JKR Model Research Articles

A new discrete element method for small adhesive non-spherical particles

Small adhesive particles with non-spherical shapes are common in natural and industrial processes. However, it is challenging to accurately simulate the dynamic behaviors of non-spherical particulate systems, not only due to the complex local geometry at the contact region but also to the non-linear coupling between the van der Waals adhesion and the elastic deformation. In this paper, we develop a discrete element method (DEM) framework for small non-spherical particles. Particularly, we present a simple algorithm for solving the implicit equations of the dimensionless generalized JKR model, to accurately resolve the local surface geometry at the contact region and the strong coupling between the elastic deformation and the surface adhesion. New explicit expressions are established for the pull-off force, overlap and minor-to-major ratio of the contact ellipse, to naturally capture the pull-off point upon collision. Then the actual contact parameters including the contact radius, curvatures and overlap are used to modify the interparticle interactions, including the normal elastic-adhesive-dissipative force and sliding-rolling-twisting resistances. Finally, the framework is quantitatively validated by four random packing problems, including adhesive spheres, ellipsoids, spherocylinders and dimers, and the representative non-adhesive ellipsoids. Both the microscopic and macroscopic properties of packings agree well with a large number of classic theories, experiments and simulations, showing the satisfactory accuracy and effectiveness. The newly developed adhesive DEM framework has the full capability to dynamically simulate the collision-related behaviors of complex shaped particles in the presence of van der Waals adhesion and frictional forces.

Calibration and Verification of Discrete Element Parameters of Surface Soil in Camellia Oleifera Forest

To analyze the interaction between the surface soil and the soil-contacting component (65 Mn) in the camellia oleifera forest planting area in Changsha City, Hunan, China, in this study, we conducted discrete element calibration using physical and simulation tests. The chosen contact model was Hertz–Mindlin with JKR cohesion, with the soil repose angle as the response variable. The repose angle of the soil was determined to be 36.03° based on the physical tests. The significant influencing factors of the repose angle determined based on the Plackett–Burman test were the soil–soil recovery coefficient, soil–soil rolling friction coefficient, soil-65 Mn static friction coefficient, and surface energy of soil for the JKR model. A regression model for the repose angle was developed using the Box–Behnken response surface optimization method to identify the best parameter combination. The optimal parameter combination for the JKR model was determined as follows: surface energy of soil: 0.400, soil–soil rolling friction coefficient: 0.040, soil-65 Mn static friction coefficient: 0.404, and soil–soil recovery coefficient: 0.522. The calibrated discrete element parameters were validated through experiments on the repose angle and steel rod insertion. The results indicated that the relative errors obtained from the two verification methods were 2.44% and 1.71%, respectively. This research offers fundamental insights for understanding the interaction between soil and soil-contacting components and optimizing their design.

CFD-EDEM simulations of droplets in an airless rotary spray coating process

Numerical simulations of airless rotary spray coating process are presented using CFD-EDEM with JKR contact model. The JKR model parameters are suggested according to the virtual test of accumulation angles in the funnel device. The reasonable droplet-wall surface energy is recommended from a relation of accumulation angles. The gas turbulence model is evaluated based on the comparisons of velocities and droplet number fractions using RNG k-ε, realizable k-ε and transition SST models. The simulated film thicknesses agree with measurements in literature. The correlation of exit droplet velocity of sprayer holes is proposed with a discharge coefficient of 2.27. The velocities and film thickness are predicted with changing rotation speeds. The normal force is an order of magnitude larger than the tangential force of droplet-wall collisions, and the ratio of the normal to tangential energy losses of droplet-wall collisions varies from 2.0 to 5.0 in airless rotary spray coating processes.

A CFD-DEM Simulation of Droplets in an Airless Spray Coating Process of a Square Duct

The purpose of this paper is to provide a numerical simulation, taking into account the collisional interactions of droplets in an airless rotary spray coating process. The hydrodynamics of gas and droplets are simulated using the CFD-discrete element method (DEM) with the JKR contact model in an airless rotary spray coating process of a horizontal square duct. The surface energy parameter used in the JKR model is calibrated using a virtual accumulation angle test in the funnel device. Based on the distribution of accumulation angles, a suitable surface energy for wall droplets is proposed. A rational gas RNG k-ε model is suggested in accordance with the comparisons of velocities, standard deviations, and the skewness of droplet number fractions from three turbulence models. The simulations of droplet film thicknesses agree with measurements from the literature regarding the film thickness along a vertical panel. The correlations of the exit gas and droplet velocities of sprayer holes are proposed with a discharge coefficient of 0.85 for gas and 5.87 for droplets. A number index of droplets is introduced in order to measure the uniformity of droplet distributions. A low droplet number index is found at low rotational speeds, representing a more uniform distribution of droplets as the rotation speeds reduce within the square duct. The normal force between the droplet and the wall is approximately an order of magnitude larger than the droplet–wall tangential force of collisions.

Wet adhesion on rough surfaces: A JKR model with thermodynamic considerations

Understanding wet adhesion is vital for advancing technologies such as underwater robotics, aquatic microsystems, and sweat-interfaced devices. It involves the formation of a liquid bridge with a meniscus between two solid surfaces. This phenomenon has a significant impact on surface adhesion, particularly in relation to roughness. Determining the profile of this liquid bridge is critical for accurately characterizing wet adhesion. In this paper, we propose a JKR mechanical model combined with a thermodynamic approach to investigate adhesive contact between a spherical indenter and an axisymmetric wavy surface in a wetting environment. The numerical solution for the pull-off force is obtained by considering parameters such as waviness, roughness, liquid volume, and liquid surface energy. The theoretical findings validated by experimental results provide insights into wet adhesion mechanisms on rough surfaces.

Effect of temperature on adhesion behavior of layered piezoelectric structure

The effect of temperature on adhesion is neglected in classical adhesive contact theories. However, an increasing number of experimental results indicate that temperature has a prominent effect on adhesion behaviors. In this study, the anisothermal adhesive contact behaviors between two transversely isotropic piezoelectric cylinders with different initial temperatures is investigated by virtue of the generalized JKR model, where the contact interface is assumed to be perfectly bonded. The considered problem is reduced to coupled singular integral equations, which is derived by using the Fourier integral transform. The closed-form solutions of anisothermal generalized stress fields are obtained by taking the series expansion of the integrand induced by temperature difference. The effect of temperature difference on adhesion behaviors of two different types of layered piezoelectric structures under the action of mechanical-electro loadings is revealed. It is found that the pull-off force and contact size at pull-off moment decrease with increasing the temperature difference. The adhesion weakening effect induced by temperature difference diminishes when the electric loading is exerted. The results derived from this paper shed lights on understanding the adhesive contact behaviors of piezoelectric materials in the presence of temperature difference.

Calibration of Model Parameters for Soda Saline Soil-Subsoiling Component Interaction Based on DEM

To apply the discrete element method (DEM) to simulate the interaction process between soda saline–alkali soil and subsoiling component in Northeast China, establishing the soda saline–alkali soil particle model and selecting more accurate simulation parameters are important. In this paper, we studied the soda saline–alkali soil of the Songnen Plain in China. First, we studied the geometric shape of soda saline–alkali soil particles and proposed a modeling method for single soil particles based on the multisphere combination method. Considering the cohesion of soda saline–alkali soil particles, the Hertz–Mindlin with JKR (JKR) model was used as the contact model between soil particles. Then, the calibration method was used to obtain simulation parameters of soils that are difficult to obtain experimentally. We conducted soil angle of repose (AoR) tests, the Plackett–Burman (PB) tests, and steepest ascent (SA) tests in turn to perform a sensitivity analysis for microscopic contact parameters and select the parameters that have a significant effect on the response value (static AoR), i.e., soil surface energy, soil–soil static friction coefficient, and soil–soil rolling friction coefficient. Then, the optimal combination of simulation parameters was obtained via the Box–Behnken (BB) tests, using ANOVA to optimize the multiple regression equation. Finally, the optimal parameter combination was verified by the AoR test and the direct shear (DS) test. The results showed that the parameters had good adaptability for the AoR test. However, the simulation results of the DS test were significantly different from the experimental values. Therefore, the contact model needs to be further modified by adding Bonding bonds between soil particles based on the JKR model and further correcting for Rayleigh time step, shear modulus, and surface energy. By comparing the simulation and the experimental results, it was found that the simulation results obtained from both the DS test and AoR test had relatively small errors relative to physical tests, the two trends are the same, and the values are similar. This verified the feasibility and effectiveness of the soda saline–alkali soil particle modeling method and parameter selection proposed in this paper.

Dynamics of underwater microparticle adhesion to soft hydrated surfaces: Modeling and analysis by time-dependent AFM force spectroscopy

HypothesisUnderstanding the attachment and detachment of microparticles and living cells to surfaces is crucial for developing antifouling strategies. Hydrogel coatings have shown promise in reducing fouling and particle adhesion due to their softness and high water content, yet the mechanisms involved are dynamic and complex, and relevant parameters are not easily accessible. AFM-based force spectroscopy (FS) experiments with colloidal probe particles is a direct way of evaluating adhesive and mechanical relaxational dynamics, yet their interpretation and modeling has been challenging. The present study proposes and examines several dynamic models, suitable for quantitative analysis of FS results with model probe particle on hydrogels surfaces. ExperimentsFS were performed using polyethylene glycol (PEG) hydrogels and polystyrene microspheres including particle attachement to the hydrogel surface (loading), holding the particle on the surface with a constant force for variable times (dwell) and pulling the particle away from the surface (unloading) FindingsIt was found that a viscoelastic extension of the classical JKR model with energy of adhesion unevenly distributed over the contact area and vanishing at its circumferences accurately described all FS experiments and yielded physically consistent viscoelastic and adhesive dynamic parameters, steadily changing with dwell time and applied force. The observed time evolution and force dependence were rationalized as combination of osmotic and osmo-mechnical relaxation in the contact region.

Comparing particle shape representations and contact models for DEM simulation of bulk cohesive behaviour

The Discrete Element Method (DEM) offers great potential as a design tool for the bulk simulation of cohesive systems. However, DEM simulations may require simplified particle shapes. Accordingly, the simulation of bulk dynamic, cohesive behaviour, which employs either single-sphere or multi-sphere shape replication, was compared. Additionally, the most auspicious cohesive contact models were examined, namely the Full JKR, SJKR, liquid-bridge and linear cohesive model. To this end, the elevation of a cohesive particle-bed’s centre of gravity in a rotating drum was utilised to examine the resultant cohesive behaviour. The single-spheres and multi-spheres performed similarly when replicating bulk cohesive behaviour. In addition, comparable results were observed between the simulated bulk cohesive behaviour of the Full JKR and SJKR contact models. The bulk cohesive behaviour replicated by the liquid-bridge contact model was more sensitive to the specified surface tension parameter value than the specified moisture content parameter value. The linear cohesive model could replicate bulk cohesive behaviour by only specifying a rupture force. However, including a rupture distance enhanced the bulk cohesive response, whilst the magnitude of the rupture distance was uninfluential. However, large rupture distances increased a particle’s number of contacts, which resulted in increased computational times.

Effect of adhesion on the frictionless receding contact between an elastic layer and a substrate

ABSTRACT In the present work, adhesion has been incorporated in a model for receding contact between an elastic layer and a half plane under flat and parabolic punches. Based on the JKR model for adhesion and with the help of integral transformation, solution of the problem may be reduced to a system of singular integral equations. A numerical scheme has been proposed and verified. The effect of adhesion on contact size and the stresses has been demonstrated.

New Mechanical Models to Study the Impact of Contact, Wear, and Adhesion of Lunar Dust on Space Materials

Lunar dust significantly impacts spacecraft and spacesuits during lunar exploration. The mechanical properties of lunar dust, including adhesion, contact, and wear, are investigated using new mechanical models proposed herein. First, the main contribution for mechanics of this paper was implementing the conical Johnson, Kendall, and Roberts (JKR) model using the energy method for investigating the normal and tangential mechanical characteristics of lunar dust. Additionally, the mechanical properties of lunar dust, such as adhesion, contact, and wear are proposed considering the adhesion effect using the mechanical model. The validity and accuracy of the conical JKR model were verified by comparing the results with experimental data and existing spherical and cylindrical JKR models. Furthermore, a new wear mechanical model for typical lunar dust is proposed considering the adhesion effect. The wear width and coefficients based on the wear model fit well with the existing experiment; therefore, the proposed model can be used to calculate the wear coefficient. Additionally, it can be used to estimate the contact force using an atomic force microscope (AFM) probe and analyze the adhesion between rough particles. The mechanical properties of lunar dust based on our models can be valuable for the characteristic research of in situ resource development and manned lunar landings.

Study on mesoscopic adhesion characteristics of deep-sea sediment for self-cleaning mechanism of bionic grouser

Deep-sea soil adhering to the grouser of mining machines may decrease mining efficiency. To realize the self-cleaning function of grouser, this paper proposes a bionic corrugated grouser. A small soil groove cutting model is established based on the adhesion characteristics of deep-sea sediments and the theory of the Discrete Element Method (DEM). Using Hertz-Mindlin with JKR model to express the adhesive properties of soil. Simulation results show that the bionic grouser can significantly reduce the adhesion force with soil particles. When the waveform function of the bionic grouser is Y = 2sin(X/10), the surface adhesion force is the smallest, and it has the best self-cleaning effect. The experiment of cutting deep-sea soil with a self-designed bulldozer verifies the correctness of the conclusions obtained from the simulation. To further improve the self-cleaning performance of grouser, nano-silica materials were used to modify the surface, and indoor traction tests obtained positive results.

Adhesive behavior between dissimilar materials subjected to thermo-elastic loadings with normal-tangential coupling effect

The temperature difference always exists between contacting objects in various thermal bonding technologies, where the adhesion strength is found to be very sensitive to the temperature. In this paper, the anisothermal adhesive contact between an elastic cylinder subjected to the external force with an inclined angle and an elastic substrate is investigated based on the non-slipping JKR model, where the coupling effect between the normal and tangential tractions within the contact region is taken into consideration. The stated problem is reduced to a system of coupled singular integral equations, which can be solved with the analytical function theory. The full analytical solutions of the oscillatory stress fields are obtained for the first time by taking the series expansion of the integrand induced by the thermoelastic effect, which is of substantial significance. The relationship between the contact size and the external loadings is established by virtue of the Griffith energy balance criterion. The difference between the oscillatory and non-oscillatory solutions of stress fields is discussed in detail. Numerical results demonstrate that the oscillatory solution cannot be well approximated by the corresponding non-oscillatory solution for the cases of large Dundurs’ index and external compressive force. Furthermore, it is found that both the thermoelastic effect and the inclined angle of the applied force have significant influences on the adhesive contact behaviors. The presence of temperature difference between contacting objects can either enhance or weaken the adhesion effect, which is related to the inclined angle of the external force. The results obtained from this paper may provide a new insight into the influence mechanism of the temperature on adhesion behaviors.

Indentation of pre-deformed compressible soft electroactive layer on substrate

Layer-substrate system penetrated by a rigid indenter has been frequently used as the physical model for interpreting the indentation test of advanced materials. In this paper, the indentation of a pre-deformed compressible soft electroactive (SEA) layer on an elastic substrate is formulated as a Fredholm integral equation of the second kind, which is solved by a customized finite-difference scheme to fulfil the full-field analysis. Especially, the modified JKR model established in the half-space case is invoked to take account of surface adhesion for the peculiar layer-substrate system. As an example, the neo-Hookean ideal dielectric elastomer is considered, and the effects of adhesion (due to surface energy) and substrate (due to different mechanical and electrical properties from the layer) on the indentation responses are scrutinized. Numerical results indicate that, when a soft layer overlies a stiffer substrate, the contact radius should be smaller than the layer thickness for the validity of linear analysis. In this case, as the contact radius exceeds about 1/10 of the layer thickness, the indentation responses are found to vary significantly with the shear modulus ratio between the layer and the substrate while they are insensitive to the variation of Poisson's ratio of the substrate within the linear regime. Moreover, an interesting phenomenon is revealed that the indentation responses (e.g., the surface normal stress) induced by adhesion will be suppressed by stiffening of the substrate, and vice versa.

Adhesion of graded elastic materials: A full self-consistent model and its application

A full self-consistent model (FSCM) of the axisymmetric adhesive contact between a rigid punch with an arbitrary surface shape and a power-law graded elastic half-space is developed. The self-consistent equation between the surface gap and the surface interaction (e.g., the Lennard–Jones force law) involves a nonlinear singular integral, posing a great challenge to numerical calculations. By applying the properties of Gauss’s hypergeometric function, the integral singularity is eliminated in the numerical calculation through Riemann–Stieltjes integral. Case studies for power-law punch profiles are performed and the self-consistent equation can be expressed in a dimensionless form with three dimensionless parameters, namely a shape index, a gradient exponent, and a new generalized Tabor number. The FSCM results are obtained by solving the self-consistent equation through the surface central gap control method and Newton–Raphson iterative method. For large generalized Tabor numbers, the force–displacement curves are ‘S-shaped’ and condense to the extended JKR limit in the high-load branch. As the generalized Tabor number decreases, a continuous transition from the extended JKR model to the Bradley model for the adhesion of power-law graded materials is obtained. It is found that the pull-off force of a graded material usually depends on the three dimensionless parameters, but for some cases of the shape index, it is not sensitive to the gradient exponent when the generalized Tabor number is fixed. Asymptotic solutions are derived to predict the unstable jump points, which coincide well with the FSCM predictions. The FSCM is applied to validate the extended Maugis–Dugdale (M–D) model of graded materials and it is found that the accuracy of the original M–D-n-k model using the maximum strength condition to determine the cohesive stress is limited. By introducing the rigid-limit-consistency condition of the pull-off force to determine the cohesive stress, the M–D-n-k model is improved and its predictions show good consistency with the FSCM results.

Boundary element analyses on the adhesive contact between a rigid cylinder and an elastic layer bonded on a rigid half-space

The adhesive contact between a rigid cylinder and an elastic layer bonded on a rigid half-space is investigated. In the past, several analytical models were proposed in the frame of the JKR model. In this research, boundary element method is employed. The traction is derived on the basis of the Lennard-Jones potential and the Derjaguin approximation. The whole solutions are obtained. The effects of Tabor parameter and layer thickness are investigated. The results are compared with the analytical models. The limitations of the analytical models are obtained. The empirical formulas for pull-off forces, jump-in distance, and pull-off distance are proposed.

Combined effects of viscoelasticity and surface roughness on the adhesion behavior of a flat-end cylindrical microstructure

A theoretical modeling approach is developed to simulate the rate-dependent adhesion contact between a single flat-end cylindrical microstructure and a randomly rough rigid surface. This model combines the Greenwood-Williamson rough contact model and the rate-dependent JKR model for viscoelastic dynamic contact, which can comprehensively consider the roughness-induced adhesion hysteresis and the rate-dependent adhesion hysteresis. A numerical scheme is proposed to make the rate-dependent adhesion model compatible with the randomly rough contact equation. The proposed method is verified well by comparing with the Fuller & Tabor model at a very low approach/detachment speed. The effects of surface roughness and viscoelastic material constant on adhesion strength and energy dissipation are evaluated. Results indicate that there is an optimal surface roughness at which the surface adhesion strength is the strongest, and a worst roughness that minimizes the energy dissipation. The effect of viscoelastic material constant depends on the approach/detachment speed of the microstructure. A higher approach/detachment speed causes the adhesion strength and the energy dissipation to change significantly with viscoelastic material constant, while a low speed does not.

Calibration of wet sand and gravel particles based on JKR contact model

The parameters of wet sand and gravel particles with different shapes are calibrated based on JKR contact model. The results reveal that surface energy and rolling friction coefficient are the significant factors affecting the tangent of repose angle, indicating the great influence on the simulation accuracy of wet sand and gravel particles during vibration screening. In addition, the tangent of repose angle and error between simulation and experiment both increase with the filling ball radius increasing, and the corresponding simulation accuracy decreases. Then the screening efficiency is further investigated to verify the accuracy of the calibration parameters. The parameters calibrated can well simulate the screening process. And it is found that non-spherical model instead of spherical model can better simulate the screening process of sand and gravel particles. Meanwhile, JKR model is also verified to better simulate the screening process than Hertz-Mindlin model. Moreover, as the filling ball radius increases, the screening efficiency increases while the simulation time and file size are greatly reduced. However, the corresponding error between simulation and experiment increases. Considering the error and screening time, the optimum filling ball radii for flat, triangular cone and ellipsoid particles are 2 mm, 1.5 mm and 1 mm, respectively.

Adhesive behavior of transversely isotropic piezoelectric bimaterials

The adhesive contact behavior between two dissimilar transversely isotropic piezoelectric cylinders is investigated in this paper. The effect of adhesion on the contact behavior between piezoelectric bimaterials is considered within the framework of the non-slipping JKR model, which takes the coupling effect between the tangential and normal tractions inside the contact region into account. The explicit analytical solutions of stress and electric displacement fields within the contact region are obtained by solving the resulting coupling singular integral equations with the analytical function theory. The relationship between the contact size and external loadings are established by adopting the Griffith energy balance criterion at the edges of the contact zone. It is found that different types of piezoelectric bimaterials show the same adhesive contact behaviors, which is different from the case of a single layer piezoelectric material. The result obtained from the present paper should be helpful for the design of micro-electro-mechanical systems (MEMS) devices involving multi-layered smart structures.

Mechanical models for the adhesive friction of nano- and micro-particles

Friction is common in human’s daily life and production that may be either detrimental or beneficial. The friction law at microscale or even smaller scales nevertheless is lacking. In the present work, on the basis of JKR model for adhesive contact and by analogy with the emission of dislocations at a crack tip, the critical tangential force has been obtained for the onset of sliding. When the tangential force in adhesive contact induces a torque at the interface, a mechanical model for rolling adhesion has been presented on the basis of the assumption that it is governed by adhesion hysteresis. The critical torque and tangential force for rolling onset have been determined, which may be taken as measure for the rolling friction force. Comparisons with relevant experiments and models have been made to support the present concept. A kind of friction duality in small sized particles can thus be predicted.