SPECIALTY GRAND CHALLENGE
published: 19 November 2018
doi: 10.3389/fmech.2018.00016
Frontiers in Mechanical Engineering | www.frontiersin.org 1November 2018 | Volume 4 | Article 16
Edited by:
Jun Qu,
Oak Ridge National Laboratory (DOE),
United States
Reviewed by:
Peter J. Blau,
Blau Tribology Consulting,
United States
*Correspondence:
Valentin L. Popov
Specialty section:
This article was submitted to
Tribology,
a section of the journal
Frontiers in Mechanical Engineering
Received: 31 May 2018
Accepted: 16 October 2018
Published: 19 November 2018
Citation:
Popov VL (2018) Is Tribology
Approaching Its Golden Age? Grand
Challenges in Engineering Education
and Tribological Research.
Front. Mech. Eng. 4:16.
doi: 10.3389/fmech.2018.00016
Is Tribology Approaching Its Golden
Age? Grand Challenges in
Engineering Education and
Tribological Research
Valentin L. Popov*
Technische Universität Berlin, Berlin, Germany
In spite of its obvious importance, the subject of tribology has relatively low visibility in the
engineering community and among the general public. The author’s hypothesis is that
this problem is at least partly due to the poor “availability” of tribology. In other words,
there are practically no simple methods or concepts having high predictive power for
tribological problem-solving. That situation is due to the extremely inter-disciplinary and
multi- scale character of tribological processes. Fortunately, however, recent methodical
and didactical developments in the field of tribology offer hope that the situation may
soon change. It is time to integrate certain basic aspects of the mechanics of interfaces
into the curricula of technical universities. The author further argues that one of the key
problems confronting tribology and its future grand challenges is solving the problem of
the “third body.”
Keywords: contact mechanics, lubrication, wear, adhesion, tribochemistry, elastohydrodynamics, boundary
element method, third body
INVISIBLE TRIBOLOGY
Whether a technical device or a living being—every system is made up of connected parts. These
connections of various kinds—from simple supports to rivets, screws, glued connections, various
types of bearings, wheels, and so on are the subject of a science named Tribology. Tribology
is a subject integral to any mechanical system containing moving parts or joints—starting with
molecular “machines” (as motor proteins in living cells) (Dudko et al., 2003) and micro and nano
mechanical systems (Bhushan et al., 1995) over the huge field of traditional macroscopic tribology
(Dowson, 1979) up to the contacts between tectonic plates (Scholz, 2002). The word “Tribology”
was introduced 1966 by the British commission guided by Jost (1966). The Jost Report identified
incorrect lubrication and the accompanying wear and friction issues as the main reasons for the
failure of mechanical systems. Since then it is has been (somewhat) widely recognized that tribology
has immediate influence on global energy consumption, costs and emissions—key technological
and hot political issues of the modern society (Holmberg and Erdemir, 2017). And yet, if you ask
people on the street what “Tribology” is, most of them will not be able to associate this word with
any practical object or problem. How can the tremendous importance of tribology be reconciled
with its relatively low social and technological visibility?
Popov Is Tribology Approaching Its Golden Age?
WHAT IS THE REASON FOR LOW
VISIBILITY OF TRIBOLOGY?
The answer may lie in the poor availability of tribology to the
broader engineering community. Scientific and technological
visibility and public perception of each discipline is determined
not only by its importance but very decisively also by its
availability. Thus, Analysis was almost a sacral science only
for a few “initiates” until Leibnitz invented his intuitive
and practical notations (Leibnitz, 1674-1676). This seemingly
“merely didactical” invention made Analysis available literally
for everybody—now it is a part of the curriculum of any high
school. The availability of a subject is strongly associated with
its complexity, and the complexity of the mechanics and physics
of interfaces is notoriously high. Just a superficial glance in an
anatomic atlas (Bourgery, 2017) shows that the main elements
of the supporting structure of the human body, bones, are—
in spite of their complicated internal structure—much simpler
than the joints. The latter have a truly spectacular architecture
and very specialized material properties, which still cannot be
reproduced artificially (Jin and Dowson, 2013). No wonder that
it is much more difficult to repair the joints than it is to mend
bones. Structural elements and their joints are both omnipresent
in a variety of systems—they are both generic, unavoidable
aspects of any structure. The difference between them is in the
availability of models used to describe them: For the basics of
mechanics of materials students only need proficiency in analysis
of one variable and the simplest ordinary differential equations,
while the simplest (Hertzian) contact problem is formulated
as an integral equation with mixed boundary conditions. This
qualitative difference in complexity is the reason for the fact that
students of almost all engineering majors study the theory of
beams in their first or second semester, but only acquire a very
rudimentary notion of the mechanics of connections.
DID TWO CENTURIES SINCE THE WORK
OF COULOMB BRING PROGRESS?
Tribology is the science of friction, wear and lubrication.
The first experimental study of friction that was broadly
publicly discussed and had a decisive impact on the subsequent
development of science and engineering seems to be the memoir
of Amontons (1699). He was the first to formulate, based on
experimental observations, the “law of friction” which is now
widely known as “Amontons’ law.” In 1781 Charles Augustin
de Coulomb published his remarkable, timeless book on friction
(see available later edition, Coulomb, 1821) where he described
many properties of dry friction that even today remain subjects
of active research. In particular, he investigated the dependency
of the coefficient of friction on time, velocity, normal force,
apparent contact area, humidity and material pairing. Some of his
observations—e.g., the explicit time dependency of the coefficient
of friction—have been understood only two hundred years later
(Rice and Ruina, 1983; Dieterich and Kilgore, 1994) and many
remain not understood to this day. For example, Coulomb found
that the intensity of friction in the contact of wood on metal,
depending on the duration of contact, slowly increases and
reaches its peak after 4–5 days, and sometimes more. In contact
of two metals, friction shows completely different behavior: it
achieves the stationary value in an instant. In wood on wood
contact friction achieves the stationary value in a few minutes
(Popova and Popov, 2015). These observations are more than 200
years old, but only began to be understood on the micro scale very
recently (Carpick and Bennewitz, 2014).
The most striking deficiency in the current state of the art
of tribology, is that we still cannot predict the coefficient of
friction in practically any pairing, and in many cases we even do
not really understand what the main governing parameters are.
This is due to the complexity of physical processes determining
tribological properties (Persson and Tosatti, 1996): contact
interactions, adsorbed layers (Robbins and Krim, 1998; He
et al., 1999; Müser et al., 2001), tribochemical reactions, mixing
processes and wear (Scherge et al., 2003), elastohydrodynamic
lubrication (Ertel, 1939; Hamrock and Dowson, 1977), boundary
lubrication (Kenausis et al., 2000), shear melting (Persson and
Popov, 2000), cavitation (Etsion, 2013; Savio et al., 2016),
adhesion (Rabinowicz, 1961), interaction with system dynamics
(Kado et al., 2014; Teidelt, 2015; Milahin, 2016; Wetter, 2016)
material properties (Khadem et al., 2017) and fracture mechanics
(Ciavarella et al., 1999)—to mention only some.
Clearly, there are many complex tribology problems which
have been solved, as e.g., those connected with hydrodynamic
and elastohydrodynamic lubrication. It should also be noted that
many tribological problems have been met with working practical
solutions—otherwise we would not have functioning cars, trains,
airplanes, and other modern conveniences. Nonetheless, many
such solutions were arrived at mostly by trial and error, in
combination with iterative improvement. Many fundamental
problems, particularly those involving dry and boundary
lubrication remain not well understood.
IS THE TIME RIPE FOR A “REVOLUTION”
IN TRIBOLOGY?
Several developments of the last decades have the potential to
change the future standing of tribology among other engineering
sciences. Consider, for example, the theories of hydrodynamic
and elastohydrodynamic lubrication (Hamrock and Dowson,
1981), understanding of hard coatings (Donnet and Erdemir,
2008) and lubrication additives (Spikes, 2004).
In the following I would like to discuss in more detail two key
developments that concern contact mechanics.
FFT-Based Boundary Element Method:
Searching for Consensus and New
Paradigms in Tribology
The first of these developments is an extremely effective
numerical simulation method of contact of rough surfaces.
It is known as the Fast Fourier Transform-based Boundary
Element Method, or FFT-BEM. Following years of debate on
the underlying theory, the engineering community created a
Frontiers in Mechanical Engineering | www.frontiersin.org 2November 2018 | Volume 4 | Article 16
Popov Is Tribology Approaching Its Golden Age?
tool that allows direct calculation of realistic contact conditions.
Several modifications of this method are mentioned in Müser
et al. (2017). The most common version of the FFT-Based
Boundary Element Method (Putignano et al., 2012) can be
applied both to normal and tangential contacts with arbitrary
contact interaction (Pohrt and Li, 2014), to viscoelastic bodies
(Carbone and Putignano, 2013; Kusche, 2016) and adhesive
(Popov et al., 2017; Rey et al., 2017) contacts. This method
recently became the standard method of numerical simulation
of tribological contacts both in academic and industrial
research and development and changed significantly the ways
of thinking and the direction of further development of
tribology. While around 2010 high resolution simulations
of contact of rough surfaces were available to only a few
leading groups worldwide, now they can be carried out in
practically every tribological group, the corresponding programs
are even provided for on-line simulations (Tribology Simulator,
2018).
Progress in Didactics of Contact
Mechanics Since Hertz
The second development is more of didactical nature. It does
not contribute much to the results obtained in 136 years since
the seminal work of Hertz (1882) but merely presents them in
a form accessible even to undergraduate students. This didactic
invention is the Method of Dimensionality Reduction (MDR)
(Popov and Heß, 2015) which can be considered a reformulation
of the solution method for contact of axi-symmetrical bodies
first developed by Schubert (1942). In the literature, Schubert’s
method is mostly associated with the name of Sneddon, due
to the Sneddon’s highly cited paper (Sneddon, 1965). In reality,
the method was suggested not only by Schubert but (later)
also by Green and Zerna (1954),Collins (1959), and Galin
(1961) but it took decades until it became well-known and
“established” and Sneddon indeed did much for advertising this
solution, including the translation and publication of the book of
Galin.
The MDR, according to Barber (2018), is basically a
reinterpretation of the equations of Schubert-Galin-Sneddon
using a simple contact with a one-dimensional elastic foundation.
MDR summarizes the known solutions and presents them
in a simply reproducible mnemonic form. The true added
value of the MDR becomes visible only when considering
more general problems. Due to theorems allowing for (exact
or approximate) reduction of tangential contact problems
(Cattaneo, 1938; Mindlin, 1949; Jäger, 1995; Ciavarella, 1998),
viscoelastic contact problems (Radok, 1957) and adhesive
contact problems (Johnson et al., 1971) to non-adhesive normal
contact, the MDR becomes a very compact, universal and
intuitive tool for understanding and analyzing a great variety
of contact problems. As a matter of fact, it provides a sort
of “pocket edition” of all solutions in contact mechanics of
point contacts obtained by researchers in the last 136 years.
This didactic tool requires only the basics of analysis for its
application and thus makes contact mechanics available to
a broad engineering community. Barber notes that MDR is
comparable with the moment-area method for the solution of
beam deflection problems in the mechanics of materials. Both
have restricted fields of applicability—but wide enough to be
worth studying by engineers; both are simple and instructive.
All major problems of the mechanics of connections—such
as normal and tangential contact, stresses at the surface and
inside the material, viscoelastic contacts, adhesion, wear and
fretting, influence of shape, and material gradients (Heß,
2016) on adhesive strength and wear as well as damping
in oscillating contacts—this complete spectrum of essential
contact problems can be analyzed with MDR without using
complicated mathematical tools. However, integrating contact
mechanics in the basic engineering courses remains a great
challenge.
A GRAND CHALLENGE IN RESEARCH OF
FRICTION: “THIRD BODY”
Surfaces have essentially different properties compared with the
bulk of materials, and tribological loading massively changes
the properties of surface layers. The interface properties of
tribological contacts may be influenced by the composition of the
atmosphere, humidity, presence of lubricants, adsorbed layers,
and wear debris. The intermediate space of and around the
interface essentially determines the tribological properties and
is called “third body” (Godet, 1990). To exaggerate somewhat,
understanding friction means understanding the third body.
The influence of the third body in a broad sense has been
demonstrated on all scales. Thus, one of the great discoveries
of nanotribology was structural superlubricity in the contact
of well-prepared atomically smooth surfaces (Dienwiebel et al.,
2004). However, the presence of flakes of lamellar solids that
can freely rotate completely destroys the effect of superlubricity
(Filippov et al., 2008). A similar effect can be due also to other
impurities in the interface, even of single atoms (Müser et al.,
2001). Under other conditions, interfacial processes are needed to
achieve the state of low friction (Li et al., 2011). Intermixing and
surface modification are also essential in classical macroscopic
tribology, such as in combustion engines, where the formation
of a chemically modified surface layer was shown to be the key
for understanding tribological properties (Scherge et al., 2003).
Even in systems with hard coatings, where, at the first glance,
the essential role should be played by material properties, in
reality it is the surface modification of these properties which
does matter (Pastewka et al., 2010). The same is valid on the
mesoscale: surface changes lead to time dependent kinetics of
tribological properties (Ostermeyer, 2003). Contact mechanics
of rough surfaces made enormous progress in recent years,
but its necessary input, the surface topography, doesn’t remain
static in the course of a tribological process. Thus, one of the
most valuable and effective modern tools of looking into the
interface—the FFT-based BEM helps understanding the given
configuration of the surfaces but does not help understanding its
changes as it cannot describe inelastic behavior and is not capable
of describing such highly non-linear processes as formation of
wear debris and material intermixing. Finding new concepts for
Frontiers in Mechanical Engineering | www.frontiersin.org 3November 2018 | Volume 4 | Article 16
Popov Is Tribology Approaching Its Golden Age?
characterizing and understanding the third body is therefore an
urgent need of tribology and one of its great challenges.
We hope that now is the right time to approach this
“problem of the third body.” On the empirical level it could be
a combination of non-equilibrium thermodynamics of surface
layers, similar to the framework used in Bryant et al. (2008) and
kinetics of formation and wear of the surface layers similar to
the works of Ostermeyer and Müller (2006). For example, it is
generally recognized that in lubricated contacts the wear process
is controlled by formation and wearing out of the boundary
lubrication layer build trough mechanochemical reactions of
additives with the surfaces. The wear process of this boundary
layer could be described in the general framework suggested
in 1958 by Rabinowicz (1995) and confirmed by direct quasi-
molecular simulations in Aghababaei et al. (2016). This concept
is a generic and robust approach as it basically says that
the wear particles can appear if the stored elastic energy is
sufficient for their formation. The process of wear particle
initiation has to be completed by mechanics of wear debris in
the gap between two bodies and the transport of wear particles.
The latter could be described using a macroscopic empirical
framework similar to Schargott (2009). The reverse process of
the layer deposition can be described using the classical concept
of mechanically activated thermal processes (Spikes, 2018) which
was validated experimentally also for the particular process of
additive deposition (Gosvami et al., 2015). Detailed discussion
of the current state of tribology and its topical problems can be
found in a collaborative analysis (Vakis et al., 2018). The above
suggestions are of course only my personal attempt to predict the
future development of understanding of the third body.
GOLDEN AGE OF TRIBOLOGY
Classical tribology covering such applications as ball bearings,
gear drives, clutches, brakes, etc. was developed in the context
of mechanical engineering. But now contact mechanics and
tribology expand to qualitatively new fields of applications,
which are at the forefront of the global development trends of
technology and society, in particular micro- and nanotechnology
(Bhushan, 2017) as well as biology (Gorb, 2009) and medicine
(Willert et al., 2005; Paterson, 2007; Li et al., 2008). At
the same time, tribology developed experimental methods,
theoretical concepts, and numerical tools allowing effectively
mastering the seemingly complicated physics and mechanics of
interconnections. After intensive and controversial discussions,
recently, several attempts have been undertaken to achieve
consensus on the present state and available tools of tribology
(Müser et al., 2017; Vakis et al., 2018). These attempts and the
rapid expansion into new research areas such as nano-technology
and life sciences give hope that the coming years will be a true
golden age of tribology.
AUTHOR CONTRIBUTIONS
The author confirms being the sole contributor of this work and
has approved it for publication.
ACKNOWLEDGMENTS
I am deeply grateful to the reviewer, Peter J. Blau, for constructive
criticism and many valuable suggestions.
REFERENCES
Aghababaei, R., Warner, D. H., and Molinari, J.-F. (2016). Critical length
scale controls adhesive wear mechanisms. Nat. Commun. 7:11816.
doi: 10.1038/ncomms11816
Amontons, G. (1699). De la resistance cause’e dans les machines (About resistance
and force in machines). Mem l’Acedemie R: 257–282.
Barber, J. R. (2018). Contact Mechanics.Solid Mechanics and Its Applications.
Springer.
Bhushan, B. (Ed.) (2017). Nanotribology and Nanomechanics. Heidelberg: Springer
International.
Bhushan, B., Israelachvili, J. N., and Landman, U. (1995). Nanotribology:
friction, wear and lubrication at the atomic scale. Nature 374, 607–616.
doi: 10.1038/374607a0
Bourgery, J. M. (2017). Jean Marc Bourgery. Atlas of Human Anatomy and Surgery,
12th Edition. Cologne: Taschen.
Bryant, M., Khonsari, M., and Ling, F. (2008). On the thermodynamics of
degradation. Proc. R. Soc. 464, 2001–2014. doi: 10.1098/rspa.2007.0371
Carbone, G., and Putignano, C. (2013). A novel methodology to predict sliding and
rolling friction of viscoelastic materials: theory and experiments. J. Mech. Phys.
Solids 61, 1822–1834. doi: 10.1016/j.jmps.2013.03.005
Carpick, R. W., and Bennewitz, R. (2014). Let it slip. Nat. Phys. 10, 410–411.
doi: 10.1038/nphys2985
Cattaneo, C. (1938). Sul Contatto di Due Corpi Elastici: Distribuzione Locale Degli
Sforzi. Rendiconti dell’Accademia nazionale dei Lincei. 27, 342-348, 434-436,
474–478.
Ciavarella, M. (1998). The generalized Cattaneo partial slip plane
contact problem. I—Theory. Int. J. Solids Struct. 35, 2349–2362.
doi: 10.1016/s0020-7683(97)00154-6
Ciavarella, M., Demelio, G., and Hills, D. A. (1999). “The use of almost complete
contacts for fretting fatigue tests,” in Fatigue and Fracture Mechanics: 29th
Volume. eds T. L. Panontin and S. D. Sheppard (West Conshohocken, PA:
American Society for Testing and Materials), 696–709.
Collins, W. D. (1959). On the solution of some axisymmetric boundary value
problems by means of integral equations, II: further problems for a circular
disc and a spherical cap. Mathematika 6:120. doi: 10.1112/s0025579300002023
Coulomb, C. A. (1821). Theorie des Machines Simple (Theory of Simple Machines).
Paris: Bachelier.
Dienwiebel, M., Verhoeven, G. S., Pradeep, N., Frenken, J. W. M., Heimberg, J.
A., and Zandbergen, H. W. (2004). Superlubricity of Graphite. Phys. Rev. Lett.
92:126101. doi: 10.1103/physrevlett.92.126101
Dieterich, J. H., and Kilgore, B. D. (1994). Direct observation of frictional contacts:
new insights for state-dependent properties. Pure Appl. Geophys. 143, 283–302.
doi: 10.1007/bf00874332
Donnet, C., and Erdemir, A. (Eds.) (2008). Tribology of Diamond-Like Carbon
Films. New York, NY: Springer.
Dowson, D. (1979). History of Tribology. New York, NY: Longman Limited.
Dudko, O. K., Filippov, A. E., Klafter, J., and Urbakh, M. (2003). Beyond the
conventional description of dynamic force spectroscopy of adhesion bonds.
Proc. Natl. Acad. Sci. U.S.A. 100, 11378–11381. doi: 10.1073/pnas.15345
54100
Ertel, A. M. (1939). Hydrodynamic lubrication based on new principles. Akad.
Nauk. SSSR, Prikladnaya Matematika i Mekhanika 3, 41–52
Etsion, I. (2013). Modeling of surface texturing in hydrodynamic lubrication.
Friction 1, 195–209. doi: 10.1007/s40544-013-0018-y
Filippov, A. E., Dienwiebel, M., Frenken, J. W. M., Klafter, J., and Urbakh, M.
(2008). Torque and Twist against Superlubricity. Phys. Rev. Lett. 100:046102.
doi: 10.1103/physrevlett.100.046102
Frontiers in Mechanical Engineering | www.frontiersin.org 4November 2018 | Volume 4 | Article 16
Popov Is Tribology Approaching Its Golden Age?
Galin, L. A. (1961). Contact Problems in the Theory of Elasticity. Raleigh, NC: North
Carolina State College.
Godet, M. (1990). Third-bodies in tribology. Wear 136, 29–45.
doi: 10.1016/0043-1648(90)90070-q
Gorb, S. N. (Ed.) (2009). Functional Surfaces in Biology. Springer.
Gosvami, N. N., Bares, J. A., Mangolini, F., Konicek, A. R., Yablon, D.
G., and Carpick, R. W. (2015). Mechanisms of antiwear tribofilm growth
revealed in situ by single-asperity sliding contacts. Science 348, 102–106.
doi: 10.1126/science.1258788
Green, A. E., and Zerna, W. (1954). Theoretical Elasticity. Oxford: Clarendon Press.
Hamrock, B. J., and Dowson, D. (1977). Isothermal elastohydrodynamic
lubrication of point contacts: part iii—fully flooded results. J. Lubric. Tech. 99,
264. doi: 10.1115/1.3453074
Hamrock, B. J., and Dowson, D. (1981). Ball Bearing Lubrication. New York, NY:
Wiley & Sons.
He, G., Müser, M. H., and Robbins, M. O. (1999). Adsorbed layers and the origin
of static friction. Science 284, 1650–1652.
Hertz, H. (1882). Über die Berührung fester elastischer Körper. Journal für die reine
und angewandte Mathematik 92, 156–171. doi: 10.1515/crll.1882.92.156
Heß, M. (2016). A simple method for solving adhesive and non-adhesive
axisymmetric contact problems of elastically graded materials. Int. J. Eng. Sci.
104, 20–33. doi: 10.1016/j.ijengsci.2016.04.009
Holmberg, K., and Erdemir, A. (2017). Influence of tribology on global
energy consumption, costs and emissions. Friction 5, 263–284.
doi: 10.1007/s40544-017-0183-5
Jäger, J. (1995). Axi-symmetric bodies of equal material in contact under torsion or
shift. Arch. Appl. Mech. 65, 478–487. doi: 10.1007/s004190050033
Jin, Z., and Dowson, D. (2013). Bio-friction. Friction 1, 100–113.
doi: 10.1007/s40544-013-0004-4
Johnson, K. L., Kendall, K., and Roberts, A. D. (1971). Surface energy and the
contact of elastic solids. Proc. R. Soc. 324, 301–313. doi: 10.1098/rspa.1971.
0141
Jost, H. P. (Ed.) (1966). Lubrication (Tribology) – A Report on the Present Position
and Industry’s Needs. Department of Education and Science, HM. Stationary
Office, London.
Kado, N., Tadokoro, C., and Nakano, K. (2014). Kinetic friction coefficient
measured in tribotesting: influence of frictional vibration. Tribology Online 9,
63–70. doi: 10.2474/trol.9.63
Kenausis, G. L., Vörös, J., Elbert, D. L., Huang, N., Hofer, R., Ruiz-Taylor, L., et al.
(2000). Poly(l-lysine)-g-Poly(ethylene glycol) layers on metal oxide surfaces:
attachment mechanism and effects of polymer architecture on resistance
to protein adsorption. J. Phys. Chem. B 104, 3298–3309. doi: 10.1021/jp99
3359m
Khadem, M., Penkov, O. V., Yang, H.-K., and Kim, D.-E.
(2017). Tribology of multilayer coatings for wear reduction:
a review. Friction 5, 248–262. doi: 10.1007/s40544-017-
0181-7
Kusche, S. (2016). Frictional force between a rotationally symmetric indenter
and a viscoelastic half-space. ZAMM 97, 226–239. doi: 10.1002/zamm.2015
00169
Leibnitz, G. W. (1674-1676). Infinitesimalmathematik, Internetausgabe: Available
online at: http://www.gwlb.de/Leibniz/Leibnizarchiv/Veroeffentlichungen/
VII5A.pdf; http://www.gwlb.de/Leibniz/Leibnizarchiv/Veroeffentlichungen/
VII5B.pdf
Li, J., Zhang, C., and Luo, J. (2011). Superlubricity behavior with phosphoric
acid–water network induced by rubbing. Langmuir 27, 9413–9417.
doi: 10.1021/la201535x
Li, Q. S., Lee, G. Y. H., Ong, C. N., and Lim, C. T. (2008). AFM indentation
study of breast cancer cells. Biochem. Biophys. Res. Commun. 374, 609–613.
doi: 10.1016/j.bbrc.2008.07.078
Milahin, N. (2016). Robuste Einflussparameter für Reibung und
Oberflächenmodifizierung unter Einfluss von Ultraschall. Ph.D. thesis.
Technische Universität Berlin.
Mindlin, R. D. (1949). Compliance of elastic bodies in contact. J. Appl. Mech. 16,
259–268.
Müser, M. H., Dapp, W. B., Bugnicourt, R., Sainsot, P., Lesaffre, N., Lubrecht, T.
A., et al. (2017). Meeting the contact-mechanics challenge. Tribol. Lett. 65:4.
doi: 10.1007/s11249-017-0900-2
Müser, M. H., Wenning, L., and Robbins, M. O. (2001). Simple microscopic
theory of amontons’s laws for static friction. Phys. Rev. Lett. 86, 1295–1298.
doi: 10.1103/PhysRevLett.86.1295
Ostermeyer, G. (2003). On the dynamics of the friction coefficient. Wear 254,
852–858. doi: 10.1016/s0043-1648(03)00235-7
Ostermeyer, G. P., and Müller, M. (2006). Dynamic interaction of friction
and surface topography in brake systems. Tribology Int. 39, 370–380.
doi: 10.1016/j.triboint.2005.04.018
Pastewka, L., Moser, S., Gumbsch, P., and Moseler, M. (2010). Anisotropic
mechanical amorphization drives wear in diamond. Nat. Mater. 10, 34–38.
doi: 10.1038/nmat2902
Paterson, M. (2007). The Senses of Touch : Haptics, Affects and Technologies.
Oxford: Berg.
Persson, B. N. J., and Popov, V. L. (2000). On the origin of the
transition from slip to stick. Solid State Commun. 114, 261–266.
doi: 10.1016/s0038-1098(00)00045-4
Persson, B. N. J., and Tosatti, E. (Eds.) (1996). Physics of Sliding Friction.
Heidelberg: Springer.
Pohrt, R., and Li, Q. (2014). Complete boundary element formulation for
normal and tangential contact problems. Phys. Mesomechan. 17, 334–340.
doi: 10.1134/s1029959914040109
Popov, V. L., and Heß, M. (2015). Method of Dimensionality Reduction in Contact
Mechanics and Friction. Berlin: Springer.
Popov, V. L., Pohrt, R., and Li, Q. (2017). Strength of adhesive contacts:
influence of contact geometry and material gradients. Friction 5, 308–325.
doi: 10.1007/s40544-017-0177-3
Popova, E., and Popov, V. L. (2015). The research works of Coulomb
and Amontons and generalized laws of friction. Friction 3, 183–190.
doi: 10.1007/s40544-015-0074-6
Putignano, C., Afferrante, L., Carbone, G., and Demelio, G. (2012). A new efficient
numerical method for contact mechanics of rough surfaces. Int. J. Solids Struct.
49, 338–343. doi: 10.1016/j.ijsolstr.2011.10.009
Rabinowicz, E. (1961). Influence of surface energy on friction and wear
phenomena. J. Appl. Phys. 32, 1440–1444. doi: 10.1063/1.1728375
Rabinowicz, E. (1995). Friction and Wear of Materials. Second Edition. New York,
NY: John Wiley & Sons, Inc.
Radok, J. R. M. (1957). Viscoelastic stress analysis, Quart. Appl. Math 15, 198–202.
Rey, V., Anciaux, G., and Molinari, J.-F. (2017). Normal adhesive contact on rough
surfaces: efficient algorithm for FFT-based BEM, resolution. Comput Mech. 60,
69–81. doi: 10.1007/s00466-017-1392-5
Rice, J. R., and Ruina, A. L. (1983). Stability of steady frictional slipping. J. Appl.
Mech. 50:343. doi: 10.1115/1.3167042
Robbins, M. O., and Krim, J. (1998). Energy dissipation in
interfacial friction. MRS Bull. 23, 23–26. doi: 10.1557/s088376940
003058x
Savio, D., Pastewka, L., and Gumbsch, P. (2016). Boundary lubrication of
heterogeneous surfaces and the onset of cavitation in frictional contacts. Sci.
Adv. 2:e1501585. doi: 10.1126/sciadv.1501585
Schargott, M. (2009). A multi-scale approach for dynamical simulations of the
surface topography in high-pressure frictional contacts: bridging simulation
scales. Tribol. Lett. 39, 9–17. doi: 10.1007/s11249-009-9500-0
Scherge, M., Shakhvorostov, D., and Pöhlmann, K. (2003). Fundamental wear
mechanism of metals. Wear 255, 395–400. doi: 10.1016/s0043-1648(03)00273-4
Scholz, C. H. (2002). The Mechanics of Eathquakes and Faulting, Second Edition.
Cambridge: Cambridge University Press.
Schubert, G. (1942). Zur Frage der Druckverteilung unter elastisch gelagerten
Tragwerken. Ingenieur-Archiv. 13, 132–147. doi: 10.1007/bf02095912
Sneddon, I. N. (1965). The relation between load and penetration in the
axisymmetric boussinesq problem for a punch of arbitrary profile. Int. J. Eng.
Sci. 3, 47–57. doi: 10.1016/0020-7225(65)90019-4
Spikes, H. (2004). The history and mechanisms of ZDDP. Tribol. Lett. 17, 469–489.
doi: 10.1023/b:tril.0000044495.26882.b5
Spikes, H. (2018). Stress-augmented thermal activation: tribology feels the force.
Friction 6, 1–31. doi: 10.1007/s40544-018-0201-2
Teidelt, E. (2015). Oscillating Contacts: Friction Induced Motion and Control of
Friction. PhD thesis, Technische Universität Berlin.
Tribology Simulator (2018). Available online at: http://www.tribonet.org/
cmdownloads/tribology-simulator/
Frontiers in Mechanical Engineering | www.frontiersin.org 5November 2018 | Volume 4 | Article 16
Popov Is Tribology Approaching Its Golden Age?
Vakis, A. I., Yastrebov, V. A., Scheibert, J., Nicola, L., Dini, D., Minfray,
C., et al. (2018). Modeling and simulation in tribology across scales:
an overview. Tribol. Int. 125, 169–199. doi: 10.1016/j.triboint.2018.
02.005
Wetter, R. (2016). The Interplay of System Dynamics and Dry Friction: Shakedown,
Ratcheting and Micro-Walking. Ph.D. thesis, Technische Universität Berlin.
Willert, H.-G., Buchhorn, G. H., Fayyazi, A., Flury, R., Windler, M., Köster,
G., et al. (2005). Metal-on-metal bearings and hypersensitivity in patients
with artificial hip joints. J. Bone Joint Surg. 87, 28–36. doi: 10.2106/
jbjs.a.02039pp
Conflict of Interest Statement: The author declares that the research was
conducted in the absence of any commercial or financial relationships that could
be construed as a potential conflict of interest.
Copyright © 2018 Popov. This is an open-access article distributed under the terms
of the Creative Commons Attribution License (CC BY). The use, distribution or
reproduction in other forums is permitted, provided the original author(s) and the
copyright owner(s) are credited and that the original publication in this journal
is cited, in accordance with accepted academic practice. No use, distribution or
reproduction is permitted which does not comply with these terms.
Frontiers in Mechanical Engineering | www.frontiersin.org 6November 2018 | Volume 4 | Article 16
