by embankment surcharge and seismic loads. The discrete element method (DEM) is employed to analyze and compare the static and cyclic shear performance of OSCs and geosynthetic‐encased stone columns (GESCs). The vertical and shear deformation, deformation of encasement, contact force distribution, porosity, coordination number, and radial stress coefficient are investigated. Furthermore, the effect of five critical factors on the cyclic behavior of GESC is explored. Numerical results show that GESC installation substantially enhances the shear resistance of sand compared to OSC. The column‐soil systems exhibit rapid stabilization during the initial loading cycles. The vertical strain, shear stress, porosity change, and average coordination number variation of GESC or OSC under cyclic conditions are larger than under static conditions. The maximum vertical strain in GESC demonstrates a positive correlation with loading amplitude (sm) and normal stress (σn), while inversely correlating with loading frequency (f), encasement length‐to‐column length ratio (Le/Lc), and column diameter (D). High f or sm amplifies the shear stress within GESC systems.

ABSTRACTThe application of biochemical reinforcement techniques in ordinary stone columns (OSCs) has garnered considerable interest, with scarce investigations into their micromechanical behavior and particle‐scale interactions. Three‐dimensional discrete‐element method (DEM) models are developed to analyze the micromechanical behavior of bio‐grouted stone columns (BSCs) and OSCs in clay under vertical loading. The DEM models of clay foundation, OSC, and BSC are successively verified by experimental works. The column‐soil stress ratio (n), radial stress coefficient (Kps), contact force distribution, porosity change, coordination number, and load‐displacement behavior of BSC and OSC were compared. Furthermore, the effects of contact‐bond strength (σcb), column length‐to‐foundation thickness (L/H), area replacement ratio (Ar), relative density (Dr), loading plate diameter‐to‐column diameter (DL/D), sand particle size‐to‐clay particle size ratio (Ss/Sc) on the behavior of BSC and OSC are systematically investigated and evaluated through a parametric study. The numerical results show that the bulging forms at the bottom of the BSC and within 3D in OSC. The passive earth pressure coefficient (Kp) design method underestimates the bearing capacity of BSC but overestimates that of OSC and geosynthetic‐encased stone column (GESC). Dilation is observed in OSC, whereas compression occurs in BSC. Short‐floating BSCs with an L/H less than 0.33 are not recommended in deep clay deposits. Large‐diameter GESC exhibits a lower bearing capacity, in contrast to the large‐diameter BSC. The bearing capacity of BSC with an Ss/Sc of 2.5–3.5 is similar to the OSC, indicating that the change in size of column material from reduced‐scale models to field‐scale implementations requires careful consideration.

The aim of this study is a comparative analysis of the stress–strain state of busbar punching tools after restoration using different methods. An overview of existing methods for restoring punches and dies was conducted. The analysis showed that each method has its own advantages and limitations. To address this issue, two restoration methods for the busbar punching tool are proposed: hardfacing of worn and damaged surfaces, and replacement of the working part with an insert made of carbon steel. A numerical simulation using the ANSYS software package was carried out to investigate the stress-strain state of busbar punching tools restored by two proposed methods. The simulation focused on determining the stresses in the working zones of the tool, deformations, and the distribution of contact forces. The results made it possible to identify critically loaded areas of the tool design and evaluate the effectiveness of the proposed restoration and modernization methods. The research, the results of which are presented in this article.

There is a strong coupling between two arms in cooperative operations of dual-arm robots. To enhance the coordination and cooperation ability of dual-arm robots, a force-closure-based weighted hybrid force/position fuzzy coordination control method is proposed. Firstly, to improve the grasping stability of dual-arm robots, the force-closure dynamic constraints are established by combining the friction cone constraints with the force and torque balance constraints. Then the optimal distribution of contact force is performed according to the minimum energy consumption principle. Secondly, to enhance the coordination of dual-arm robots, the weighted hybrid force/position control method is modified by adding the synchronization error between two arms. Then the Lyapunov method is adopted to prove the stability of the proposed coordination control method. Thirdly, the fuzzy self-tuning technique is adopted to adjust the control gains automatically. Lastly, a simulation and experiment are performed for collaborative transport. The results show that, compared with the position coordination control and the traditional hybrid force/position control, the weighted hybrid force/position fuzzy coordination control can improve control accuracy and has good cooperation ability and strong robustness. Therefore, the proposed method can effectively realize the coordination control of dual-arm robots.

Contact-force perception is a critical component of safe robotic grasping. With the rapid advances in embodied intelligence technology, humanoid robots have enhanced their multimodal perception capabilities. Conventional force sensors face limitations, such as complex spatial arrangements, installation challenges at multiple nodes, and potential interference with robotic flexibility. Consequently, these conventional sensors are unsuitable for biomimetic robot requirements in object perception, natural interaction, and agile movement. Therefore, this study proposes a sensorless external force detection method that integrates SuperPoint-Scale Invariant Feature Transform (SIFT) feature extraction with finite element analysis to address force perception challenges. A visual analysis method based on the SuperPoint-SIFT feature fusion algorithm was implemented to reconstruct a three-dimensional displacement field of the target object. Subsequently, the displacement field was mapped to the contact force distribution using finite element modeling. Experimental results demonstrate a mean force estimation error of 7.60% (isotropic) and 8.15% (anisotropic), with RMSE < 8%, validated by flexible pressure sensors. To enhance the model’s reliability, a dual-channel video comparison framework was developed. By analyzing the consistency of the deformation patterns and mechanical responses between the actual compression and finite element simulation video keyframes, the proposed approach provides a novel solution for real-time force perception in robotic interactions. The proposed solution is suitable for applications such as precision assembly and medical robotics, where sensorless force feedback is crucial.

ABSTRACTThe wear problem of disc cutters during large‐diameter shield tunneling in hard rock stratum has become increasingly prominent, significantly increasing engineering construction costs. Aiming at the disc cutter wear problem during large‐diameter shield tunneling in hard rock stratum, this paper analyzes the rock‐breaking form and contact force distribution in the cutter‐rock contact area, and establishes the prediction model for normal force, rolling force, and wear of disc cutter. The numerical simulation of disc cutter rock‐breaking is carried out using discrete element software, to explore the force and wear laws under different installation radius, cutter speed, and penetration depth. The wear partition phenomenon of disc cutter in different areas of the cutterhead is revealed, and the relationship between the wear law and installation position changes and its causes are analyzed. The wear prediction model is verified by the measured data of the Shantou Bay Undersea Tunnel Project. The research results provide a scientific basis for the wear prediction of large‐diameter shield disc cutters in hard rock stratum, which has important theoretical significance and engineering application.

Hybrid model of deep learning and contact theory for predicting distributed contact force in space debris de-tumbling

This paper performs a series of laboratory static lateral pressure coefficient (K0) tests on coral sands with five typical gradations in dry and saturated states via water bladder type lateral pressure apparatus to investigate their ranges of K0 values. The results reveal that the K0 values of coral sands in dry and saturated states range from 0.22 to 0.32 and 0.27 to 0.33, respectively, and that there is an exponential function relationship between the particle gradation and the K0. On this basis, a discrete element model is established with the aid of particle flow code (PFC), and the numerical simulation and laboratory test are in good agreement. The displacement field of coral sand with a narrower gradation is revealed to be more prone to exhibit a horizontally stratified compression feature at the meso-scale. The coral sand with a wider gradation exhibits a more obvious gradient distribution of internal contact forces with more uniform directional distribution and better compaction. The K0 decreases and then stabilizes with increasing particle bonding strength, and the evolution law between them conforms to the exponential function form. A theoretical calculation formula of K0 for coral sand based on the distribution coefficient is further proposed according to the laboratory test results. The research results of this paper can provide parameter support for construction and design of wharf retaining structures on islands and reefs.

Rough feature quantitatively described by the roughness indexes is the key to evaluating the shear mechanical characteristics of rock fractures in advance. However, the correspondence between roughness index and fracture shear mechanical characteristics has not been verified. In this study, the specific relationship between the roughness index θ*max/(C + 1) and the shear mechanical characteristics of rock fractures was discussed through numerical direct shear tests of fracture specimens based on the discrete element method (DEM). To explore this, rough rock fractures having the same θ*max/(C + 1) were established by adjusting the ten standard roughness profiles. The microscopic mechanics parameters of the rock and fracture in the numerical model were determined by calibrating the macroscopic parameters with physical model experiments. The test results show that fracture specimens with the same roughness grade exhibit varying shear mechanics indicators, with the degree of dispersion increasing as the roughness increases. However, due to differences in morphology, specimens with the same roughness grade exhibit distinct contact force distribution and failure characteristics. It has been observed that θ*max/(C + 1) can well reflect the roughness grade and even macroscopic shear properties of fractures when discretisation is not taken into account.

Abstract Two coupled part components such as bearings or connecting rods have a wide application in mechanical systems. The performance, efficiency, and durability of these components depend on the tolerances and surface quality obtained after being manufactured. One of the main problems that two coupled part components usually present is the appearance of discontinuities in their union interface, affecting the machining that will be performed in their interior housing once the assembly is carried out. In this work, the effect of pressure distribution for different tightening torque values applied in the two coupled part elements is studied, using the finite element method with non-linear contact elements and a matrix method of simplifying the model based in deformation energy. The latter is based on obtaining the distribution of contact forces through the conditions of Kuhn-Tücker and the method of Lagrange multipliers, which allows knowing what effects occur in the contact area. Subsequently, an experimental boring study has been carried out where the cutting forces are measured and the power spectrum is analyzed to determine if there are disturbances that can affect the roundness and quality surface of the manufactured component, and consequently, to a possible anomalous operation of the mechanical system in which the bi-components will be mounted.

This paper presents an application of numerical continuation to a lumped parameter model of an automotive wiper blade. The presented model includes considerations of a real contact force distribution of a wiper blade that is calculated through finite element analysis, as well as the nonlinear freeplay that is a common feature of movable joints which is captured through a cubic function. Performing bifurcation analysis allows the model’s parameter space to be mapped and qualitative assessments of the dynamics to be made; with the identified regions in the parameter space corresponding to transitions of stability of the presented model. Key quantities that can be related back to shaping of the contact distribution are studied, which include the wiper blade stiffness, total load, loading asymmetry, and a consideration of blade wrap.

Abstract To investigate the dynamic characteristics of the double-ring planetary gear transmission system with composite faults, a combined fault simulation study based on SolidWorks and ADAMS was conducted. An accurate virtual prototype model of composite faults, featuring pitting faults on the sun gear and cracks on the planet gear, was established to solve the tooth contact forces and analyze the dynamic characteristics of different composite faults. The results indicate that under healthy conditions, the contact forces of the gear pair exhibit stable periodic variations. When different gears have crack-pitting composite faults, the contact forces show distinct periodic peak values, accompanied by significant distributions of peak contact forces. With an increase in the severity of the pitting-crack composite faults, the peak values of the initial sidebands increase, and the sideband frequencies become denser. By observing the data variations in the time-domain and frequency-domain curves of the contact forces of composite faults, it is possible to preliminarily determine the presence of composite faults in the transmission system, offering a new method for fault diagnosis in physical prototype systems.

ABSTRACTSand‐rubber mixture (SRM), a composite material made of recycled rubber and sand, is gaining increasing attention in construction engineering due to its lightweight nature, cost‐effectiveness, ease of processing, and other advantages. However, the mechanical behavior of SRM remains a complex issue as the addition of rubber not only increases the types of contacts between grains, but also changes the contact topology with rubber undergoing significant deformation. This study presents a numerical investigation of the intricate mechanical behavior of SRM based on the material point method (MPM) tailored for modeling the assembly of deformable grains. The employed approach introduces multiple meshes for handling the kinetic and deformation of individual grains and a discrete element method (DEM)‐type contact algorithm to directly address the intricate interaction in SRM, being capable of accurately modeling the complex behavior of SRM. Furthermore, rubber membranes in the biaxial shear test are simulated with material points with sufficient deformation capacity to accurately simulate the actual loading boundary. We first validated the accuracy and effectiveness of the proposed method through a series of benchmarks. Subsequently, one‐dimensional compression and biaxial shear simulations were conducted on the SRM to investigate the influence of rubber content (RC) and confining pressures. Both macroscopic deformation and the microstructural characteristics are examined. The results indicate that increasing RC leads to a more uniform contact force distribution, and a more stable force chain network, while higher confining pressure enhances the particle connectivity within the SRM.

This study numerically investigates contact forces and the contact network in unconfined and confined compression tests on rock-like bonded granular materials using the particle-based discrete element method (DEM). Statistical analysis of contact force magnitudes and polar distributions under varying confining pressures reveals a significant influence of confining pressure on force evolution. Additionally, contact force distribution is closely related to internal structures and external loads. The relationship between contact force and geometrical features of the contact network is analyzed, along with the three-stage evolution of the relationship between force anisotropy and stress ratio, driven by contact network changes. Tensile force chain lengths follow an exponential distribution. Without confinement, tensile force chains remain stable until crack formation, whereas under confinement, they increase in number and length before decreasing due to the occurrence of cracks. Higher confinement results in shorter, fewer tensile force chains. Finally, the number, orientation and force magnitude of new tensile contacts are analyzed to further elucidate tensile contact evolution in bonded granular materials.

BackgroundOcclusion plays a crucial role in maintaining masticatory function and temporomandibular joint (TMJ). Single implant supported restorations are widely used for posterior tooth replacement, but they require careful occlusal adjustment due to the absence of periodontal ligament. Digital occlusal analysis methods, such as digital impressions and Occlusense, provide quantitative assessments of occlusal contacts and force distribution. However, their accuracy and clinical relevance remain uncertain.MethodsIn this prospective clinical study, occlusal force distribution was evaluated before and after placement of single implant supported restoration using the Medit i700 intraoral scanner and OccluSense system. Measurements were performed before and after prosthesis under standardised conditions. Occlusal contact areas and force distributions were analysed using CloudCompare and ImageJ software. Statistical analysis was performed using Kruskal–Wallis test and Kendall's Tau-B correlation analysis.ResultsA total of 20 patients were included in the study. Post-restoration measurements revealed significant changes in occlusal force distribution in different segments of the dental arch (p < 0.001). Strong correlations were observed between Medit and OccluSense measurements (p < 0.001).ConclusionSingle-unit implant restorations significantly alter the occlusal force distribution, affecting not only the restored tooth but also the adjacent and opposing teeth. Both Medit i700 and OccluSense provided valuable information, with OccluSense providing a more detailed representation of occlusal force density. These findings suggest that digital occlusal analysis methods can help optimise occlusal adjustments for implant restorations.Trial registrationThe current study was registered in ClinicalTrials.gov (ID: NCT06862973) First posted: 07/03/2025. Retrospectively registered.

ABSTRACTGeotextile‐encased stone columns (GESCs) for improving weak foundations commonly experience static and dynamic loads. However, the effectiveness of GESCs in resisting dynamic loading remains a concern. Three‐dimensional numerical models using a continuum‐discrete coupled method are developed to investigate the dynamic response of GESC groups in sand under sinusoidal loading. The models capture the dynamic variations in settlement (δz), lateral displacement (δr), porosity, coordination number, contact force distribution, and radial stress coefficient (). A parametric study further examines the effect of six key factors. The results reveal that the column group effect notably reduces δr of the central column by 52.78% compared to a single GESC. GESCs exhibit shear deformation and translational movement, with δr increasing as the distance from the group center grows. The position of maximum δr shifts downward from a z/D ratio of 0.83–2.5 with increasing distance in the x‐direction, while remaining stable in the y‐direction. High contact forces accumulate at the GESC bases, peaking initially before declining over time. The remains below 2.0, considerably lower than the passive earth pressure coefficient (Kp). Kp for design purposes overestimates the bearing capacity of GESCs under dynamic loading. GESC groups are more sensitive to lower loading frequencies, while larger relative density, soil strength, or column diameter improves dynamic resistance.

The force chain network within asphalt mixtures serves as the primary load-bearing structure to resist external forces. The objective of this study is to quantitatively characterize the contact force distribution and force chain topology structure. The discrete element method (DEM) was employed to construct simulation models for two stone matrix asphalt (SMA) and two open-graded friction course (OGFC) mixtures. Load distribution characteristics, including average contact force, load bearing contribution and contact force angle, and force chain topological network parameters, clustering coefficient, edge betweenness and average path length, were analyzed to elucidate the load transfer mechanisms. The findings of the present study demonstrate that the average contact force between aggregate-aggregate contact types in specific particle sizes significantly exceeds the average contact force of the same particle size aggregates. For SMA16 and OGFC16 asphalt mixtures, the load-bearing contribution of aggregates initially increases and then decreases with decreasing particle size, peaking at 13.2 mm. SMA13 and OGFC13 mixtures demonstrate a consistent decline in load bearing contribution with decreasing aggregate size. The analysis of the force chain network topology of the asphalt mixture reveals that SMA mixtures exhibited higher average clustering coefficients in force chain topological features in comparison to OGFC mixtures. It indicates that SMA gradations have superior skeletal load-bearing structures. While the maximum nominal aggregate size minimally influences the average path length with a relative change rate of 3%, the gradation type exerts a more substantial impact, exhibiting a relative change rate of 7% to 9%. These findings confirm that SMA mixtures have more stable load-bearing structures than OGFC mixtures. The proposed topological parameters effectively capture structural distinctions in force chain networks, offering insights for optimizing gradation design and enhancing mechanical performance.

To address the environmental hazards caused by coal gangue waste, coal gangue concrete (CGC) has been proposed as a solution. However, due to its porosity and low strength, CGC faces numerous challenges in practical applications. To further improve its performance, fiber reinforced polymer (FRP) material was introduced to confine it. In this study, the PFC3D-FLAC3D coupling analysis method was employed to simulate the uniaxial compression test of FRP confined coal gangue concrete specimens. The influence of different FRP types (GFRP, CFRP, BFRP) and coal gangue replacement rates (0%, 50%, 100%) on the axial compression performance of coal gangue concrete columns was analyzed. Based on the indoor uniaxial compression test of glass fiber reinforced polymer (GFRP) confined coal gangue concrete, the modeling and calibration of coal gangue concrete columns confined by different FRP sheets were conducted. The strength variation and microstructure evolution mechanism of coal gangue concrete specimens confined by three kinds of FRP were discussed. The results indicated that the numerical model is highly accurate and consistent with existing experiments. The type of FRP significantly influences the confinement effect on coal gangue concrete specimens. As the coal gangue replacement rate increases, both the strength and elastic modulus of the specimens decrease. The difference of the spatial distribution of strong contact number and strong contact force reflect the microscopic manifestation of the macroscopic strength. The crack evolution of FRP confined coal gangue concrete went through three stages during uniaxial compression. This study is of great significance for selecting the appropriate type of FRP confinement for concrete under different coal gangue replacement rates.

High-temperature friction and high-speed impact are the primary sources of mechanical damage to artillery steel, severely restricting the interior ballistic properties and service life of barrel weapons. A hydrodynamic friction model is first proposed to express the high-temperature friction behavior between the rotating band and the barrel. Additionally, this article deduces a contact force model to describe the high-speed impact behavior between the center band and the barrel. The general expression of mechanical damage can be obtained by the hydrodynamic friction and contact force models. Meanwhile, this article calculates the frictional coefficient and contact force distribution during the artillery launching combined ABAQUS with polynomial chaos expansion. The experimental verification of the hydrodynamic friction and contact force models is organized, and the detailed assessments show that the frictional coefficient and contact force responses have good agreement with experimental data. Finally, this article gives the mechanical damage evolution based on the general mechanical damage model. The mechanical damage of the barrel chamber is mainly located at the muzzle and 1/6 barrel length position from the beginning of rifling.

An accurate finite element model for tooth contact and meshing force distribution of crown gear coupling