Viscoelastic Contact Mechanics Research Articles

Experimental and theoretical investigation of Chronic Lymphocytic Leukemia cell's viscoelastic contact mechanics using atomic force microscope

Chronic Lymphocytic Leukemia (CLL) is a type of cancer usually appearing in old age. In this research, a method for detecting CLL cells in young age through the analysis of geometrical and mechanical properties of human Leukocytes has been presented. For this purpose, the CLL cells are cultured and their geometric characteristics, adhesion force, and contact behavior have been examined using an Atomic Force Microscope (AFM) device. Subsequently, the obtained experimental results have been compared with the geometric and mechanical properties of Leukocytes. Furthermore, the manipulation process has been mathematically modeled using different adhesive and non-adhesive contact theories. The results showed that blood cancer cells have up to 8.17% smaller dimensions and up to 23.57% greater elastic modulus compared to leukocytes.

Applications of generalized fractional hemivariational inequalities in solid viscoelastic contact mechanics

This paper studies a generalized fractional hemivariational inequality in infinite-dimensional spaces. Under the suitable assumptions, the existence result is delivered by using the temporally semi-discrete scheme and the surjectivity result for multivalued pseudomonotone operator. As an illustrative application, we propose a frictional contact model that describes the quasi-static contact between a viscoelastic body and a solid foundation. The viscoelastic constitutive equation is modeled by fractional Kelvin-Voigt law with ψ-Caputo derivative, and the frictional contact conditions are expressed as the Clarke subdifferentials of the nonconvex and nonsmooth functionals. Finally, the weak solvability of the mechanical system is obtained by using our abstract mathematical result.

Applications of Generalized Fractional Hemivariational Inequalities in Solid Viscoelastic Contact Mechanics

Applications of Generalized Fractional Hemivariational Inequalities in Solid Viscoelastic Contact Mechanics

Evolutionary variational\u2013hemivariational inequalities with applications to dynamic viscoelastic contact mechanics

The purpose of this work is to introduce and investigate a complicated variational–hemivariational inequality of parabolic type with history-dependent operators. First, we establish an existence and uniqueness theorem for a first-order nonlinear evolution inclusion problem, which is driven by a convex subdifferential operator for a proper convex function and a generalized Clarke subdifferential operator for a locally Lipschitz superpotential. Then, we employ the fixed point principle for history-dependent operators to deliver the unique solvability of the parabolic variational–hemivariational inequality. Finally, a dynamic viscoelastic contact problem with the nonlinear constitutive law involving a convex subdifferential inclusion is considered as an illustrative application, where normal contact and friction are described, respectively, by two nonconvex and nonsmooth multi-valued terms.

Viscoelastic rough contact mechanics: A multiscale investigation

The full understanding of the viscoelastic contact mechanics between rough surfaces is a crucial issue in modern engineering research. This paper investigates the role that the number of rough scales, i.e. the cut-off of the power spectrum of the surface roughness, has on quantities like contact area, mean separation, and friction. Furthermore, an effective, though approximate, definition of an equivalent modulus is provided in order to reduce the viscoelastic contact domain to an elastic equivalent one.

Analysis of nanocontact problems of layered viscoelastic solids with surface energy effects under different loading patterns

Surface stresses have a remarkable effect on nanocontact response of layered viscoelastic solids, especially under specific loading patterns. In the framework of nonlinear viscoelastic contact mechanics, a numerical model is developed to investigate the quasistatic nanocontact response of elastically layered viscoelastic solids under different loading patterns. The developed model accounts for surface energy effects by adopting the complete Gurtin–Murdoch surface elasticity model. The Schapery’s constitutive viscoelastic creep model is used for the stress, strain, and time relationships. The transient term in the creep compliance is expressed by Prony’s series. Frictionless contact condition is assumed throughout the contact interface. The equilibrium contact configuration, in which the contact constraints are exactly satisfied without any need for an appropriate value for the penalty parameter, is obtained by using the Lagrange multiplier method in the framework of the Newton–Raphson procedure. The developed model is applied to study and analyze the quasistatic nanocontact response of two different problems under different loading patterns. Results show the significant effect of the type of loading pattern and its rate on the nanocontact response of elastically layered viscoelastic solids.

Influence of surface energy on the nanoindentation response of elastically-layered viscoelastic materials

In the context of integrated nonlinear viscoelastic contact mechanics, a nonlinear finite element model is developed to predict and analyze the quasistatic response of nanoindentation problems of an elastically-layered viscoelastic materials considering the surface elasticity effects. Effects of surface energy are accounted for by employing the Gurtin–Murdoch continuum model for surface elasticity. The linear viscoelastic response is modeled by the Schapery’s creep model with a Prony’s series to express the transient component in the creep compliance. The viscoelastic constitutive equations are cast into a recursive form that needs only the previous time increment rather than the entire strain history. To satisfy the contact constraints exactly, the Lagrange multiplier method is adopted to enforce the contact conditions into the system. The equilibrium indentation configuration is obtained through the Newton–Raphson iterative procedure. The developed model is verified then applied to investigate the quasistatic nanoindentation response of two different indentation problems with different geometry and loading conditions. Results show the significant effects of surface energy and viscoelasticity on the quasistatic nanoindentation response.

A theoretical and experimental study of viscoelastic rolling contacts incorporating thermal effects

Viscoelastic contacts are present in countless industrial components including tires, dampers and rubber seals. The effective design of such components requires a full knowledge of viscoelastic contact mechanics in terms of stresses, strains and hysteric dissipation. To assess some of these issues, this paper describes a series of experiments on the contact area and penetration in a rolling contact between a nitrile rubber ball and a glass disk. The experimental results are compared with the theory proposed by Carbone and Putignano1 showing close agreement at low speeds. However, discrepancies arise at speeds above 100 mm/s because of the frictional heating. In order to evaluate this effect, the temperature of the sliding interface is measured for different rolling speeds using infrared microscopy. Thermal results showed that interfacial temperature remained constant at low rolling speeds before rising significantly when speeds above 100 mm/s were reached. These temperature effects are incorporated into the numerical simulations by means of an approximated approach, which corrects the viscoelastic modulus based on the mean measured temperature in the contact. The result of this approach is to extend the region of agreement between experimental and numerical outcomes to higher speeds.

Viscoelastic modeling of nanoindentation experiments: A multicurve method

ABSTRACTNanoindentation is an increasingly used method of extracting surface mechanical properties of viscoelastic materials, especially polymers. Recently, Hutcheson and McKenna used a viscoelastic contact mechanics model to analyze the contact problem between a nanosphere and polystyrene surface. In nanoindentation experiments, the ramp loading test is a similar problem to the particle embedment experiment except that the indentation load function differs. The motivation in this work is to expand the Hutcheson and McKenna analysis to the nanoindentation problem. In particular, we illustrate the limitations of analyzing only a single load‐indentation curve, which does not provide enough information to determine the full range of the viscoelastic response of a polymer, and we show that performing a test sequence that includes multiple loading rates or indentation rates spanning two or more orders of magnitude greatly improves the extracted viscoelastic properties. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014, 52, 633–639

Simulation Analysis of Working Process for Core Seed Metering Device Based on Discrete Element Method

Discrete element method is an important technical tool for analysis of motion law of granular material. Based on the principle of discrete element method, using linear viscoelastic contact mechanics model, simulation calculate for discrete element simulation was developed by MFC. Through the combination of arc modeling a geometric model of the different core seed were built, and simulation of the work process of corn precision metering device was conducted. Suitability of parameters on working procedure of the metering device was analyzed.

Theoretical analysis of thermoviscoelastic contact between friction lining and wire rope in mine friction hoists

Serious accidents of mine hoists caused by high-speed sliding between friction lining and wire rope are often seen in coal mines. In order to solve this problem, we analyzed the contact characteristics between friction lining and wire rope. Then we carried out a dynamic mechanical analysis (DMA) to explain the change in mechanical properties of the friction lining as function of temperature and load frequency and found that temperature has a stronger effect on the mechanical properties than the frequency. We used multiple regression analysis to obtain the thermoviscoelastic constitutive relations of the friction lining. As well we derived the analytic solution for the thermoviscoelastic contact radius and pressure by combining the theory of viscoelastic contact mechanics with thermoviscoelastic constitutive relations.

Characterization of the linearly viscoelastic behavior of human tympanic membrane by nanoindentation

Human tympanic membrane (or eardrum) is composed of three membrane layers with collagen fibers oriented in the radial and circumferential directions, and exhibits viscoelastic behavior with membrane (or in-plane) properties different from through-thickness (or out-of-plane) properties. Due to the interaction of bundled fibers and ground substance, which is inhomogeneous, these properties could change with locations. In this paper, we use nanoindentation techniques to measure the viscoelastic functions of four quadrants of tympanic membrane (TM). For measurement of in-plane Young’s relaxation modulus we fixed a sectioned quadrant of the TM on a circular hole and used a spherical nanoindenter tip to apply force at the center of the suspended circular portion of the specimen. An inverse problem solving methodology was employed using finite element method to determine the average in-plane Young’s relaxation modulus of the TM quadrant. Results indicate that the in-plane steady-state Young’s relaxation modulus for four quadrants of the TM does not vary significantly. However, a variation of the modulus from 25.73 MPa to 37.8 MPa was observed with measurements from different individuals. For measurement of Young’s relaxation modulus in the through-thickness direction a spherical indenter tip was used to indent into different locations on the surface of the TM specimen supported by a substrate. Viscoelastic contact mechanics analysis of the load–displacement curve, representative primarily of the through-thickness stiffness of the TM, was conducted to extract the Young’s relaxation modulus in the out-of-plane direction. Results indicate a wide variation in steady-state Young’s relaxation modulus, from 2 MPa to 15 MPa, in the through-thickness direction over the TM.

Comment on “The properties of free polymer surfaces and their influence on the glass transition temperature of thin polystyrene films” by J.S. Sharp, J.H. Teichroeb and J.A. Forrest

Sharp, Teichroeb and Forrest [J.S. Sharp, J.H. Teichroeb, J.A. Forrest, Eur. Phys. J. E 15, 473 (2004)] recently published a viscoelastic contact mechanics analysis of the embedment of gold nanospheres into a polystyrene (PS) surface. In the present comment, we investigate the viscoelastic response of the surface and conclude that the embedment experiments do not support the hypothesis of a liquid surface layer of sufficiently reduced "rheological temperature" to explain reports of very large reductions in the glass temperature of freely standing ultrathin polystyrene films. We also report some errors and discrepancies in the paper under comment that resulted in an inability to reproduce the reported calculations. We present our findings of error in a spirit of clarifying the problem of embedment of spheres into surfaces and in order that others can understand why they may not reproduce the results reported by Sharp, Teichroeb and Forrest. In the comment, we also examine the effects of the magnitude of the forces that result from the polymer surface-nanosphere particle interactions on the viscoelastic properties deduced from the embedment data and we provide a comparison of apparent surface or "rheological" temperature vs. experimental temperature that indicates further work needs to be performed to fully understand the surface embedment experiments. Finally, we comment that the nanosphere embedment measurements have potential as a powerful tool to determine surface viscoelastic properties.

Mechanical Characterization of Polymers on a Nanometer Scale through Nanoindentation. A Study on Pile-up and Viscoelasticity

The analysis of nanoindentation force curves collected on polymers through the common Oliver and Pharr procedure does not lead to a correct evaluation of Young's modulus. In particular, the estimated elastic modulus is several times larger than the correct one, thus compromising the possibility of a nanomechanical characterization of polymers. Pile-up or viscoelasticity is usually blamed for this failure, and a deep analysis of their influences is attempted in this work. Piling-up can be minimized by indenting on a true nanometer scale, i.e., at penetration depth smaller than 200 nm. On the other side, it is common knowledge that fast indentations minimize the effect of viscoelasticity. However, changing the indentation time in a broad range of contact time (fractions of second up to hundreds of seconds) did not allow the correct estimation of Young's modulus for the polymers used in this work. The final result is that the Oliver and Pharr procedure as well as any other procedure analyzing the unloading curve with elastic contact mechanics models cannot be employed to measure Young's modulus of polymers because its application is incorrect from a theoretical point of view, unless the analysis is limited to the very first nanometers of penetration depth when the contact is perfectly elastic. Viscoelastic contact mechanics models should instead be employed to characterize these materials.

Elastic and viscoelastic contact mechanics of coating/substrate composites in axisymmetric indentation

Indentation contact mechanics of coating/substrate composites is addressed in elastic and viscoelastic regimes. An analytical solution for the elastic Boussinesq problems is examined first using an appropriate contact pressure distribution. The analytical expression for the elastic modulus E eff of layered composites is then converted to the corresponding stress relaxation modulus Y eff (t) using the correspondence principle of linear elastic and linear viscoelastic deformations. Several numerical simulations for the stress relaxation behaviour of layered composites, i.e., a viscoelastic coating on an elastic substrate, an elastic coating on a viscoelastic substrate, etc., are demonstrated to obtain rheological insights into the contact behaviour of coating/substrate composites for flat-ended cylindrical indentation. The assumptions and approximations included in the theoretical considerations are carefully addressed. The viscous squeezing flow, in a thin coating film, out of the geometrically constrained space beneath the indenter is also examined.

Measurement of Young’s relaxation modulus using nanoindentation

In a previous paper (Lu et al., Mechanics of Time-Dependent Materials, 7, 2003, 189–207), we described methods to measure the creep compliance of polymers using Berkovich and spherical indenters by nanoindentation. However, the relaxation modulus is often needed in stress and deformation analysis. It has been well known that the interconversion between creep compliance and relaxation function presents an ill-posed problem, so that converting the creep compliance function to the relaxation function cannot always give accurate results, especially considering that the creep data at short times in nanoindentation are often not reliable, and the overall nanoindentation time is short, typically a few hundred seconds. In this paper, we present methods to measure Young’s relaxation functions directly using nanoindentation. A constant-rate displacement loading history is usually used in nanoindentations. Using viscoelastic contact mechanics, Young’s relaxation modulus is extracted using nanoindentation load-displacement data. Three bulk polymers, Polymethyl Methacrylate (PMMA), Polycarbonate (PC) and Polyurethane (PU), are used in this study. The Young’s relaxation functions measured from the nanoindentation are compared with data measured from conventional tensile and shear tests to evaluate the precision of the methods. A reasonably good agreement has been reached for all these materials for indentation depth higher than a certain value, providing reassurance for these methods for measuring relaxation functions.

Nanosphere Embedding into Polymer Surfaces: A Viscoelastic Contact Mechanics Analysis

Teichroeb and Forrest [Phys. Rev. Lett. 91, 016104 (2003)] image gold nanosphere embedment into a polystyrene surface and imply the existence of a liquid surface layer. We use a viscoelastic contact mechanics model of their results to give a contrary interpretation. The surface interactions between gold and polystyrene and the indentation depth determine the loads on the nanospheres. Using bulk properties, quantitative agreement between the model and the data is obtained, implying little or no depression in the glass temperature or existence of a liquid layer at the polystyrene surface.

Rheological properties and adhesive failure of thin viscoelastic layers

Methods have been developed for measuring the linear viscoelastic properties of thin adhesive layers, and for determining the stress intensity factor characterizing the driving force for adhesive failure. Both methods involve bringing a hemispherical indenter in contact with the adhesive layer while simultaneously monitoring the load, displacement, and radius of contact between the indenter and the adhesive. Dynamic moduli for the adhesive layer are obtained by oscillating the indenter, and the adhesive properties are obtained by pulling the indenter completely out of contact with the adhesive layer. Existing theories of viscoelastic contact mechanics were extended to account for the fact that the adhesive layer thickness is not substantially larger than the contact radius, as is generally assumed. A variety of correction factors were introduced that depend on the ratio of the contact radius to the adhesive layer thickness. These methods were applied to a model adhesive based on an acrylic triblock copolymer. Determination of the time-dependent creep and relaxation functions for this material was simplified by the power-law frequency response of the dynamic moduli. The large stress intensity factors observed were related to a Dugdale model of the cohesive zone at the contact edge.