Viscoelastic Contact Model Research Articles

Modeling and simulation of three-dimensional manipulation of viscoelastic folded biological particles considering the nonlinear model of the cell by AFM

Previous research on biological particles manipulation has taken into account linear cellular models and spherical geometry, Whereas, particles such as bacteria and cancer cells have cylindrical and crushed cylindrical geometry. On the other hand, cell behavior is nonlinear. Therefore, it is important to apply above mentioned models in the manipulation models and to investigate the modes of motion in the cylindrical nanoparticle manipulation to calculate the critical time and forces in order to understand the properties and behavior of these particles. In this paper, we present the analytical nonlinear cellular mechanical models that lead to the extraction of the creep function proportional to the biological particle behavior. Cylindrical and crushed cylindrical geometry considered in manipulation simulation. The cell is modeled with 2nd and 3rd order nonlinear spring and damper which are parallel and series. At the end, 2nd order nonlinear Kelvin selected as the most appropriate model. Comparison with the cell model of power-law and experimental data led to correction coefficients in models. Hereafter, JKR viscoelastic contact model was proposed for nanoparticles with cylindrical and crushed cylindrical geometry. Then, the application of cell models in the contact model and subsequently modeling of the first phase of the manipulation, considering folding factor, has been done. By simulating the main motion modes, including the mode of the slip of the probe tip on the particle, particle's rotation on the surface and the mode of slipping the particle on the surface, the force and critical times were obtained. According to the results, for a particle with a cylindrical geometry, the slip mode of the particle on the surface happens in 505.4 milliseconds and 5 microseconds faster than other modes. Besides, applying the folding factor causes an increase of 7% in the critical time. Because the folded shape of the cell surface causes more disturbance and friction, it requires more time and force to move the particle away and is matched to the physics of the problem. For a particle with a crushed cylindrical geometry, the slip of the probe tip on the particle occurs in 420.7 milliseconds and 10 milliseconds faster than other modes and under the force of 0.7255 micro N and about 71 percent less than the others. Also, the application of the folding factor for this particle contributes to an increase of 24% in critical force and an increase of 11% in the critical time.

Measurement of viscoelastic properties for polymers by nanoindentation

A new method has been proposed and verified to measure the viscoelastic properties of polymers by nanoindentation tests. With the mechanical response of load–displacement curves at different loading rates, the parameters of creep compliance and relaxation modulus are calculated through the viscoelastic contact model. Dynamic thermomechanical analysis (DMA) tests are conducted to compare the results by the proposed technique. The results show that the correlation coefficients between DMA tests and the new method are above 0.9 in the entire range, which verified the feasibility of the method. The loading curves fitted by the model are identical to the experimental curves within the discrete points and so it shows that this technique is more suitable for general linear viscoelastic materials. Numerical creep tests are carried out to examine the effectiveness of the proposed method by input the Prony series calculated by the three-element Maxwell model and the viscoelastic contact model. The good agreement shows that the proposed technique can be applied in practice.

Rate-dependent adhesion of cartilage and its relation to relaxation mechanisms

Cartilage adhesion has been found to play an important role in friction responses in the boundary lubrication regime, but its underlying mechanisms have only been partially understood. This study investigates the rate dependence of adhesion from pre-to post-relaxation timescales of cartilage and its possible relation to relaxation responses of the tissue. Adhesion tests on cartilage were performed to obtain rate-dependent cartilage adhesion from relaxed to unrelaxed states and corresponding relaxation responses. The rate dependence of cartilage adhesion was analyzed based on experimental relaxation responses. Cartilage adhesion increased about 20 times from relaxed to unrelaxed states. This rate-dependent enhancement correlated well with the load relaxation responses in a characteristic time domain. These experimental results indicated that the degree of recovery (or relaxation) in the vicinity of contact during unloading governed the rate dependence of cartilage adhesion. In addition, the experimentally measured enhancement of adhesion was interpreted with the aid of computationally and analytically predicted adhesion trends in viscoelastic, poroviscoelastic, and cohesive contact models. Agreement between the experimental and predicted trends implied that the enhancement of cartilage adhesion originated from complex combinations of interfacial peeling and negative fluid pressure generated within the contact area during unloading. These findings enhance the current understanding of rate-dependent adhesion mechanisms explored within short time scales and thus could provide new insight into friction responses and stick-induced damage in cartilage.

Comparative behavior of damping terms of viscoelastic contact force models with consideration on relaxation time

This paper presents a comparative investigation into behaviors of different damping terms of viscoelastic contact models, and introduces a novel damping term with dimensional reasoning analysis and by considering the effect of relaxation time of viscoelastic spheres. Behaviors of different contact models are compared in terms of predictions of non-dimensional variables, where the influence of damping parameters on behaviors of viscoelastic models is analyzed and the relationship between non-dimensional damping parameters and the coefficient of restitution is discussed. The damping parameter related to relaxation time is found to affect behaviors of the current viscoelastic contact model significantly. Viscoelastic models of different damping terms exhibit different behaviors, especially for a heavily damped case. Comparison between simulation and free fall impact test of viscoelastic balls demonstrates that the current contact model involving relaxation time fits experimental results better than other contact models.

The Indentation Rolling Resistance in Belt Conveyors: A Model for the Viscoelastic Friction

In this paper, we study the steady-state rolling contact of a linear viscoelastic layer of finite thickness and a rigid indenter made of a periodic array of equally spaced rigid cylinders. The viscoelastic contact model is derived by means of Green’s function approach, which allows solving the contact problem with the sliding velocity as a control parameter. The contact problem is solved by means of an accurate numerical procedure developed for general two-dimensional contact geometries. The effect of geometrical quantities (layer thickness, cylinders radii, and cylinders spacing), material properties (viscoelastic moduli, relaxation time) and operative conditions (load, velocity) are all investigated. Physical quantities typical of contact problems (contact areas, deformed profiles, etc.) are calculated and discussed. Special emphasis is dedicated to the viscoelastic friction force coefficient and to the energy dissipated per unit time. The discussion is focused on the role played by the deformation localized at the contact spots and the one in the bulk of the thin layer, due to layer bending. The model is proposed as an accurate solution for engineering applications such as belt conveyors, in which the energy dissipated on the rolling contact of idle rollers can, in some cases, be by far the most important contribution to their energy consumption.

Development of rough viscoelastic contact theories and manipulation by AFM for biological particles: any geometry for particle and asperities

Researchers are interested in simulating the manipulation of biological micro/nanoparticles by the atomic force microscope. However, there are many obstacles practically, and there are still numerous unknowns and uncertainties regarding the interactions in bio-environments between biological micro/nanoparticles with different geometries. Most of the previous works performed on the manipulation of biological particles have been conducted on various particles with presumed spherical, and sometimes cylindrical, shapes. But, as we know, the real biological particles have different shapes and geometries. On the other hand, in the case of biological particles, according to their softness and damping properties, elastic assumption can lead to inevitable errors in simulations. So, in this paper new viscoelastic contact model applicable for different geometries has been developed and applied in force indentation simulations. Results show good compatibility with experimental data. Moreover, topography images showed that cell surface is not smooth and contains asperities, so, new viscoelastic roughness theory has been also developed for these particles with different geometries. Outputs of this model have been also compared with experimental data which showed results’ modification. Application of these models in manipulation of biological cells can help to obtain more accurate results.

Optimization problems for a viscoelastic frictional contact problem with unilateral constraints

We consider a mathematical model which describes the contact between a viscoelastic body and a rigid-deformable foundation with memory effects. We derive a variational formulation of the model which is in the form of a history-dependent variational inequality for the displacement field. Then we prove the existence of a unique weak solution to the problem. We also study the continuous dependence of the solution with respect to the data and prove two convergence results, under different assumptions on the data. The proofs are based on arguments of lower semicontinuity, pseudomonotonicity, and compactness. Finally, we use our convergence results in the study of several optimization problems associated to the viscoelastic contact model.

Optimal control simulation predicts effects of midsole materials on energy cost of running

Testing sports equipment with athletes is costly, time-consuming, hazardous and sometimes impracticable. We propose a method for virtual testing of running shoes and predict how midsoles made of BOOSTTM affect energy cost of running. We contribute a visco-elastic contact model and identified model parameters based on load-displacement measurements. We propose a virtual study using optimal control simulation of musculoskeletal models. The predicted reduction in energy cost of for BOOSTTM in comparison to conventional materials is consistent with experimental studies. This indicates that the proposed method is capable of replacing experimental studies in the future.

Developing viscoelastic contact models and selecting suitable creep function for spherical biological cells.

In most contact theories, the most popular of which are the three models of Hertz, Derjaguin, Muller and Toporov (DMT) and Johnson, Kendall and Roberts (JKR), biological cells were considered as an elastic material which is not a proper assumption. The elastic assumption in the case of biological cells could lead to neglecting the loading history as a result of which the stresses and strains applied to the material would not be studied accurately. In this paper, developing the three mentioned elastic models into viscoelastic models, simulating and comparing them with empirical data obtained through the indentation test of the MCF-7 cancer cell showed that the viscoelastic state presents a better prediction of biological cell behavior compared to that of an elastic state. The selection of the suitable creep function for objects in contact is another issue that has a significant importance in the viscoelastic case and this was investigated. Different mechanical models of a cell were studied and simulated for all three named theories among which the creep function obtained from the Kelvin model, a parallel combination of spring-damper, simplified the simulation and gave more precise results for modeling due to the fact that the obtained results from this model are closer to experimental ones and simpler than other models. On the other hand, for a more exact prediction of cell behavior, this model was modified by an equivalent elasticity module which considered cell components instead of the cell cortex only. The results of the simulation confirmed that a new elasticity module can improve the accuracy of cell models. After choosing the suitable mechanical model for the cell, we scrutinized the capability of the developed theories in predicting the results for biological liquid environments. Although the results of the Hertz and DMT viscoelastic models are closer to experimental ones in comparison with viscoelastic JKR, neglecting adhesion makes their prediction in biological liquid environments weak and erroneous. Therefore, it can be concluded that the developed viscoelastic model of JKR is more accurate and has a better performance in different environments than the other mentioned models.

A traveling wave ultrasonic motor with a metal/polymer-matrix material compound stator

This study proposes a traveling wave ultrasonic motor with a metal/polymer-matrix material compound stator. The stator is composed of a metal ring and polymer-matrix teeth. The resonance frequency of the stator with different structural dimensions was analyzed by the finite element method. From the results, the structure parameters of the metal ring were obtained. The effects of the density and elastic modulus of the tooth material on the resonance frequency were also investigated. A viscoelastic contact model was built to explore the contact state between the compound stator and rotor. Considering the density, elastic modulus and tribological properties, the tooth material was prepared by a molding process. The load–torque and efficiency–torque characteristics of the motor with different tooth thicknesses were measured under different preloads using a preload controlled ultrasonic motor test device. The maximum no-load speed of the motor was about 85 r min−1 with a tooth thickness of 3 mm and a preload of 100 N, the maximum stall torque of the motor was about 0.5 N · m with a tooth thickness of 4 mm and a preload of 125 N, and a maximum efficiency of about 5.5% occurred with a tooth thickness of 4 mm, a preload of 100 N and a torque of 0.3 N · m. The main merits of the proposed ultrasonic motor are low cost, light weight, high processing efficiency and long life.

Determination of the restitution coefficient of seeds and coefficients of visco-elastic Hertz contact models for DEM simulations

In this study, we determine the coefficients of restitution (CoRs) of seeds coming from three plants, namely the pea (Pisum sativum L. cv. Piast), soybean (Glycine max (L.) Merr. cv. Annushka) and rapeseed (Brassica napus L. cv. Licosmos), at three levels of moisture content for an impact velocity V0 ranging from 0.17 to 8.8 m s−1. We obtain high-speed camera measurements as well as single-drop and repeated-bounce tests. We record the impact force–time relationships Fn(t) using a piezo-ceramic pressure sensor. The results show that the rate of decrease of the CoR with an increase in V0 was the highest for rapeseed having the highest moisture content (MC), and it was the lowest for pea seeds having the lowest MC. We perform experiments to model the relationships CoR(V0) using visco-elastic contact models based on Hertz contact theory. The impacts of dry seeds for three crops were best illustrated using three different contact models, for pea – Kuwabara and Kono (1987), soybean – Alizadeh et al. (2013) and rapeseed – Hu et al. (2011). For higher MC, models which provide a more nonlinear CoR(V0) relationship appeared to be more appropriate, i.e. Kuwabara and Kono (1987) for the pea and soybean, while the model of Alizadeh et al. (2013) better described the behaviour of rapeseed. Visco-elastic contact models which were selected using the least-square method provided a very good approximation of CoR(V0) and impact time tc(V0) relationships, and a sufficiently good approximation of the shape of Fn(t) relationships.

A size-dependent viscoelastic normal contact model for particle collision

Considering different energy dissipation mechanisms, many normal contact models have been proposed. However, the size effect and velocity effect of normal restitution coefficient (NRC) cannot always be accurately described. In addition, most of the normal contact models have unphysical tension stage for particles without adhesion during the simulation of particle collisions. Such problems limit the application of discrete element method (DEM) in particle dynamics. Given such limitations, the normal contact model proposed in the present work consists of a nonlinear Hertz spring and a size-dependent nonlinear dashpot, and the model parameters are determined by the NRC obtained in lab tests. Compared with other viscoelastic contact models, the current model can effectively alleviate the influence of unphysical tension force stage on the calculated results, satisfying the accuracy requirement of calculation, and accurately describe the size effect and velocity effect of the NRC of marble spheres at the same time. Besides, due to the viscous force, the contact time calculated by the current model is a little larger than the elastic contact time. The relationship between model parameters and particle size has been analyzed, which shows the law of K1 conforms to exponential decay law and the K2 conforms to hyperbolic tangent function.

Method for Estimating Normal Contact Parameters in Collision Modeling Using Discontinuous Deformation Analysis

AbstractThis paper presents a contact parameter estimation method for collision modeling using discontinuous deformation analysis (DDA). Most DDA codes and discrete element method (DEM) codes use the viscoelastic contact model for contact-stress calculation. The contact parameters of the viscoelastic contact model, such as normal stiffness and damping constant, affect the computation results observably. Although the DDA method has been proposed for more than 20 years, the contact parameters in DDA modeling are still difficult to determine. In collision dynamics, the coefficient of restitution (COR) is considered the critical parameter for describing the changes of motion state after collision between two objects. In the proposed method, the normal COR is used for evaluating calculation results of rockfall modeling with three-dimensional DDA. The normal COR of the two-object model is obtained by tests or empirical methods. The relation curve of contact parameters and the normal COR is generated on the basi...

Discrete Element Method Modeling of the Rheological Properties of Coke/Pitch Mixtures.

Rheological properties of pitch and pitch/coke mixtures at temperatures around 150 °C are of great interest for the carbon anode manufacturing process in the aluminum industry. In the present work, a cohesive viscoelastic contact model based on Burger’s model is developed using the discrete element method (DEM) on the YADE, the open-source DEM software. A dynamic shear rheometer (DSR) is used to measure the viscoelastic properties of pitch at 150 °C. The experimental data obtained is then used to estimate the Burger’s model parameters and calibrate the DEM model. The DSR tests were then simulated by a three-dimensional model. Very good agreement was observed between the experimental data and simulation results. Coke aggregates were modeled by overlapping spheres in the DEM model. Coke/pitch mixtures were numerically created by adding 5, 10, 20, and 30 percent of coke aggregates of the size range of 0.297–0.595 mm (−30 + 50 mesh) to pitch. Adding up to 30% of coke aggregates to pitch can increase its complex shear modulus at 60 Hz from 273 Pa to 1557 Pa. Results also showed that adding coke particles increases both storage and loss moduli, while it does not have a meaningful effect on the phase angle of pitch.

Convergence of viscoelastic constraints to nonholonomic idealization

Abstract Rolling motion, which is usually described by means of nonholonomic constraints, can occur in many technical systems e.g. roller bearings or gear wheels in gearboxes. The idealized modeling of mechanical multibody systems with rolling elements leads to differential algebraic equations (DAEs). The kinematical condition of a vanishing relative velocity is enforced by constraint forces. However contact areas are not ideally rigid, but compliant due to local deformations of asperities and elasticity of the contacting bodies. For this reason a sensible physical description should take these effects into account. Thus the contact forces are modeled in the present paper using a tangential viscoelastic force element in the contact. The rolling motion is then enforced by applied forces, instead of constraint forces in the ideally rigid case. The objective of this work is to show that under certain conditions, solutions of the general multibody system with viscoelastic contact model converge to the solutions of the multibody system containing idealized nonholonomic constraint equations, if the viscoelastic constants approach infinity. An ansatz in form of an asymptotic series expansion with initial layer terms is introduced to prove the convergence under appropriate assumptions on the viscoelastic parameters. In order to suppress high frequency oscillations in the contact, the choice of the damping parameter is inspired by the critical damping, known in linear systems theory.

A New Formula of Impact Stiffness in Linear Viscoelastic Model for Pounding Simulation

The phenomenon of earthquake-induced structural pounding was extensively studied by some researchers using different models for the impact force. The aim of this paper is to provide a new formula of impact stiffness in the linear viscoelastic contact model, based on the assumption that the maximum impact deformation from the distributed mass model should be equal to that from the equivalent lumped mass model. The correctness and accuracy of the proposed formula have been confirmed by comparing the pounding simulation using the present formula of impact stiffness with those using the existing formulae.

A superellipsoid-plane model for simulating foot-ground contact during human gait

Musculoskeletal models and forward dynamics simulations of human movement often include foot–ground interactions, with the foot–ground contact forces often determined using a constitutive model that depends on material properties and contact kinematics. When using soft constraints to model the foot–ground interactions, the kinematics of the minimum distance between the foot and planar ground needs to be computed. Due to their geometric simplicity, a considerable number of studies have used point–plane elements to represent these interacting bodies, but few studies have provided comparisons between point contact elements and other geometrically based analytical solutions. The objective of this work was to develop a more general-purpose superellipsoid–plane contact model that can be used to determine the three-dimensional foot–ground contact forces. As an example application, the model was used in a forward dynamics simulation of human walking. Simulation results and execution times were compared with a point-like viscoelastic contact model. Both models produced realistic ground reaction forces and kinematics with similar computational efficiency. However, solving the equations of motion with the surface contact model was found to be more efficient (~18% faster), and on average numerically ~37% less stiff. The superellipsoid–plane elements are also more versatile than point-like elements in that they allow for volumetric contact during three-dimensional motions (e.g. rotating, rolling, and sliding). In addition, the superellipsoid–plane element is geometrically accurate and easily integrated within multibody simulation code. These advantages make the use of superellipsoid–plane contact models in musculoskeletal simulations an appealing alternative to point-like elements.

Implementation and Verification of Linear Cohesive Viscoelastic Contact Model for Discrete Element Method

PURPOSES: Implementation and verification of the simple linear cohesive viscoelastic contact model that can be used to simulate dynamic behavior of sticky aggregates. METHODS: The differential equations were derived and the initial conditions were determined to simulate a free falling ball with a sticky surface from a ground. To describe this behavior, a combination of linear contact model and a cohesive contact model was used. The general solution for the differential equation was used to verify the implemented linear cohesive viscoelastic API model in the DEM. Sensitivity analysis was also performed using the derived analytical solutions for several combinations of damping coefficients and cohesive coefficients. RESULTS : The numerical solution obtained using the DEM showed good agreement with the analytical solution for two extreme conditions. It was observed that the linear cohesive model can be successfully implemented with a linear spring in the DEM API for dynamic analysis of the aggregates. CONCLUSIONS: It can be concluded that the derived closed form solutions are applicable for the analysis of the rebounding behavior of sticky particles, and for verification of the implemented API model in the DEM. The assumption of underdamped condition for the viscous behavior of the particles seems to be reasonable. Several factors have to be additionally identified in order to develop an enhanced contact model for an asphalt mixture.

Generalized Maxwell Viscoelastic Contact Model-Based Discrete Element Method for Characterizing Low-Temperature Properties of Asphalt Concrete

AbstractA universal asphalt concrete discrete element method (DEM) model was established in this paper. Coarse aggregates consisting of balls bonded by elastic contact models were simulated using irregular particles. Asphalt mastic consisting of balls bonded by a generalized Maxwell viscoelastic contact model held coarse aggregates together. The generalized Maxwell viscoelastic contact model was developed based on a finite difference scheme using Visual Studio 2005. The relationship between microscale model input and macroscale properties of asphalt mastics and coarse aggregates was derived to calibrate contact parameters of the proposed DEM model. Dynamic modulus tests, static creep tests, bending tests at low temperature, and the corresponding DEM simulations were implemented to contrast the simulation effect of the proposed DEM model and the existing DEM model. Simulation results show that the proposed DEM model exhibits an improved accuracy using a universal mathematical structure. The averaged and ma...

On the Applicability of Sneddon's Solution for Interpreting the Indentation of Nonlinear Elastic Biopolymers

Indentation has been widely used to characterize the mechanical properties of biopolymers. Besides Hertzian solution, Sneddon's solution is frequently adopted to interpret the indentation data to deduce the elastic properties of biopolymers, e.g., elastic modulus. Sneddon's solution also forms the basis to develop viscoelastic contact models for determining the viscoelastic properties of materials from either conical or flat punch indentation responses. It is worth mentioning that the Sneddon's solution was originally proposed on the basis of linear elastic contact theory. However, in both conical and flat punch indentation of compliant materials, the indented solid may undergo finite deformation. In this case, the extent to which the Sneddon's solution is applicable so far has not been systematically investigated. In this paper, we use the combined theoretical, computational, and experimental efforts to investigate the indentation of hyperelastic compliant materials with a flat punch or a conical tip. The applicability of Sneddon's solutions is examined. Furthermore, we present new models to determine the elastic properties of nonlinear elastic biopolymers.