Document [original]

Friction ISSN 2223-7690

https://doi.org/10.1007/s40544-020-0482-0 CN 10-1237/TH

RESEARCH ARTICLE

Adhesion and friction in hard and soft contacts: theory and

experiment

Valentin L. POPOV1,2,*, Qiang LI1,*, Iakov A. LYASHENKO1,3, Roman POHRT1

1 Technische Universität Berlin, Berlin 10623, Germany

2 National Research Tomsk State University, Tomsk 634050, Russia

3 Sumy State University, Sumy 40007, Ukraine

Received: 02 June 2020 / Revised: 14 October2020 / Accepted: 10 December 2020

Abstract: This paper is devoted to an analytical, numerical, and experimental analysis of adhesive

contacts subjected to tangential motion. In particular, it addresses the phenomenon of instable, jerky

movement of the boundary of the adhesive contact zone and its dependence on the surface roughness. We

argue that the "adhesion instabilities" with instable movements of the contact boundary cause energy

dissipation similarly to the elastic instabilities mechanism. This leads to different effective works of

adhesion when the contact area expands and contracts. This effect is interpreted in terms of “friction” to

the movement of the contact boundary. We consider two main contributions to friction: (a) boundary line

contribution and (b) area contribution. In normal and rolling contacts, the only contribution is due to

the boundary friction, while in sliding both contributions may be present. The boundary contribution

prevails in very small, smooth, and hard contacts (as e.g., diamond-like-carbon (DLC) coatings), while

the area contribution is prevailing in large soft contacts. Simulations suggest that the friction due to

adhesion instabilities is governed by "Johnson parameter". Experiments suggest that for soft bodies

like rubber, the stresses in the contact area can be characterized by a constant critical value.

Experiments were carried out using a setup allowing for observing the contact area with a camera

placed under a soft transparent rubber layer. Soft contacts show a great variety of instabilities when

sliding with low velocity – depending on the indentation depth and the shape of the contacting bodies.

These instabilities can be classified as "microscopic" caused by the roughness or chemical inhomogeneity

of the surfaces and "macroscopic" which appear also in smooth contacts. The latter may be related to

interface waves which are observed in large contacts or at small indentation depths. Numerical

simulations were performed using the Boundary Element Method (BEM).

Keywords: adhesion; friction; adhesion hysteresis; Boundary Element Method (BEM); hard solids; soft

matter

1 Introduction

Since the famous work by Johnson, Kendall, and

Roberts (JKR) from 1971 [1], adhesive contacts

have remained in focus of research in contact

mechanics and tribology. In the JKR theory, the

action range of adhesive forces is assumed to be

zero (or much smaller than any characteristic

length of contact). In 1975, Derjaguin, Muller, and

Toporov (DMT) suggested a model in which the

final interaction range was considered explicitly

(in particular, the interaction outside the contact

* Corresponding authors: Valentin L. POPOV, E-mail: v.pop[email protected]; Qiang LI, E-mail: [email protected]

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area) [2]. Tabor solved in 1977 the controversy

between both theories stating clearly that the JKR

and DMT theories are limiting cases for very small

and very large range of action of adhesive forces

and introduced a parameter (now known as Tabor

parameter) which describes transition between these

two limiting cases [3]. In the early 2000s, the interest

in adhesive contacts was driven by studying adhesion

in biological adhesion "devices" like in gecko feet

[4] or other biological structures [5]. In the last

years, adhesive contacts have become again a hot

topic, in particular in the context of adhesion of

functionally graded materials [6], the loading-unloading

hysteresis in rough contacts [7] as well as adhesive

contacts under tangential loading [8]. In particular,

rough contacts have been very intensively studied,

for example, evaluation of effective adhesion work

based on the Maugis–Dugdale model [9, 10],

description of rough surfaces and development of

experimental methods [11].

Two developments of the last years greatly

facilitated the advancement in adhesive contact’s

research:

1) The development of the Fast-Fourier-Trans-

formation-assisted Boundary Element Method (FFT-

assisted BEM) [12–14], in particular, its adaptation

for simulation of adhesive contacts [15].

2) The development of experimental methods for

direct observation of the processes of attachment

and detachment [16, 17].

One of the striking experimental findings are

complicated stick–slip dynamics of tangential adhesive

contacts [17]. These are far from being understood

well and are subject of intense debates [18‒20].

The present paper is devoted to an analytical,

numerical, and experimental investigation of adhesive

contacts under tangential loading and rolling. However,

the dissipative properties of normal adhesive contacts

are also considered as far as this helps understanding

friction.

For slow sliding of adhesive contacts, the application

of some force is needed, which can be interpreted

as force of friction. There are two main generic

mechanisms of friction in adhesive contacts: (a)

Either the friction in the boundary line – due to its

unstable sliding as described in Ref. [21], or (b) the

friction directly in the inner part of the contact

area [8, 22]. In the present paper, both mechanisms

are investigated analytically and numerically. For

the former one, the numerical study is conducted

by use of the BEM for the JKR-type adhesive contact.

The analysis is restricted to the elastic contact

under very slow normal and tangential movement

(quasi-static contact), so that viscoelastic and inertia

properties can be neglected.

We will consider both basic types of friction due

to relative movement of bodies: rolling and sliding

friction. These types have important differences

stemming from the different local direction of

movement of surfaces. Pure rolling is essentially a

normal contact problem, because the surfaces at

the leading edge are approaching each other in the

normal direction and on the rear edge they separate

in normal direction, both without any tangential

movement. It is important to note that the absence

of relative tangential movement of surfaces in the

case of a rolling contact suppresses the contribution

from shearing of the contact area, while in a sliding

contact this contribution not only exists but presumably

represents the main contribution to friction in most

cases.

The structure of the paper reflects this understanding.

The first part of the paper is devoted to numerical

simulation of adhesive contacts. Section 2 reports

results on adhesive hysteresis in normal and rolling

contacts. Section 3 considers sliding adhesive contacts

with both boundary and area contributions.

The second part of the paper is devoted to

experimental investigation on the contacts of rigid

indenters and soft rubber. Reported are results for

normal contacts and sliding.

2 Normal and rolling contacts: numerical

simulation

The solution of Johnson, Kendall, and Roberts (JKR)

[1] assumes that the tangential stresses in the

contact area vanish. For ideally smooth surfaces,

this assumption is a logical consequence of the

independence of the potential energy of an adhesive

contact on its lateral position. Real adhesive

contacts, on the contrary, typically show very high

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friction, which physically is caused by microscopic

heterogeneities. However, there exists a class of

adhesive contacts in which the friction in the contact

area could be small. To have this property, the

contacting bodies have to be free of viscosity, plasticity

and should not show elastic instabilities (which,

according to Prandtl, are the main mechanism of

energy dissipation in purely elastic systems [23–25].)

Under these conditions, the surfaces would be in a

state of "structural superlubricity" as described in

[26–28]. The tangential friction in the contact area

does not appear also in the pure normal and

rolling contacts. We therefore start with this class

of dynamic contacts, focusing our attention first on

the boundary contribution to energy dissipation.

2.1 Methodology

Numerical simulations presented in Section 2 were

carried out for adhesive contact of a parabolic

indenter with the radius of curvature R superimposed

with a two-dimensional waviness with amplitude

h and wave length









 





22 2π2π

, sin sin

zxy h x y

R (1)

see subplot of Fig. 1(b) for an example. In the

following subsections, simulations were performed

using the FFT-assisted BEM [29] under displacement-

controlled conditions and with the same assumptions

as in JKR theory: The materials behave as linear

elastic half-spaces with surface slopes being low

and adhesion only acts in the regions of intimate

contact. Validation of this method was provided in

[15, 29–31]. Typically, a grid with 512 × 512 points

was used.

2.2 Normal adhesive contact of rough surfaces

Contrary to a non-adhesive contact of elastic bodies,

an adhesive contact has intrinsic dissipative properties,

which can best be seen in a complete cycle of

formation and destruction of contact. The area

between the indentation and detachment branches

of force-displacement relation (e.g., in the JKR theory)

is the dissipated energy per cycle. The JKR theory

is based on the principle of virtual work, meaning

Fig. 1 Simulation of an adhesive indentation test using a

parbolic indenter with waviness according to (1) and h/λ = 0.05.

(a) Force–distance and (b) force–contact radius dependencies

during indenting and pull-off stages. The contact area remains

constant immediately after turning from the indentation to the

pull-off (phase II). The gray dashed curve is the JKR solution

without waviness.

that adhesive contact is reversible in all phases

when static equilibrium is possible [32]. Irreversible

energy dissipation occurs only during the instable

jumps from one equilibrium state to the other. This

occurs in the moments of coming into contact and

in the sudden destruction of contact. Independently

from whether such jumps occur during a normal

or a tangential movement, energy is dissipated.

We therefore start in this Section with discussion

of dissipation in the normal adhesive contacts.

According to the JKR theory, the system jumps into

contact and then moves forth and back on the same

curve. The situation changes for more complicated

shapes. Even for flat-ended stamps with compact

face shape, the detachment may occur in a series of

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consecutive instabilities [15]. The same is valid

when surfaces are rough. Our numerical simulations

show that during approach and detachment, the

movement of the contact boundary proceeds in both

continuous changes and instable jumps. Each jump is

irreversible and, in its course, energy is lost. Due to

the multiple microscopic instabilities, the indentation

differs from the detachment curve at all values of the

indentation depth: the dissipation leads to an

apparent “friction” counteracting the movement of

the contact boundary.

Figure 1 shows the results of a simulation of the

indentation and detachment of a parabolic indenter

with superposed waviness into an elastic half-

space. The above mentioned instabilities are clearly

visible in the curves in Fig. 1 as microstructure of

the lines. When observing the evolution of the

contact zone, the corresponding local instabilities

can be clearly identified.

In the following analysis, the normal force FN,

the indentation depth d, and the contact radius a

will be normalized by the critical values of JKR

solution for a smooth sphere [1, 33]:

JKR 0

3π



 (2)

1/3

JKR *2

3π











(3)

1/3

JKR *

9π











(4)

where 0

γ is the work of adhesion per unit area

and E* = E/(1–ν2) is the effective elastic modulus of

a half-space with Young's modulus E and Poisson’s

ratio ν.

In 1995, Johnson studied the adhesive contact

between a wavy surface and a half-space [34], and

showed that the distinction between rough and

smooth surfaces is governed by the parameter,

which we now call the "Johnson parameter":

22 *

πhE







 (5)

In the following sections, we show that the

Johnson parameter is an essential governing parameter

for both adhesion and friction.

2.3 Effective surface energies for shrinking and

expanding of adhesive contacts

Figure 1 represents typical simulation results for

the force-indentation and force-contact area relations.

Since the contact boundary is generally non-

circular, we define the contact radius as the distance

from the center of contact to the furthest remote

contact point, independently of whether the contact

area is compact or consists of a "cloud of contact

spots" as shown in the right hand side of Fig. 2(b).

Figure 1 allows to explain general features

which are important for the following analysis:

1) Both indentation and pull-off curves follow

very closely the JKR solutions, shown in Fig. 1(b)

with red lines, but with different values for the

specific work of adhesion. The value 1

γ for the

approach is smaller than 2

γ for pull-off. See Section

2.5 for limitations of this simple picture with

respect to very large roughness values.

2) When the direction of loading changes from

Fig. 2 (a) Dependence of the force on the contact radius, for

four different roughness amplitudes h/λ, varying from 0.029

to 0.12, and for the same maximal indentation depth dmax/

|dJKR| = 15. (b) Shapes of contact areas for different roughness

amplitudes.

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approach to pull-off, the contact area remains

constant for a while. This feature is seen very

clearly in the dependence of force on contact

radius in Fig. 1(b) or Fig. 2(a). The dependence of

force on the indentation depth is linear in this

phase. This behavior is as if a force of static

friction acted on the boundary line, keeping it in

place when the motion of the indentation depth is

reversed. A similar phenomenon is theoretically

described in Ref. [35] where the effect is caused by

microscopic chemical heterogeneities.

The above findings mean that the normal adhesive

contact of rough surfaces can be characterized by

effective energies for approach and pull-off, in

other words for the expansion and retraction of the

contact zone. The values of the effective energies

are expected to approach zero for very rough

surfaces and roughly the microscopic value of the

specific work of adhesion 0

γ for smooth surfaces.

Figure 3 shows the results of systematic parametric

studies of effective specific surface energies 1

γand

γ. All data points collapse to well-defined master

curves if the effective energies are plotted as function

of the Johnson parameter [36]. In most simulations,

all parameters have been fixed and only the

roughness amplitude was varied. These results are

plotted in Fig. 3 with gray squares. However, we

also performed a large number of simulations in

which the elastic modulus, the roughness amplitude

and wave-length, and the microscopic specific work

of adhesion 0

γ were varied in a random fashion.

These additional data points provide a proof of the

hypothesis, that the true determining parameter is

the Johnson parameter. They are shown in Fig. 3

with open triangles having different colors for

different sets of parameters.

For the normalized effective surface energies

γγ and 20

γγ, as well as the maximum force

of adhesion |Fad|/|FJKR|, all data points collapse

on a well identified dependencies, confirming that

they depend indeed only on the Johnson parameter:

10 1

()γγ f



 (6)

20 2

()γγ f



 (7)

ad JKR ()FF



 (8)

Let us discuss the above dependencies in more

detail. For large values of the Johnson parameter,

all three dependencies tend towards 1. This is

expected, since higher values of α correspond to

small roughness amplitude, thus approaching an

ideally smooth surface.

An increase of the roughness amplitude corresponds

to a decrease of the Johnson parameter. The effective

specific work of adhesion describing the indentation

phase 1

γ, is continuously decreasing together with

the Johnson parameter. A particularly sharp drop

to almost zero occurs in the vicinity of α = 0.5. A

closer analysis of the contact configuration shows

that this sharp drop is associated with the change

from the compact contact area to a cloud of separated

contact spots. This reaffirms the conclusions from

the original paper by Johnson [34]. For α > 0.5, the

contact area has a relatively well-defined outer

border, and the force–distance dependence can be

accurately described by the regular JKR theory

Fig. 3 Dependence on Johnson parameter of the effective specific work of (a) adhesion γ1 for approach, (b) γ2 for detachment,

and (c) the maximum adhesive force Fad. The gray squares correspond to numerical results by varying only the roughness

amplitude, and the triangles by randomly varied parameters (including roughness amplitude, elastic modulus and specific work

of adhesion γ0). In all cases, the wave length was kept small in comparison to the sphere radius λ/R ranged from 0.005 to 0.0075.

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with a modified specific work of adhesion. Surfaces

with α > 0.5 are practically non-adhesive.

A slightly different behavior is found in the

effective specific energy 2

γdetermining the detachment

process. A decrease of the Johnson parameter, or

increase of roughness, first leads to an increase of

the effective surface energy followed by an abrupt

decrease, see also Ref. [36]. The maximum value is

found at α = 0.6073. The force of adhesion is

observed of course during the detachment process,

so it is strongly correlated with 2

γ, as for parabolic

bodies, the specific work of adhesion directly

determines the force of adhesion ad 2

3π

FRγ.

2.4 Influence of size effects

In Fig. 1, the instabilities due to roughness are

seen as small fluctuations of the indentation and

pull-off curves. In some applications like the contact

between a cell and the tip of an atomic force

microscope, the contact radius can be very small. When

it is comparable with the scale of the roughness,

the microstructure becomes pronounced, as exemplified

in Fig. 4. The observable jumps are sometimes

interpreted as results of detachment of discrete

adhesive bonds [37], but our simulations suggest,

that this kind of discontinuity can also be due to

the roughness of the indenter or the soft body

studied.

2.5 Friction of the contact boundary

Note that the above simple picture of two effective

surface energies works well only when amplitude

of roughness is not too large. With reference to the

Fig. 4 An exemplary dependence of the normal force on the

indentation depth for a spherical indenter with a superimposed

roughness of the form (1) in the case when the scale of

roughness approaches the characteristic size of the contact.

Note that the instable detachments are distributed irregularly

despite of the regular waviness of the indenter.

first of pictures in Fig. 2(b), one can state that this

concept is applicable with reasonable accuracy to

contacts which are compact or at least mainly compact,

which corresponds to α > 0.5. It is not applicable to

the regimes when the contact consists of a cloud of

separate points, which happens for α < 0.5. This

can be seen from the leftmost curve of Fig. 2(a): in

this case, the force of adhesion practically vanishes.

However, the indentation and detachment curves

do not coincide. On the contrary, they show an

even bigger hysteresis compared with smaller

amplitudes of roughness. For α < 0.5 neither the

indentation nor the detachment is well-described

by JKR theory.

For now, let us concentrate our attention on the

range α > 0.6. This is the interval in which the

contact area possesses a well-defined boundary,

even when it is not exactly circular, but represents

a "rough line" or even consists of a narrow band of

separated contact spots. On the other hand, we see

from Fig. 5 that in this interval, the mean value of

the effective surface energies, ( 

γγ

)/2, is roughly

constant and equal to its microscopic value 0

γ.

The effective surface energies for indentation and

detachment can thus be approximately written as



112 210

212 210

γγγ γγγγ





(9)

with

γγ γ



 (10)

It is well-known that the specific surface energy

can be interpreted as the linear force density acting

Fig. 5 Dependence of (γ1–γ2)/(2γ0) and (γ1+γ2)/(2γ0) on the

Johnson parameter.

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on the boundary line. We explain it [38] with an

example of a soap film stretched within a square-

shaped wire frame with length l. The work done

by the external force F for a displacement x is We =

Fx, the surface area is increased by lx, and the

surface energy by Ws = 2 0

γlx. Equilibrium of

both gives that linear force density is equal to F/l =

γ. The force pro length for pulling on a movable

side of the frame is twice of the surface energy of

liquid [38]. For smooth surfaces in the studied case,

this linear force density is equal to the specific

surface energy 0

γ. For rough surfaces, it depends

on the direction of the movement of the boundary,

increasing by γ/2 for moving in one direction and

decreasing by the same value for moving in the

opposite direction. Thus, the quantity

qγ

(11)

can be interpreted as a linear density of the force

of friction, acting always opposite to the motion

direction of the contact boundary.

The dependence of the boundary friction on the

Johnson parameter is also shown in Fig. 5. In contrast

to the absolute values of the surface energies, their

difference, and thus the boundary friction vanishes

for both small and large roughness values and

exhibits an extremum at the boundary of the

considered interval, i.e., at α 0.6.

2.6 Rolling adhesive contact

During rolling, tangential movement of the contact

area occurs due to superposition of approach at

the front edge and detachment at the rear edge.

Due to the adhesive hysteresis, the whole system

dissipates energy and rolling friction emerges. The

dissipated energy can directly be estimated analytically.

As shown in Section 2.2, the closing of the contact

and its opening can be characterized by two different

specific surface energies 1

γ and 2

γ. Consider an

adhesive contact with contact radius a, which is

moved tangentially by the distance x. During this

movement, surface area A = 2ax will come into

contact at the front side and the same area will detach

at the back side. The net dissipated energy thus

will be W = A(

γγ)=2a(

γγ)x. The friction

force can be defined as the ratio of the dissipated

energy to the sliding distance:



T21

2Faγγ (12)

If the rolling contact does not have an exact

circular form, then the half-width of the contact in

the direction perpendicular to the rolling direction

should be used in Eq. (12) as the contact radius.

We see that the adhesion contribution to rolling

friction is indeed the friction of the contact boundary

from Eq. (11) times the boundary width, twice

(since both the leading and the trailing edge advance).

A similar approach was used and experimentally

confirmed by Kendall [39] for the rolling friction

of cylindrical rollers.

Now let us consider results of numerical simulation

of rolling spheres with the same type of waviness

as defined by Eq. (1). Simulations have been carried

out under condition of fixed indentation. As can be

seen in Fig. 6(a), the normal force shows only very

small fluctuations, so that there is no substantial

Fig. 6 An example of rolling of a rough rigid sphere on a

smooth elastic half-space: (a) dependencies of the normal and

tangential forces (normalized by the absolute value of Eq. (2))

on the rolling distance. (b) Typical contact shapes for different

roughness amplitudes (characterized by the Johnson parameter

α). The first snapshot corresponds to the process shown in (a).

It is seen that the contact shape is not circular, showing

smaller radius (corresponding to smaller γ) on the leading

edge, and a larger radius (corresponding to larger γ) on the

trailing edge.

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difference between indentation control and force

control. In the simulation for tangential contact,

the indenter slides or rolls very slowly (statically),

so at each moment, the adhesive normal contact

solution obtained through BEM, then the tangential

force was calculated as the integral over the contact

area of the local pressure multiplied with the

x-component of the gradient of the rigid surface.

The tangential force shows considerable fluctuations

caused by instabilities of the boundary line but

these can still be characterized as "microscopic" so

that the macroscopic force of friction can be identified

easily. A snapshot of the contact configuration is

shown in the first picture of Fig. 6(b). One can see

that the boundary of the contact area is irregular

and the macroscopic shape of the contact is not

ideally circular.

To verify hypothesis Eq. (12), a large number

simulations with varying parameters were carried

out. Figure 7 shows values of the tangential force

plotted against 2a(

γγ). Both FT and a were

found numerically. For the values of Johnson

parameter larger α = 0.506, all results collapse to a

linear dependency with slope 1, thus indeed

confirming Eq. (12). Note that this contribution to

the force of rolling friction is proportional to the

contact radius rather than to the contact area.

Fig. 7 Comparision of tangential force from numerical

simulation with prediction of 2a(21



). For large enough

Johnson parameters, for which the contact area is compact,

the tangential force is equal to this value. Otherwise, the

contact is non-compact in form of a cloud of contact spots

and the tangential force is overestimated by Eq. (12). Numerical

results have been obtained for 13 different indentation depths

from dmax/|dJKR| = 1–13. Both the tangential force and 2a

(21



) are normalized by FJKR.

For smaller values of the Johnson parameter, as

explained above, the concept of effective surface

energies for opening and closing the adhesive crack

cannot be applied. Thus, as expected, the data do

not fit the linear dependence Eq. (12). Rolling

resistance for this range of Johnson parameter was

considered in [40–43].

Analytical estimation of the force of rolling

friction according to Eq. (12) requires two specific

surface energies and the contact radius. For determining

the contact radius, one could argue that a rolling

contact is a combination of indentation at the

leading edge and detachment at the rear edge.

Thus, in average, it should approximately correspond

to a smooth contact with the true surface energy γ0.

Numerical simulations show that the contact radius

of a rolling contact corresponds to an effective energy

of about 3

γ1.15 0

γ(Fig. 8). Similar to normal contact,

we use the JKR solution with another adhesion work

γto approximate the tangential force-contact radius

curve. The dependence of 3

γon Johnson parameter

is seen in Fig. 8. The contact radius thus can be

obtained from the usual JKR relation:



 

2π2π(1.15 )aa

dRR

γ (13)

3 Sliding adhesive contact: numerical

simulations

For rolling, as for any other normal contact, it is of

Fig. 8 Dependence of the effective specific work of adhesion,



, determining the contact radius of a rolling contact, on the

Johnson parameter. 3



was obtained using the JKR solution

to approximate the dependence of the normal force on the

contact radius.

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no importance whether the stiff or the elastic body

is rough since only the relative (composed) roughness

of both bodies plays a role. In contrast, the sliding

contact is a purely tangential contact and it is

important which of the bodies is rough. For example,

in a contact of a rigid rough indenter and a smooth

elastic half-space, the sliding force is zero (assuming

of course the validity of presuppositions of the

JKR theory). When a smooth indenter slides on a

rough elastic surface, it is not zero. In the first case,

the contact configuration remains unchanged all

the time, in the second it generally changes and

may also include instable configurations leading

to dissipation and friction.

For numerical simulation of sliding friction, we

considered a contact of a rough rigid sphere with a

rough elastic half-space. The "roughness" of both

bodies was modeled by the two-dimensional waviness

Eq. (1) with identical h and λ. The direction of the

axes of waviness of two bodies were rotated relative

to each to make the surfaces incommensurable.

The simulation procedure was the same as in the

case of rolling contact, only the changes of the

interfacial gap were caused by relative sliding

instead of rolling. As discussed in the introduction,

the frictional force in adhesive sliding contacts may

contain two parts: friction at the contact boundary

FB, and a contribution of the inner contact area, FC:



Friction B C

FFF (14)

3.1 Friction of the contact boundary

As in the case of rolling, the dynamics of the

contact configuration consists of both continuous

movements of the boundary and instable jumps.

The continuous movement is based on energy balance

and is completely reversible. The jumps lead to

energy dissipation and irreversibility of the tangential

sliding, which is perceived macroscopically as the

force of friction. This process is illustrated in Fig. 9

showing four snapshots of the contact configuration

during sliding process. For this simulation, the

wavelength of the roughness was chosen relatively

large to visualize the irregularity of the boundary

and its jerky behavior.

Figure 10 shows the dependence of the contribution

to the friction force due to boundary jumps on

Fig. 9 Consecutive snapshots of the contact area during

sliding. The dynamics of the contact configuration consists of

the phases of continuous evolution and instable jumps.

Fig. 10 (a) Dependence of the boundary contribution to the

force of friction and (b) contact area contribution to the force

of friction on Johnson parameter.

the Johnson parameter α. The tangential force is

small both in the limit of very smooth and very

rough surfaces, and achieves a maximum exactly

at the transition from smooth (adhesive) to rough

(nonadhesive) surfaces, corresponding to α 0.65.

3.2 Area contribution to friction

The contribution from the area can be interpreted

in different ways: either as a microscopic coefficient

of friction to be multiplied with the adhesive

pressure or as shearing of some physically existing

boundary layer [8, 22]. In the latter case, there

exists some characteristic tangential stress τ0 to be

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overcome. The corresponding contribution to the

tangential force during sliding is then proportional to

the real contact area, A. For large Johnson parameters

(small roughness), the contact area is compact and

practically coincides with a2. The compactness of

the contact, expressed as the numerically calculated

value for the real contact area normalized by τ0a2

is shown in Fig. 10(b). For values of α < 0.65

approximately, it decays quickly. It is seen that at

the large value of Johnson Parameter, the friction

is roughly equal to the production of contact area

and this characteristic tangential stress.

4 Experimental setup

The second part of the paper is devoted to an

experimental study of adhesive contacts between

rigid indenters and very soft transparent rubber.

The softness of one of the contacting bodies is the

necessary pre-requisite for formation of a large

contact area whose configuration can be recorded

with high resolution. The instabilities at the contact

boundary leading to the boundary friction are

directly observable in this system and will be

studied in detail. However, we will see that for the

total frictional force, the area contribution is

prevalent in our experiments.

Experiments have been conducted using the setup

depicted in Fig. 11. Steel spheres having various

radii of curvature were indented into a 5 mm thick

layer of transparent rubber TARNAC CRG N3005,

and subsequently pulled off or moved tangentially

Fig. 11 Experimental setup. Left panel: general view, right

panel: contact between the steel indenter and the rubber layer,

with the lighting system.

with precision linear stages attached to a strain

gage sensor recording normal and tangential forces.

The contact region was illuminated from the side

with 80 LEDs and was recorded from underneath

using a digital camera with the resolution of 1600 ×

1200 pixels. An inclination mechanism was used to

ensure a parallel orientation between the rubber

surface and tangential indenter movement.

5 Normal adhesive contact

5.1 Flat-ended elliptic punch

Let us start with consideration of an adhesive

contact of a flat ended stamp with a face surface in

form of an ellipse with an elastic flat body. Assuming

that the detachment starts at the points where the

stress intensity factor for the first time exceeds the

critical value, it can be easily shown that the

detachments should start at the ends of the major

axis of the contact ellipse [29]. Numerical simulations

of the detachment process confirm that detachment

starts at these maximally remote from the center

points and propagates inwards (Fig. 12). However,

Fig. 12 Detachment process of a flat-ended punch with an

elliptical face surface. (a) Three dependencies of the normal

force on the distance from the plane surface (negative indentation

depth); for a homogeneous system and for two heterogeneous

(quadratic) distributions of the specific work of adhesion

along the indenter face surface. (b) The corresponding series

of contact configurations, showing the first moment when

detachment starts, some intermadiate configurations, as well

as the final instable configuration after which the contact is

lost in a jump-like manner.

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in experiment, the detachment starts at the ends of

the minor axis of the ellipse and leads to constriction

of the contact in the middle of the ellipse with final

separation in two not connected areas, Fig. 13.

The physical reason for this striking difference

between experiment and theoretical prediction has

not been clarified yet. One possible explanation

could be a heterogeneity of the surface energy in

the direction of the large axis of the ellipse, which

could be caused e.g., by various heating of central and

peripheral parts of the indenter during production

process. Results of numerical simulations with

artificially introduced heterogeneity of the specific

work of adhesion are shown in Fig. 13. A heterogeneity

can indeed lead to force-displacement relations and

sequences of contact configurations very similar to

those found in experiment. However, for starting

detachment at the ends of the minor axis, the ratio

of surface energies at the end of the ellipse and in

its middle must achieve at least 13, and for complete

constriction in the middle, this ratio should be at

least 20. It is hardly imaginable that such huge

variations of the specific surface energies can appear

due to preparation of the samples. Thus, the reason

for this striking discrepancy of theory and experiment

remains not clarified.

However, we would like to stress that for many

Fig. 13 Experimental observations of the detachment process

of a flat-ended punch with an elliptical face surface: (a)

Dependencies of the normal force on the distance from the

plane surface (negative indentation depth); three curves are

just three repetitions of the same experiment. (b) Contact

configurations in the initial state, at the beginning of the

detachment process at the ends of the minor axis, and further

constriction of the contact area in the middle. Two instabilities

are seen: 1) the "constriction instability" leading to a rapid

division of the contact area in two separated parts, and 2) the

final detachment of the two remaining contacts in the vicinity

of the vertices of the ellipse.

other shapes that were not as slim as those shown

in Fig. 13, a good correspondence between theory

and experiments has been shown (e.g., many

shapes studied in Ref. [15]).

5.2 Hysteresis of the surface energy and its time

dependence

An important question in experiments is their

repeatability. Our studies of repeatability revealed

a number of effects which have to be taken into

account when interpreting experimental studies of

adhesive contacts.

If a freshly manufactured indenter is pressed

and pulled off several times, the adhesive force is

significantly different in the first impression compared

to the second and all subsequent ones. The reason

for this effect could be chemical changes in the

surface due to the first contact leading to a change

of the specific surface energy after the first impression.

If a body is indented to the same depth and

remains in this state for different time, it will follow

different curves when it is subsequently pulled off

(Fig. 14(a)). The dependence of the adhesive force

on the waiting time is shown in Fig. 14(b). It can be

approximated as follows:

0.0883

,min 0.07292

Ft (15)

where the force is measured in Newton and time

in minutes.

This means that the specific separation energy

increases with the waiting time.

Fig. 14 (a) Dependence of the normal force on the indentation

depth, for a spherical indenter with the a radius R = 40 mm,

for the soft rubber CRG N0505. Different curves correspond

to different waiting time at the maximal depth of penetration.

The adhesive force increases with the waiting time. (b)

Dependence of the adhesive force in the pull-off phase on the

waiting time. The shortest time was t = 1 min. The inset

shows the same curve on the double-logarithmic scale.

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Note that after the reversal point, all curves

initially coincide and follow a linear dependence.

Video recordings show that the contact area does

not change during this phase. This "pinning of the

boundary of contact area" is seen also in numerical

simulations (Fig. 1(a)). Such behavior shows that

the boundary line of the contact area is inhibited

to reverse the movement immediately after

reversing the loading, which means presence of a

frictional force experienced by the boundary line.

Such behavior has been observed and described in

Ref. [44].

Before the reversal and after the linear stage, the

indentation and the pull-off curves follow the

theoretical JKR curve ‒ only with different specific

separation energies for the closing and opening of

the contact, in correspondence with the numerical

results shown in Fig. 1(b).

6 Sliding adhesive contact

In experiments with sliding of adhesive contacts,

spherical steel indenters with radii of 11, 22, and

100 mm were used. They were first pressed into

the rubber layer, and then were lifted up to a fixed

indentation depth. We studied both positive indentation

depth (represented by the value 0.2 mm, zero

indentation depth and negative "indentation depth"

of –0.015 mm (in the latter case, the contact does

exist only due to adhesion). Subsequently, it was

slowly moved in the tangential direction (typically

at v = 1 µm/s) over the distance x = 15 mm. After

that, the direction of the movement was reversed,

and the indenter moved over the same distance x =

15 mm back to the point of initial contact. Finally, the

indenter was lifted until complete loss of contact.

The general feature of the dynamics of contact

area during sliding is that it is not exactly circular

(due to microscopic chemical heterogeneity and

roughness). The rougher the surface (Fig. 15), the

"rougher" is the contact boundary and the more

discontinuous occurs its movement when increasing

tangential loading. Most of the time, the boundary

remains pinned by heterogeneities and the movement

occurs in form of rapid jumps from one stable

configuration to the other. Each jump is irreversible

and during each jump, energy is lost.

Fig. 15 Snapshots of the contact area, for different roughnesses

of the indenter with radius R = 100 mm and zero indentation

depth d = 0 mm during phase of detachment. The numbers

P2000, P180, P60, and P0 describe the sand paper used for

preparation of samples. The larger numbers correspond to

smaller grain size and correspondingly to smoother surface,

as listed in Table 1. The highest roughness was obtained by

manual treatment with a hacksaw (P0).

Table 1 Average grain sizes of the sand paper depending on

its number.

Grain number P2000 P180 P60

Grain size (µm) 10.3 82 269

As the detailed character of the development of

the contact area during sliding depends on the

radius of the indenter, in the following we describe

separately the results for each of the radii studied.

Indenter radius R = 22 mm

Figure 16 shows images of the contact area during

lateral displacement. Comparison of snapshots "1"

and "2" shows that the displacement of the boundary

of the contact area starts on the right side (front

line), while it remains pinned on the left side (rear

side of the contact). This behavior means that the

friction force acting on the boundary line is

asymmetric (smaller for propagation of the contact

area and larger for shrinking).

Fig. 16 Snapshots of the contact area in a contact with a

spehere (R = 22 mm). The transparent elastomer is fixed and

the rough steel sphere moves to the right. The snapshot (1)

corresponds to the indentation to the depth d = 0.2 mm. The

white line was inserted in the center of the contact with

respect to the rigid indenter. Snapshot (2) shows the contact

under subsequent displacement in the lateral direction by 0.6

mm. The asymmetry of the contact area is seen clearly. The

snapshots "3-2" and "4-2" show further evolution of the

contact configuration by two subsequent displacements by 1

micrometer each. New areas formed are marked with red, and the

parts which disappeared (compared to the state "2") with blue.

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Secondly, the propagation of the contact area

occurs in jumps. Thus, the tangential displacement

separating snapshots 3-2 and 2 is equal to 1

micrometer, but the changes of the contact area are

disproportionally large (up to the moment of the

jump the boundary is pinned and does not move

at all). However, the jumps of the rear part have a

much smaller amplitude than those of the front

area.

Let us stress that the tangential displacement

can lead not only to the propagation of the front

boundary in the direction of movement (red areas)

but also to shrinking (moving "back", blue areas).

This may be caused by a stress redistribution

either due to propagation of the line in adjacent

regions or due to detachment waves propagating

through the contact area from the front to the rear

side. These waves are not seen in the snapshots

but can be easily seen in the corresponding videos.

At large indentation depth, the contact size in

the direction perpendicular to the direction of

sliding, tangential force as well as tangential stress

do not change substantially (Fig. 17).

An essentially different behavior is observed in

the case of small or negative indentation depths. In

Fig. 18, the dynamics of contact area is shown for

d0 = 0 mm.

Fig. 17 A small fragment of the time dependencies of left-

hand-side (rear) area (blue line in the upper part of Figure)

and right-hand-side (front) area (red line in the lower part of

Figure), tangential force and tangential stress in the case of

R = 22 mm and d = 0.2 mm.

Fig. 18 Snapshots of the contact area in a contact with a

sphere (R = 22 mm) corresponding to the indentation depth

d = 0 mm. Other conditions are similar to those of Fig. 16.

The snapshot "1" shows the contact before beginning

of tangential motion, after the body has been

indented to the depth d = 0.2 mm and moved back

to the position d = 0 mm. Snapshots 2–4 show the

contact area during tangential movement by the

distance x = 0.42 mm at the fixed (zero) indentation

depth. Finally, a stationary mode of motion is

established consisting of pronounced macroscopic

stick and slip phases, Fig. 19.

In this case, the difference between the dynamics

of the front line and the back line of the contacts is

especially pronounced. The rear contact area does

not change during tangential motion (Fig. 19, blue

line). The front area, on the contrary, changes

vividly (Fig. 19, red line). The changes in the total

area are thus mostly due to the changes in the front

area. Tangential force oscillates correspondingly.

However, the tangential stress τ, determined as

ratio of the total tangential force and the total area,

remains during the sliding phase practically constant

and equal to τ ≈ 36 kPa. Detailed view provided

in the right part of Fig. 19 shows what exactly

happens in the contact. During the stick phase, the

contact area not only does not change but also does

not move, so that the force linearly increases with

tangential displacement. In the subsequent sliding

phase, the sliding occurs in the whole contact area

at practically constant tangential stress which only

weakly depends on the indentation depth (Fig. 20).

This suggests that in the system studied experimentally,

the main contribution to the force of friction is the

area contribution.

Finally, consider the case of negative indentation

depth d = –0.015 mm. In this case, the contact does

exist only due to adhesion. The indenter was first

pressed into the rubber sheet, then lifted up to

d = –0.015 mm (snapshot "1" in Fig. 21) and moved

subsequently in tangential direction. The size of

the contact decreases monotonously (in Fig. 21,

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Fig. 19 Dependencies of the tangential force Fx, parts of contact areas A (front area, rear area, and total area), and tangential

stresses τ on time. Radius of indenter R = 22 mm; indentation depth d = 0.0 mm.

Fig. 20 Dependencies of tangential stress for forth and back

movement of an indenter with radius of curvature R = 22 mm

and 6 different indentation depths.

Fig. 21 Snapshots of the contact area in a contact with a

sphere (R = 22 mm), corresponding to the indentation depth d =

–0.015 mm. Other conditions are similar to those of Fig. 16.

snapshot "2" corresponds to tangential displacement

0.0369 mm, "3" corresponds to x = 0.0668 mm, and

"4" to 0.0768 mm). Finally the contact gets lost.

Figure 22 presents the normal and tangential

forces, as well as the normal pressure and the

tangential stress, during all of the essential stages

of the experiment. The indenter was first pressed

up to the depth 0.2 mm, then lifted up to d = –0.015

mm, and subsequently moved tangentially. The

tangential force first increases and then decreases,

and eventually vanishes (Fig. 22(b)). At the same

time, the normal pressure vanishes too. This is due

to the above-described decrease of the contact area

until the contact completely disappears.

Fig. 22 Dependencies of: (a) the normal force, FN, (b) the

tangential force Fx, (c) the normal mean pressure p = FN /A,

and (d) the tangential stress τ = Fx/A on time t. Radius of

indenter R = 22 mm; indentation depth d = –0.015 mm.

Fig. 23 Dependencies of the rear, front, and total area A on

the tangential displacement x. Radius of indenter R = 22 mm,

indentation depth d = –0.015 mm. Vertical lines correspond

to the configurations 2, 3, and 4 in Fig. 21.

Indenter radius R = 100 mm

To illustrate the diversity of modes observed in

experiments with sliding adhesive contacts, we

report also results of experiments with an indenter

having the curvature radius R = 100 mm. While

from the theoretical viewpoint, the behavior of

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sliding indenters with various curvature radii

should be qualitatively similar, experiments reveal

several qualitative differences.

Figure 24 shows snapshots of 4 consecutive

contact configuration after indentation by d0 = 0.2 mm

and subsequent tangential displacement. The left

snapshot corresponds to some initial tangential

displacement and serves as reference for the next

three, where the newly appeared contact regions

are highlighted with red and the parts which

disappeared with blue.

Already a study of this sequence shows that

now there are large "jumps" of the contact area in

the rare part of the contact (distinctively seen in

Fig. 25, upper graph) while the front part moves

more continuously.

Fig. 24 Snapshots of contact configurations of a spherical

indenter with radius R = 100 mm after indentation by d =

0.2 mm and subsequent tangential displacement with fixed

indentation depth. Areas highlighted with red are newly

appeared contact regions (compared with the first snapshot

which is used as reference; with blue are marked the regions

which disappeared compared with the reference configuration).

Fig. 25 Dependencies of the rear and front contact areas,

tangential force and tangential stress on time t in the "stationary"

sliding mode, for R = 100 mm and d = 0.2 mm.

Depending on the size of the indenter and

loading parameters, also more complicated regimes

have been observed. In some cases, the contact

area in the front line jumped several times forth

and back (in spite of unidirectional movement of

the indenter). Attentive studies of such regimes

always reveal interface waves propagating from

the front side of the contact towards rear part.

As in the case of the indented with R = 22 mm,

decreasing of the indentation depth leads to appearance

of a pronounced "inverted stick-slip" accompanied

by reduction or complete disappearance of the

front part of the contact area (Fig. 26). The tangential

stress during sliding phase changes only very

weakly around the value around 35 kPa.

7 Discussion and conclusions

This paper focuses on the tangential movement of

adhesive contacts by rolling or sliding. We also

studied the properties of the normal adhesive

contacts since those are directly related to the

energy dissipation and thus appearance of friction.

Investigations have been carried out experimentally

by direct observations of the contact configuration,

and numerically using the FFT-based BEM for

adhesive contacts.

Our studies suggest the following general

picture:

1) Apparently, there exist two main contributions

to friction in adhesive contacts: one coming from

the contact area and the second one coming from

Fig. 26 Dependencies of the tangential force Fx, components

of the contact areas A (rear, front, and total), and mean

tangential stress τ on time. Radius of the indenter R = 100 mm,

indentation depth d0 = 0.0 mm.

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the boundary of the contact zone.





Friction B C

Fr realiction 0

FFF

FqDA

(16)

where D is the width of the contact facing the

direction of motion, τ0 is a constant having dimension

of stress and q is a constant having dimension of

linear force density, see Eq. (11). For pure rolling

contact, FC = 0.

When the contact is relatively circular and

compact, with contact radius a, then D = 2a and

Areal A = a2. The above statement can then be

expressed as





Friction 0

2πFqAA (17)

This means that formally calculated mean tangential

stress in the contact is equal to









mea 0

2πqA (18)

and increases with decreasing contact area. This

seems to be supported by our experimental data

(see e.g., Fig. 26).

Equation (18) implies that the boundary contribution

will prevail in very small contacts, especially if

they are smooth and rigid, while the area contribution

is governing in large and soft contacts.

2) The boundary friction determines not only

the boundary contribution to the force of friction

but also the adhesive hysteresis in normal contacts.

Depending on the value of the Johnson parameter

α, we can distinguish between "smooth" contacts

having a more or less compact contact area and

identifiable contact boundary, and "rough" contacts

consisting of clouds of disconnected contact spots.

For "smooth" contacts α > 0.6, the force-indentation

relation can be described well by the JKR theory,

but with two different specific works of adhesion,

γand 2

γ for the indenting and pull-off phases.

When reversing the direction of loading, the contact

area remains constant and the force-distance relation

is linear until the system completes the transition

from one JKR curve to the other. The effective

surface energies 1

γ and 2

γ are determined by the

Johnson parameter, γ1 = γ0f1(α) and γ2 = γ0f2(α).

3) The physical nature of the boundary friction

lies in microscopic instabilities of the contact

configuration. Both numerical simulations and

experiment show that tangential movement – sliding

as well as rolling – is realized in both continuous

movements and instable jumps. Continuous displace-

ments are reversible, energy is dissipated solely

during jumps, thus leading to appearance of

macroscopic friction. This is valid even in the very

rough contacts which do not show any noticeable

adhesion.

4) We found that there are two main types of

dynamics of the contact area: either "macroscopically

continuous" (but microscopically jump-like) movement

or as a pronounced macroscopic "inverted stick-

slip" behavior. The continuous mode is realized for

small contacts and/or large indentation depth and

the "stick–slip"-like mode for large contacts or

small (in particular, zero or negative) indentation

depths. The reason for macroscopic instabilities

are apparently interfacial waves, which are observed

in all cases of pronounced macroscopic instabilities

(on the scale much larger than that of roughness).

5) The above properties have important macroscopic

implications. In a sense, one can say that the

adhesive contacts (even in the case when the

adhesion is not visible because the adhesion force

vanishes) are the most time in a "stick" state and

move only due to rapid instable changes of the

contact boundary or due to interfacial waves. This

can explain a paradox described in Ref. [45]. In

that study, it was experimentally found that the

response of a sliding elastomer contact to dynamic

loading is as if the contacts were sticking.

6) Rolling and sliding of circular contacts lead

to a change of the shape in the contact. However,

the change is more complex than discussed in Ref.

[46]. Contacts may be "compressed", either in the

sliding direction or perpendicular to it, depending

on the size, indentation depth, and possibly other

parameters.

7) Experiments with very slim indenters revealed

a fundamental discrepancy between predictions

based on the energetic detachment criterion (the

JKR theory). The physical reason for this discrepancy

remains not understood but is of utmost importance

for the correct physical understanding of the

detachment criterion and for numerical simulations

of adhesive contacts.

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Acknowledgements

This work has been conducted under partial financial

support from German Research Foundation (DFG)

(Grant No. PO 810/55-1), the Tomsk State University

Academic D.I. Mendeleev Fund Program, and the

German ministry for research and education (BMBF)

(Grant No. 13NKE011A).

The authors acknowledge valuable discussion

with A.E. Filippov.

Contributions of authors: V.L. POPOV designed

the concept of the paper, made analytical theory,

carried out analysis of numerical and experimental

data and drafted the manuscript. I. LYASHENKO

and R. POHRT designed and built the experimental

setup. I. LYASHENKO carried out experiments and

processed experimental data. Q. LI, I. LYASHENKO,

and R. POHRT contributed to the development of

the BEM program. Q. LI executed the numerical

simulations. All authors contributed equally to the

editing and reviewing of the manuscript.

Open Access This article is licensed under a

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[23] Prandtl L. Ein Gedankenmodell zur kinetischen Theorie

der festen Körper. Z Angew Math Mech 8(2): 85–106

(1928)

[24] Popov V L, Gray J A T. Prandtl-Tomlinson model:

History and applications in friction, plasticity, and

nanotechnologies. Z Angew Math Mech 92(9): 683–708

(2012)

[25] Popov V L, Gray J A T. Prandtl–Tomlinson model: a

simple model which made history. In The history of

theoretical, material and computational mechanics-

mathematics meets mechanics and engineering. Stein E,

Ed. Berlin: Springer Berlin Heidelberg, 2014: 153–168.

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atomic friction: Entering a new regime of ultralow

friction. Phys Rev Lett 92(13): 134301 (2004)

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M, Heimberg J A, Zandbergen H W. Superlubricity of

graphite. Phys Rev Lett 92(12): 126101 (2004)

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elastic solids using local mesh-dependent detachment

criterion in Boundary Elements Method. FU Mech Eng

13(1): 3–10 (2015)

[30] Li Q, Argatov I, Popov V L. Onset of detachment in

adhesive contact of an elastic half-space and flat-ended

punches with non-circular shape: Analytic estimates and

comparison with numeric analysis. J Phys D: Appl Phys

51(14): 145601 (2018)

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Kendall–Roberts adhesive contact for a toroidal indenter.

Proc Math Phys Eng Sci 472(2191): 20160218 (2016)

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mechanics and friction: Interplay of electrostatics,

theory of gravitation and elasticity from Coulomb to

Johnson–Kendall–Roberts theory of adhesion. Phys

Mesomech 21(1): 1–5 (2018)

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Problems. Berlin, Heidelberg: Springer Berlin Heidelberg,

2019.

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of rough spheres. Front Mech Eng 5:7 (2019)

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AFM cell mechanics studies. Sci Rep 8(1): 1504 (2018)

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component of the sliding friction force. Wear 270(9–10):

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surface microgeometry and adhesion in normal and

sliding contacts of elastic bodies. Friction 5(3):

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rough "Non-adhesive" contacts. Preprints, 2020050210

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Friction 19

∣www.Springer.com/journal/40544 | Friction

http://friction.tsinghuajournals.com

Valentin L. POPOV. He is a full

professor at the Technische Universität

Berlin. He studied physics and

obtained his doctorate in 1985

from the Moscow State Lomonosov

University. In 1985–1998, he worked

at the Institute of Strength Physics

and Materials Science of the Russian Academy of

Sciences and was a guest professor in the field of

theoretical physics at the University of Paderborn

(Germany) from 1999 to 2002. Since 2002, he has

been the head of the Department of System

Dynamics and the Physics of Friction at the Berlin

University of Technology. He has published over

300 papers in leading international journals and is

the author of the book Contact Mechanics and

Friction: Physical principles and applications which

appeared in nine editions in German, English,

Chinese, Russian, and Spanish. He is the member

of editorial boards of many international journals

and is the organizer of more than 20 international

conferences and workshops over diverse tribological

themes. Prof. POPOV is an Honorary Professor of

the Tomsk Polytechnic University, of the East

China University of Science and Technology, and of

the Changchun University of Science and Technology,

and the Distinguished Guest Professor of the

Tsinghua University. His areas of interest include

tribology, nanotribology, tribology at low temperatures,

biotribology, the influence of friction through

ultrasound, numerical simulation of contact and

friction, research regarding earthquakes, as well as

topics related to materials science such as the

mechanics of elastoplastic media with microstructures,

strength of metals and alloys, and shape memory

alloys.

Qiang LI. He is a postdoctoral

researcher at the Berlin University

of Technology. He studied mechanical

engineering in East China University

of Science and Technology. He

obtained his doctorate at the

Berlin University of Technology

in 2014 and now works as a scientific researcher at

the Department of System Dynamics and the

Physics of Friction headed by Prof. V. L. POPOV.

He has published over 50 papers in international

journals including Physical Review Letters. His

scientific interests include tribology, elastomer friction,

hydrodynamic lubricated contact, numerical simulation

of frictional behaviors, fast numerical method based

on boundary element method, and adhesion.

Iakov A. LYASHENKO. He is a

researcher at the Berlin University

of Technology and a full professor

at the Sumy State University (SSU),

Ukraine. He studied physical and

biomedical electronics and obtained

his doctorate in 2008 from the

Sumy State University. He joined the group of Prof.

V. POPOV in 2014. He has published over 70

papers in international journals. His areas of

interest include boundary friction, adhesion, contact

mechanics, nanostructuring burnishing, dynamical

systems, phase transitions, and fluctuations.

Roman POHRT. He is a re-

searcher at the Berlin University

of Technology. He studied physical

engineering science with special

focus on simulation and optimization

of discrete and continuous problems.

Since he joined the group of Prof.

V. POPOV in 2010, he has been conducting

experimental and numerical research on a variety

of tribology related industry problems. In his Ph.D.

thesis, he focussed on linking scales in the elastic

contact of fractal rough surfaces, for which he was

awarded by the German Tribological Society in

2013. He has authored a series of influential

papers on different tribological problems, applying

and extending state-of-the-art numerical methods.

He is the Chief-Editor of the Journal Frontiers in

mechanical engineering|Tribology. His areas of interest

include contact mechanics, adhesion, rail- wheel-

interaction of trains, manufacturing technology,

lubrication, and more generally the influence of

surface topography on tribological phenomena.