Viscoelastic Contact Research Articles

A Nonlinear Viscoelastic Contact Interphase Modeled as a Cosserat Rod-Like String

A Nonlinear Viscoelastic Contact Interphase Modeled as a Cosserat Rod-Like String

On the effective surface energy in viscoelastic Hertzian contacts

Viscoelasticity and rate-dependent adhesion of soft matter lead to difficulties in modelling the ’relatively simple’ problem of a rigid sphere in contact with a viscoelastic half-space. For this reason, approximations in describing surface interactions and viscous dissipation processes are usually adopted in the literature.Here, we develop a fully deterministic model in which adhesive interactions are described by Lennard-Jones potential and the material behaviour with the standard linear solid model.Normal loading–unloading cycles are carried out under different driving conditions. When loading is performed in quasi-static conditions and, hence, unloading starts from a completely relaxed state of the material, the effective surface energy is found to monotonically increase with the contact line velocity up to an asymptotic value reached at high unloading rates. Such result agrees with existing theories on viscoelastic crack propagation.If loading and unloading are performed at the same non-zero driving velocity and, hence, unloading starts from an unrelaxed state of the material, the trend of the effective surface energy Δγeff with the contact line velocity is described by a bell-shaped function in a double-logarithmic plot. The peak of Δγeff is found at a contact line velocity smaller than that makes maximum the tangent loss of the viscoelastic modulus. Furthermore, we show Gent&Schultz assumption partly works in this case as viscous dissipation is no longer localized along the contact perimeter but it also occurs in the bulk material.

Investigations on the Adhesive Contact Behaviors between a Viscoelastic Stamp and a Transferred Element in Microtransfer Printing

Microtransfer printing is a sophisticated technique for the heterogeneous integration of separately fabricated micro/nano-elements into functional systems by virtue of an elastomeric stamp. One important factor influencing the capability of this technique depends on the adhesion between the viscoelastic stamp and the transferred element. To provide theoretical guidance for the control of adhesion in the transfer printing process, a finite element model for the viscoelastic adhesive contact between a polydimethylsiloxane (PDMS) stamp and a spherical transferred element was established, in which the adhesive interaction was modeled by the Lennard-Jones surface force law. Effects of the unloading velocity, preload, and thermodynamic work of adhesion on the adhesion strength, characterized by the pull-off force, were examined for a loading-dwelling-unloading history. Simulation results showed that the unloading path deviated from the loading path due to the viscoelastic property of the PDMS stamp. The pull-off force increased with the unloading velocity, and the increasing ratio was large at first and then became low. Furthermore, the influence of the preload on increasing the pull-off force was more significant under larger unloading velocity than that under smaller unloading velocity. In addition, the pull-off force increased remarkably with the thermodynamic work of adhesion at a fixed maximum approach.

Aspects of modeling and numerical simulation of dry point contacts between viscoelastic solids

The virtual absence of pressure driven flow inside an elastohydrodynamic lubrication (EHL) contact leads to remarkable similarity between lubricated film thickness and separation by a viscoelastic layer as is suggested by experimental and theoretical results, see [1]. This offers interesting opportunities for mixed lubrication modeling without needing the flow continuity-based Reynolds equation. In this paper numerical simulation of viscoelastic concentrated contact modeling is revisited, first considering the problem of a viscoelastic half-space and a rigid sphere, both in static (squeeze) as well as (frictionless) rolling/sliding conditions. In particular modeling aspects are discussed so that the efficiency of computation of the viscoelastic deformation remains close to the efficiency of computation of an elastic deformation. This is achieved by rewriting Hunter’s [2] deformation equation from an integral form into a differential form by applying the Leibnitz integral theorem, even for complex materials with multiple relaxation times to represent complex viscoelastic properties of materials. The approach can be straightforwardly implemented in any (EHL) contact solver regardless of the numerical method. Detailed results are presented, such as the effect of the Deborah number, the relation between the extreme cases of the rolling problem and the static problem, and discussed in detail. In addition to the rigid sphere against a viscoelastic half-space, also the case of two viscoelastic bodies is considered.

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.

Rothe method and numerical analysis for a new class of fractional differential hemivariational inequality with an application

The goal of this paper is to introduce and study a new class of fractional differential hemivariational inequality formulated by an evolutionary hemivariational inequality and a fractional differential equation in Banach spaces. By employing the Rothe method and the surjectivity result, we derive the existence of unique solution for such a problem under some mild conditions. Moreover, we use the fully discrete scheme to approximate the fractional differential hemivariational inequality and provide an error estimate for the approximation. Finally, the main results are applied to obtain the unique solvability as well as the numerical analysis for a viscoelastic frictional contact problem with adhesion.

A Viscoelastic Contact Analysis of the Ground Reaction Force Differentiation in Walking and Running Gaits Realized in the Simplified Horse Leg Model Focusing on the Hoof—Ground Interaction

In the present study, the systematic method for the forward dynamics associated with the ground contact model was introduced to be able to consider the viscoelastic effect when contacting with the ground. In particular, we focused on the hoof-ground interaction in the simplified horse leg model because walking and running gaits are known to be different in trajectories; however, the force analysis still remains as unsolved issues. The computational experiments in Matlab, elastic and inelastic impact with the ground was resolved by using the dissipative contact force model proposed by Lankarani and Nikravesh and the ground reaction force was clearly examined in four different conditions from the combination of walking/running and elastic/inelastic contact. As result, two peaks during the stance phase in the walking condition were realized as well as the human gait and a single peak was newly observed in running with a time gap in elastic and inelastic condition. The proposed method contributes to the establishment of the detail time course analysis of the ground reaction force for animal and human gaits in a consistent manner.

Oscillating viscoelastic periodic contacts: A numerical approach

A new numerical Boundary Element methodology is developed to investigate viscoelastic periodic contacts under general kinematic conditions. The approach is based on an integral formulation, where periodicity is accounted for by introducing an ad hoc defined periodic Green’s function, and allows to study any motion law between viscoelastic bodies into contact. Results are shown for paradigmatic cases with a specific application interest and, specifically, for vertical, horizontal, and mixed oscillations. Outcomes in terms of pressure and displacement distributions, and, most crucially, of dissipated work provide key information and demonstrate the importance of taking into account viscoelasticity in the contact mechanics of soft materials. There are clear implications in all the engineering systems, where viscoelastic hysteresis is a variable to be controlled, including e.g. dampers, seals and pick-and-place devices.

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

Rate-dependent adhesion of viscoelastic contacts, Part I: Contact area and contact line velocity within model randomly rough surfaces

In this work, we investigate dissipative effects involved during the detachment of a smooth spherical glass probe from a viscoelastic silicone substrate patterned with micro-asperities. As a baseline, the pull-off of a single asperity, millimeter-sized contact between a glass lens and a smooth poly(dimethylsiloxane) (PDMS) rubber is first investigated as a function of the imposed detachment velocity. From a measurement of the contact radius a(t) and normal load during unloading phase, the dependence of the strain energy release rate G on the velocity of the contact line vc=da∕dt is determined under the assumption that viscoelastic dissipation is localized at the edge of the contact. These data are incorporated into Muller’s model (Muller, 1999) in order to predict the time-dependence of the contact size. Similar pull-off experiments are carried out with the same PDMS substrate patterned with spherical micro-asperities with a prescribed height distribution. From in situ optical measurements of the micro-contacts, scaling laws are identified for the contact radius a and the contact line velocity vc. On the basis of the observed similarity between macro and microscale contacts, a numerical solution is developed to predict the reduction of the contact radius during unloading.

EXISTENCE OF SOLUTIONS FOR FRACTIONAL EVOLUTION INCLUSION WITH APPLICATION TO MECHANICAL CONTACT PROBLEMS

The goal of this paper is to study an evolution inclusion problem with fractional derivative in the sense of Caputo, and Clarke’s subgradient. Using the temporally semi-discrete method based on the backward Euler difference scheme, we introduce a discrete approximation system of elliptic type corresponding to the fractional evolution inclusion problem. Then, we employ the surjectivity of multivalued pseudomonotone operators and discrete Gronwall’s inequality to prove the existence of solutions and its priori estimates for the discrete approximation system. Furthermore, through a limiting procedure for solutions of the discrete approximation system, an existence theorem for the fractional evolution inclusion problem is established. Finally, as an illustrative application, a complicated quasistatic viscoelastic contact problem with a generalized Kelvin–Voigt constitutive law with fractional relaxation term and friction effect is considered.

Predicting the seismic collapse capacity of adjacent SMRFs retrofitted with fluid viscous dampers in pounding condition

Severe damages of adjacent structures due to structural pounding during earthquakes have emphasized the need to use some seismic retrofit strategy to enhance the structural performance. The purpose of this paper is to study the influence of using linear and nonlinear Fluid Viscous Dampers (FVDs) on the seismic collapse capacities of adjacent structures prone to pounding and proposing modification factors to modify the median collapse capacity of structures considering the effects of pounding. The factors can be used to predict the collapse capacity of structures in pounding condition. A seismic retrofit strategy employs FVDs installed in 3-, 6- and 9-story Special Moment Resisting Frames (SMRFs). The SMRFs were assumed to have different values of separation distance according to the seismic code. To model pounding phenomenon, linear viscoelastic contact elements were used in the OpenSees software. Furthermore, to determine the seismic collapse capacities of each structure, the proposed algorithm was applied to remove the collapsed structure during the incremental dynamic analysis. The results of the analyses illustrate that the existence of FVDs can substantially improve the seismic behavior of structures having a significant influence on the collapse capacities of colliding structures. Moreover, considering the adjacent SMRFs in one or two sides of the main structure can significantly affect the median collapse capacity of the main structure itself. Finally, the proposed modification factors can be successfully used to estimate the effects of pounding on the collapse capacities of adjacent structures.

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.

Energetic criterion for adhesion in viscoelastic contacts with non-entropic surface interaction

We suggest a detachment criterion for a viscoelastic elastomer contact based on Griffith's idea about the energy balance at an infinitesimal advancement of the boundary of an adhesive crack. At the moment of detachment of a surface element at the boundary of an adhesive contact, there is some quick (instant) relaxation of stored elastic energy which can be expressed in terms of the creep function of the material. We argue that it is only this "instant part" of stored energy which is available for doing work of adhesion and thus it is only this part of energy relaxation that must be used in Griffith's energy balance. The described idea has several restrictions. Firstly, in this pure form, it is only valid for adhesive forces having an infinitely small range of action (which we call the JKR-limit). Secondly, it is only applicable to non-entropic (energetic) interfaces, which detach "at once" and do not possess their own kinetics of detachment.

Traveling fronts in dissipative granular chains and nonlinear lattices

We consider an infinite chain of particles with nonlinear elastic and dissipative nearest neighbors interactions. Assuming the existence of a traveling front between uniformly compressed (or stretched) states, we obtain jump conditions relating the wave speed and limiting particle velocities to the relative displacements at infinity. Using this result, we characterise compression fronts in chains of touching beads, for viscoelastic contact laws that include a nonlinear elastic force (generalised Hertz contact) and viscous dissipation. We compute compression fronts numerically for the generalised Kuwabara–Kono model in which the viscous contact force is proportional to the derivative of the elastic force, without precompression of the chain. Steady fronts are obtained both as the end result of the compression of one end of the chain and using a shooting method which provides numerically exact traveling waves. Depending on the magnitudes of contact damping and strain applied downstream, we obtain either overdamped (monotonic) or underdamped (oscillatory) compression fronts. To explain this transition and approximate the front profiles, we consider a continuum limit valid when the exponent of the contact nonlinearity is close to (and above) unity. Using multiscale expansions, we formally derive two different amplitude equations for long waves, a Burgers equation with logarithmic nonlinearity, and a logarithmic Korteweg–de Vries (KdV)–Burgers equation for small contact damping. Both models possess traveling front solutions that are in good agreement with the front profiles computed numerically in the granular chain. The analysis of the logarithmic KdV–Burgers equation allows one to approximate the critical damping corresponding to the transition from underdamped to overdamped fronts.

Nonlinear viscoelastic isolation for seismic vibration mitigation

The aim of this paper is to assess the effectiveness of nonlinear viscoelastic damping in controlling base-excited vibrations. Specifically, the focus is to investigate the robustness of the nonlinear base isolation performance in controlling the system response due to a wide set of possible excitation spectra. The dynamic model is derived to study a simple structure whose base isolation is provided via a Rubber-Layer Roller Bearing (RLRB) (rigid cylinders rolling on rigid plates with highly damping rubber coatings) equipped with a nonlinear cubic spring, thus presenting both nonlinear damping and stiffness. We found that, under periodic loading, due to the non-monotonic bell-shaped viscoelastic damping arising from the viscoelastic rolling contacts, different dynamic regimes occur mostly depending on whether the damping peak is overcome or not. Interestingly, in the former case, poorly damped self-excited vibrations may be triggered by the steep damping decrease.Moreover, in order to investigate the robustness of the isolation performance, we consider a set of real seismic excitations, showing that tuned nonlinear RLRB provide loads isolation in a wider range of excitation spectra, compared to generic linear isolators. This is peculiarly suited for applications (such as seismic and failure engineering) in which the specific excitation spectrum is unknown a priori, and blind design on statistical data has to be employed.

Biomechanical Model of Human Index Finger During Examination

We have developed a mathematical model based on the Hunt-Crossley’s viscoelastic contact formulation for predicting the contact forces in the upper-body. The simulations were carried out in OpenSim software package and the simulations results were compared to experimentally recorded contact forces measured using a pressure algometer for assessing pressure pain sensitivity in the pelvic region 1.
 We observed a very good agreement between the model prediction and algometer data. Our simulation revealed that by pressing down on the tissue both normal and frictional contact forces increase up to a point- ceiling effect. Moreover, viscoelastic properties of the examinee’s tissue were associated with force; specifically, as the stiffness of the tissue declined both normal and frictional contact forces similarly declined albeit in a different way.
 Once the contact force reaches a peak point (irrespective of the baseline stiffness of the tissue) additional pressure application by the examiner was associated with incremental decrease in both normal and frictional (wasted) contact force.

A ground reaction force analysis in walking and running gaits in horse leg model on viscoelastic hoof-ground contact

A ground reaction force analysis in walking and running gaits in horse leg model on viscoelastic hoof-ground contact

Accurate Contact Law for Surface Motions of Small-Body Exploration Rovers

This paper develops an accurate contact law for characterizing the hopping motion of exploration rovers on small bodies in the solar system. The availability of such a law is important to provide guidance for rover deployment and mission planning. The contact between a rover and the surface of a small body is set up as a viscoelastic contact problem, for which there have previously been no complete solutions. The proposed new contact law is derived by modifying the equation representing the geometric relation between indentation and surface displacements so that it remains valid after Laplace transformation. The validity of this approach is demonstrated by analyzing the behavior of the Stieltjes convolution involved in the solution, which is found to be consistent with that expected for a viscoelastic material. A numerical verification shows that the new contact law exhibits a good match to results obtained using the finite element method. The new contact law is applied to hopping simulations of an example rover on the asteroid (162173) Ryugu, which reveal that the rover is capable of large traverses, but has a low likelihood of inter-hemispheric traverses from the polar regions.