Viscoelastic Contact Model Research Articles

Evaluation of an Active Disturbance Rejection Controller for Ophthalmic Robots with Piezo-Driven Injector.

Retinal vein cannulation involves puncturing an occluded vessel on the micron scale. Even single millinewton force can cause permanent damage. An ophthalmic robot with a piezo-driven injector is precise enough to perform this delicate procedure, but the uncertain viscoelastic characteristics of the vessel make it difficult to achieve the desired contact force without harming the retina. The paper utilizes a viscoelastic contact model to explain the mechanical characteristics of retinal blood vessels to address this issue. The uncertainty in the viscoelastic properties is considered an internal disturbance of the contact model, and an active disturbance rejection controller is then proposed to precisely control the contact force. The experimental results show that this method can precisely adjust the contact force at the millinewton level even when the viscoelastic parameters vary significantly (up to 403.8%). The root mean square (RMS) and maximum value of steady-state error are 0.32 mN and 0.41 mN. The response time is below 2.51 s with no obvious overshoot.

Experimental and numerical study of lateral vibration of a rotor–stator rubbing system

AbstractIn this paper, lateral vibration of a rotating system with rotor–stator rubbing is investigated experimentally and numerically. An experimental study is conducted using a simple test rig to model a horizontal rotating system with a fixed stator device to simulate rubbing. Furthermore, a lumped parameter model with two degrees of freedom is established with a viscoelastic contact model that considers the stiffness and damping properties of the stator. The fourth/fifth order Runge–Kutta technique is used to solve the nonlinear equations of motion of the rotor system. The effect of changing mass unbalance and radial clearance on the dynamic response is investigated experimentally and numerically. The observed results are presented in detail through bifurcation diagrams, frequency spectra, Poincaré’s points, orbit plots, and time waveforms. The experimental results show that changing the mass unbalance and radial clearance yield significant effects on the system response. The 2 × and 3 × harmonic components are found to serve as good indicators of increasing rub severity. The numerical results show the dynamic characteristics of rub responses such as periodic no-contact, periodic with contact, quasi-periodic, and chaotic responses. The response characteristics are very sensitive to the changes in system parameters and initial conditions. Both the experimental and numerical results show qualitatively that the lateral vibration response exhibits coexistence and alternation of periodic and chaotic responses. Also, quasiperiodic response shows up in some numerical case studies. The obtained results contribute toward a better diagnosis of rotor–stator rub fault in rotating machines.

Mathematical Modeling of Collisional Heat Generation and Convective Heat Transfer Problem for Single Spherical Body in Oscillating Boundaries

The application of high-energy ball milling in the field of advanced materials processing, such as mechanochemical alloying and ammonia synthesis, has been gaining increasing attention beyond its traditional use in material crushing. It is important to recognize the role of thermodynamics in high-energy processes, including heat generation from collisions, as well as ongoing investigations into grinding ball behavior. This study aims to develop a mathematical model for the numerical analysis of a spherical ball in a shaker mill, taking into account its dynamics, contact mechanics, thermodynamics, and heat transfer. The complexity of the problem for mathematical modeling is reduced by limiting the motion to one-dimensional translation and representing the vibration of the vial wall in a shaker mill as rigid boundaries that move in a linear fashion. A nonlinear viscoelastic contact model is employed to construct a heat generation model. An equation of internal energy evolution is derived that incorporates a velocity-dependent heat convection model. In coupled field modeling, equations of motion for high-energy impact phenomena are derived from energy-based Hamiltonian mechanics rather than vector-based Newtonian mechanics. The numerical integration of the governing equations is performed at the system level to analyze the general heating characteristics during collisions and the effect of various operational parameters, such as the oscillation frequency and amplitude of the vial. The results of the numerical analysis provide essential performance metrics, including steady-state temperature and time constant for the characteristics of temperature evolution for a high-energy shaker milling process with a computation accuracy of 0.1%. The novelty of this modeling study is that it is the first to obtain such a high accuracy numerical solution for the temperature evolution associated with a shaker mill process.

Impact Stiffness of Linear Viscoelastic Model for Seismic Pounding Simulation: An Experimental Evaluation

Pounding between adjacent structures occurs when the separating distance within the two buildings is inadequate to contain the movement between them during an earthquake event. Seismic pounding can lead to significant harm or even the destruction of neighbouring structures. In creating a model for structural response, impact stiffness is considered as a critical factor in calculating the impact force throughout the collision within adjacent structures. It is important to derive realistic stiffness values when performing a numerical simulation of pounding forces within abutting structures to attain valid results. The objective of this study is to ascertain the impact stiffness within the linear viscoelastic contact model, using data obtained from shaking table experiments of pounding between neighboring five-storey and 15-storey single-bay model of steel-frame. The steel models were subjected to scaled ground acceleration records, two far-field and two near-field. The study’s findings indicate that there is a significant discrepancy between the theoretical impact parameters and the measured experimental value because the assumptions made to derive the theoretical formulas do not align with the actual impact conditions. The accuracy and precision of the experimental formula adopted in this study have been validated in comparison with the numerical results. Doi: 10.28991/CEJ-2023-09-06-01 Full Text: PDF

Generalised Kelvin contact models for DEM modelling of asphalt mixtures

ABSTRACT Rigid particle models based on the discrete element method (DEM) have been adopted to model creep, fracture, and the viscoelastic behaviour of asphalt mixtures considering an irregular micro-structure and particle contacts. Within a DEM framework, the Burgers contact model, which is known to have a narrow frequency and temperature range, is usually adopted to model viscoelastic properties. In this study, a new explicit three-dimensional generalised Kelvin (GK) contact model formulation for the DEM model is proposed for asphalt materials. The model is implemented following two different methodologies (GK 1 and GK 2 ). The models are validated in uniaxial tension-compression sinusoidal tests for predicting the dynamic modulus ( | E ∗ | ) and phase angle (ϕ) of these composites at a frequency range of 1–10 Hz at 20 ∘ C. Four mixtures are investigated based on the modelling of their mastic. The influence of the GK contact parameters on the dynamic response of mastics is assessed. Results show that κ m has an important influence on both rheological properties and that η m can be used for small adjustments focussing on the predicted phase angle. Moreover, it is shown that a viscoelastic contact model should be adopted to simulate aggregate-to-mastic contacts in mixtures. As expected, the response obtained for both GK models is the same but the simulations with the GK 1 are 14% faster. In addition, the response predicted with the proposed GK contact model is compared with the response predicted with a Burgers contact model. The DEM predictions obtained for the GK model are more accurate. For mastics, the average errors for | E ∗ | and ϕ when adopting the GK model (Burgers) are 2.40% (3.46%) and 3.64% (4.17%), respectively. For mixtures, the average errors for | E ∗ | for the GK model (Burgers) are 7.00% (7.92%). The proposed contact model greatly enhances the DEM ability to simulate the viscoelasticity of asphalt materials.

A normal contact force model for viscoelastic bodies and its finite element modeling verification

A novel normal contact force model considering the energy dissipation for viscoelastic bodies is presented. By solving the differential equation through applying Laplace transform and its inverse transform, the relationship of the stress and strain is established. The model is transformed from the stress-strain relation using the Stieltjes convolution. The proposed model involves the viscosity and relaxation time which represent dominating characteristics of viscoelastic bodies. A means to verify the model using the finite element method (FEM) is performed with a specify two-sphere model for FEM simulations and a user material subroutine applied to define viscoelastic material properties. The validity of the novel model is verified with FEM simulations by comparing the force-time and force-displacement relations. The comparisons indicate that results obtained by the model agree well with the outcomes of FEM simulations. In addition, results of the proposed model are compared with the former experimental data and results obtained by other viscoelastic contact models, which manifests that results predicted by this model fit the experimental data well in general, especially in the restitution phase.

Approximate coefficient of restitution for nonlinear viscoelastic contact with external load

We derive an approximate coefficient of restitution (CoR) for a single bead impacting the ground when a constant external load acts upon the colliding body. Some of the main applications concern classical nonlinear viscoelastic models such as the Kuwabara-Kono model, Simon-Hunt-Crossley model, and Hertzian stiffness with linear damping, however the proposed approach applies to a wide class of nonlinear viscoelastic contact models. It is shown that suitable expansions allow to derive a computable expression of the CoR which provides accurate predictions for a valuable range of external loads, viscosity coefficients and impact velocities.

A Novel Nonlinear Dynamic Model for Predicting Contact Bounce of Electromagnetic Relays With Flexible Spring Components

Contact bounce is a common phenomenon in the closing process of electromagnetic relays, which seriously affects the electrical contact reliability of the system. The whole closing process of flexible spring components consists of the free movement stage and the contact bounce stage, which increases the complexity of analyzing the electrical contact behaviors of electromagnetic relays. In this study, a novel nonlinear dynamic model of the flexible spring components in electromagnetic relays is established to analyze the physical mechanism of the electrical contact bounce. Considering the electromagnetic effect, flexible deformation, contact collision, and welding force, the proposed mathematical model can capture the dynamic closing process accurately and collect bounce parameters efficiently. The Kelvin–Voigt viscoelastic contact model is employed to evaluate the nonlinear contact force between the static and movable contacts. Based on the Galerkin method, the nonlinear equations of motion for the movable spring within electromagnetic relays are formulated. A series of experimental work are designed to measure the typical waveforms of displacements of the movable contact and currents in the coil during the closing process of the movable spring. Furthermore, the theoretical results are validated by comparing with the experimental data. The dependences of some key factors, including the structural, material, and electrical contact parameters on the contact bounce characteristics, are investigated explicitly. The theoretical results attest that the proposed model can accurately predict the dynamic behaviors of the movable spring, and the contact bounce can be effectively suppressed by adjusting the parameters of the flexible spring component.

Viscoelastic adhesive contact between a sphere and a two-dimensional nano-wavy surface

For contact involving viscoelastic materials with nanoscale roughness surfaces, both the viscoelasticity and the adhesive interaction play significant roles, and an in-depth understanding of this viscoelastic adhesive contact behavior is essential. This paper establishes a numerical viscoelastic adhesive contact model between a smooth sphere and a two-dimensional nano-wavy surface based on the Derjaguin approximation and elastic–viscoelastic correspondence principle, and the wavy surface is considered by introducing the height distribution into the surface gap equation. Influences of approach speed, contact position and wavy surface parameters on the viscoelastic adhesive contact behavior are quantitatively analyzed. It is shown that the viscoelasticity can be ignored at large approach speed, while when the speed is small, viscoelasticity significantly increases the maximum contact area and pull-off force. Variations of maximum contact area and pull-off force with contact position or wavy surface parameters are not completely consistent, where the contact positions with relatively large maximum contact area may exhibit small pull-off force. The pull-off force changes monotonically with increasing wavy parameter, while the maximum contact area changes nonmonotonically. This study can offer guidance for the application of wavy surface in viscoelastic adhesion regulation, and provide basis for the surface design and parameter determination of viscoelastic materials.

A Review of Computational Simulation Methods for a Ship Advancing in Broken Ice

Apart from breaking level ice, polar ships can interact with broken ice in various scenarios. In recent years, computational simulation models have increasingly been used for the evaluation of ship operability under broken ice conditions, presenting some challenging issues. This paper reviews existing simulation methods used to estimate ship performance and ice loads for ships advancing continuously in broken ice fields. Models for different types of broken ice, including ice floes, ice ridges, brash ice, and sliding ice pieces, are reviewed separately. A ship’s response in broken ice is divided into two categories: resistance, which relates to the overall ship performance, and local loads, which relates to structural safety. This review shows that most existing models are proposed for unbreakable ice particles, which are only applicable to broken ice of small size; most models treat fluid flow with extensive simplification, which does not reflect the influence of a ship’s wake or bow waves, and most models are aimed at resistance estimation, adopting elastic or viscoelastic contact models which do not include ice crushing. As for future work, it is suggested that more effort should be assigned to simulating a ship’s interaction with ice ridges and sliding ice pieces, the modelling of breakable ice floes, and the coupling of the Discrete Element Method (DEM) and Computational Fluid Dynamics (CFD). More attention to the local ice load estimation is also encouraged.

Viscoelastic contact model development for the discrete element simulations of mixing process in agitated drum

A discrete element contact model was developed to simulate the mixing power requirement in an agitated drum. Contact viscous dampings in normal and tangential direction, rolling and twisting resistance torques, including elastic and viscous components have been implemented. The applicability of the developed contact model was first examined by angle of repose (AoR) and direct shear box (DSB) simulations and measurements, followed by mixing power requirement (MPR) simulations. Due to the time step reduction caused by the application of contact viscous dampings, the reducing of simulation time was also investigated. It was found that the contact viscous dampings were required to set the final micromechanical parameters for mixing accurately, however, the viscous components of the resistance torques were found to be negligible. The developed contact model simulated the mixing power requirement in the agitated drum accurately over the investigated 0.48−1.58 s−1 rotational speed range and 10 % ; 15% drum loading factors.

Laboratory for Validation of Rolling-Resistance Models

In this paper, a versatile drum setup for measuring rolling resistance of small wheels is presented. The purpose is to provide a flexible setup for testing of models for rolling resistance under controlled circumstances. To demonstrate this, measurements of rolling resistance with a series of sandpapers of different grit sizes representing surface textures were carried out. The measurements show a clear increase in the rolling-resistance coefficient with increasing surface roughness, rolling speed and load. Numerical calculations in the time domain for a visco-elastic contact model run on equivalent surfaces agree with the trends found experimentally. We conclude that this approach to simplifying the experiment in order to obtain a high degree of control, accuracy and repeatability is useful for validating and testing models for calculating the rolling resistance for a given surface texture.

Micromechanical simulation of porous asphalt mixture compaction using discrete element method (DEM)

The paper aims to simulate the micromechanical behavior of asphalt mixtures during the compaction process using the Discrete Element Method (DEM). The interactions between the components of a Porous Asphalt (PA) mixture were represented using an Elastic Viscoelastic Contact Model (EVCM), which is a user-defined model implemented in EDEM software, developed based on linear elastic and Burger’s viscoelastic constitutive equations. The macroscale parameters of asphalt mortar were characterized using the nonlinear regression analysis of master curves obtained from Dynamic Shear Rheometer (DSR) tests. The verification process of EVCM successfully indicated that the computations trends fall within the range of expected values for the typical asphalt mixture material. Further, a Superpave Gyratory Compaction (SGC) test was carried out and the obtained sample was scanned using X-ray Computed Tomography (X-ray CT) to capture the air void distributions. The DEM was utilized where digital samples were established to simulate the overall process of laboratory and field compaction. The simulation results showed that the model provided a comparable prediction of responses and demonstrated the capability of SGC to fabricate a representative sample. The influence of temperature on the asphalt compaction process was explored and the results implied that temperature decreasing adversely affects the compactability and dramatically increases the demanded compaction efforts which are consistent with the law of viscoelasticity. On the contrary, when the temperature is high, the asphalt binder becomes too fluid and roller loads will simply displace, or “shove” the mat rather than compact it. Tracking the change in the air voids proportion indicates that the motion of aggregates is rather compound. The aggregates flowed vertically downwards in line with the compacting orientation while moved horizontally outwards away from the center. All in all, the findings confirm that the concept is technically practicable, affording the model great potential to help researchers understand the microstructural phases of asphalt mixture during the compaction.

Visco-elastic contact spring in numerical simulations of train – track system vibrations

Abstract: In train – track coupled systems, interaction between subsystems occurs in wheel- rail contact. The most common contact model is perfectly elastic, linearized Hert’z spring. It has wide range of application in numerical simulations. In more detailed interaction models, the energy dissipation in wheel-rail contact is taken into account. There are no known comparisons of these models in the literature, that would indicate the effects of a specific solution application. In this paper, the main purpose is to analyze and compare the effects of two contact models in terms of numerical simulations of train – track vibrations. The reference contact model taken into account is linearized, perfectly elastic Hert’z spring. The second spring, proposed by the authors is enriched with viscous element based on hysteresis damping. Application of both models, and its effects were examined in plane, train – track vibrations simulations with threshold inequality excitation in the middle of the track length. Concluding from the analyzes performed, it was found that viscoelastic contact model application is important, when track stresses and fatigue are being investigated. In addition, it was found that neglecting the damping element in contact model reduces the probability of the wheel – rail contact loss phenomenon, and thus leads to incorrect identification of its occurrence. Keywords: Wheel/rail contact; Hertz contact; Linearized contact spring; Train/track dynamics

Development and application of rough viscoelastic contact models in the first phase of 3D manipulation for biological micro-/nanoparticles by AFM

Development and application of rough viscoelastic contact models in the first phase of 3D manipulation for biological micro-/nanoparticles by AFM

On the Stickiness of CO2 and H2O Ice Particles

Abstract Laboratory experiments revealed that CO2 ice particles stick less efficiently than H2O ice particles, and there is an order of magnitude difference in the threshold velocity for sticking. However, the surface energies and elastic moduli of CO2 and H2O ices are comparable, and the reason why CO2 ice particles were poorly sticky compared to H2O ice particles was unclear. Here we investigate the effects of viscoelastic dissipation on the threshold velocity for sticking of ice particles using the viscoelastic contact model derived by Krijt et al. We find that the threshold velocity for the sticking of CO2 ice particles reported in experimental studies is comparable to that predicted for perfectly elastic spheres. In contrast, the threshold velocity for the sticking of H2O ice particles is an order of magnitude higher than that predicted for perfectly elastic spheres. Therefore, we conclude that the large difference in stickiness between CO2 and H2O ice particles would mainly originate from the difference in the strength of viscoelastic dissipation, which is controlled by the viscoelastic relaxation time.

A New Theoretical Model to Study the Closing Bounce Characteristics of the Electromagnetic Relay Under Capacitive Loads

Contact bounce is a common phenomenon in the closing process of the electromagnetic relay under capacitive loads. The investigations on the contact characteristics are mainly conducted by experimental methods. However, the experimental method is extremely complicated and time-consuming in structural design, and it cannot clearly reveal the mechanism of contact bounce. Therefore, a new theoretical model is proposed to investigate the dynamic characteristics of the electromagnetic relay under capacitive loads. The model allows for simulating dynamic process and collecting bounce parameters in a simple and effective way compared with conventional simulation and experimental methods. The physical mechanism of contact bounce for the electromagnetic relay is presented. The nonlinear contact force between the fixed and moving contacts is evaluated according to the Kelvin–Voigt viscoelastic contact model. The equations of motion considering the coupling of electromagnetic and mechanical fields are established. The theoretical results obtained in this study are validated by comparison with experimental data. The influences of the structural parameters, coil current, surge current, and contact resistance on the contact bounce are analyzed. The numerical results well demonstrate that the contact bounce can be effectively weakened by adjusting the parameters of contact spring and the mass of the moving contact.

Development of 3D manipulation of viscoelastic biological cells by AFM based on contact models and oscillatory drag

Since in the approximation made by the modeling and simulation of the manipulation, the accuracy plays an important role so it makes researchers to eliminate simplifications and limitations. Damping properties of the biological particles and consequently loading history of them is one of those simplifications considered until now. The other simplifying assumption is the ignorance of the oscillatory drag during modeling of the manipulation in a liquid environment elimination of which results in more precise modeling. To achieve this goal and increase the accuracy of the modeling in this paper, particles are considered viscoelastic and the oscillatory drag is added to the Stokes drag. To do so, several viscoelastic contact models are developed to choose the better suited model for biological particles. On the other hand, to modify the prediction of the particle and tool’s behavior, ignored rotation about z axis is also considered. Obtained results show that considering particles viscoelastic leads to the decrease of the critical force in comparison with the elastic state. This is due to the decreasing of the deformation acceleration based on the particle’s damping. These differences are about 29% for sliding of the tip on the particle, 8% for sliding of the particle on the substrate and 22% for rolling. Besides, application of the oscillatory drag force about 1.7nN leads to increasing of the drag which can be ignored in the modeling but in the case of high precision modeling this drag can be take into consideration. Therefore, it can be said that considering viscoelastic properties of the particle increases the accuracy of the modeling and simulation and as a result behavior prediction of the particles under manipulation.

A new class of hyperbolic variational–hemivariational inequalities driven by non-linear evolution equations

The aim of the paper is to introduce and investigate a dynamical system which consists of a variational–hemivariational inequality of hyperbolic type combined with a non-linear evolution equation. Such a dynamical system arises in studies of complicated contact problems in mechanics. Existence, uniqueness and regularity of a global solution to the system are established. The approach is based on a new semi-discrete approximation with an application of a surjectivity result for a pseudomonotone perturbation of a maximal monotone operator. A new dynamic viscoelastic frictional contact model with adhesion is studied as an application, in which the contact boundary condition is described by a generalised normal damped response condition with unilateral constraint and a multivalued frictional contact law.

Influence of the Mesoscopic Viscoelastic Contact Model on Characterizing the Rheological Behavior of Asphalt Concrete in the DEM Simulation

The numerical simulation based on the discrete element method (DEM) is popular to analyze the material behavior of asphalt concrete in recent years because of the advantage of the DEM in characterizing the heterogeneous microstructures. As a type of viscoelastic material, the rheological behavior of asphalt concrete is represented depending on the mesoscopic viscoelastic contact model between two particles in a contact in DEM simulations. However, what is missing in the existing literature studies is analysis of the influence of the mesoscopic viscoelastic contact models. Hence, the existing mesoscopic viscoelastic contact models are employed to build different types of DEM numerical samples of asphalt concrete in this study. Laboratory tests and the corresponding numerical tests at different temperatures and frequencies are implemented to investigate the difference in simulation precision in the case of using different mesoscopic viscoelastic contact models via the rheological index of dynamic modulus and phase angle. The results show the following: (1) the mesoscopic generalized Maxwell contact model provides the best simulation precision at low temperatures; (2) the mesoscopic generalized Kelvin contact model shows an improved precision at high temperatures; and (3) although the mesoscopic Burgers contact model has the simplest mathematical structure, the simulation precisions are obviously lower than those of the other two contact models, particularly when simulating the phase angle at low temperatures and frequencies. The results will be beneficial to select the appropriate mesoscopic contact model for the DEM modeling of asphalt concrete according to the loading conditions.