Understanding the mechanical properties of contacts at the nanoscale is key to controlling the strength of coated surfaces. In this work, we explore to which extent existing continuum models describing elastic contacts with coated surfaces can be extended to the nanoscale. Molecular dynamics (MD) simulations of hollow cylinders or coated rigid cylinders under compression are performed and compared with models at the continuum level, as two representative extreme cases of coating which is substantially harder or softer than the substrate, respectively. We show here that the geometry of the atomic-scale contact is essential to capture the contact stiffness, especially for hollow cylinders with high relative thicknesses and for coated rigid cylinders. The contact pressure profiles in atomic-scale contacts are substantially different than the one proposed in the continuum models for rounded contacts. On the basis of these results, we formulate models whose solution can be computed analytically for the contact stiffness in the two extreme cases, and show how to bridge between the atomic and continuum scales with atomically informed geometry of the contact.

References

References
1.
Popov
,
V. L.
,
2010
,
Contact Mechanics and Friction: Physical Principles and Applications
,
Springer
,
Berlin
.
2.
Gupta
,
B. K.
, and
Bhushan
,
B.
,
1995
, “
Mechanical and Tribological Properties of Hard Carbon Coatings for Magnetic Recording Heads
,”
Wear
,
190
(
1
), pp.
110
122
.
3.
Roy
,
R. K.
, and
Lee
,
K.-R.
,
2007
, “
Biomedical Applications of Diamond-Like Carbon Coatings: A Review
,”
J. Biomed. Mater. Res.
,
83B
(
1
), pp.
72
84
.
4.
Schintlmeister
,
W.
,
Wallgram
,
W.
,
Kanz
,
J.
, and
Gigl
,
K.
,
1984
, “
Cutting Tool Materials Coated by Chemical Vapour Deposition
,”
Wear
,
100
(
1–3
), pp.
153
169
.
5.
Johnson
,
K. L.
,
1985
,
Contact Mechanics
,
Cambridge University Press
,
Cambridge, UK
.
6.
Galin
,
L. A.
,
2008
,
Contact Problems
,
Springer
,
Dordrecht, The Netherlands
.
7.
Hertz
,
H.
,
1882
, “
Ueber die Berührung Fester Elastischer Körper
,”
J. Reine Angew. Math.
,
92
, pp.
156
171
.
8.
Liu
,
S.
,
Peyronnel
,
A.
,
Wang
,
Q. J.
, and
Keer
,
L. M.
,
2005
, “
An Extension of the Hertz Theory for 2D Coated Components
,”
Tribol. Lett.
,
18
(
4
), pp.
505
511
.
9.
Goltsberg
,
R.
, and
Etsion
,
I.
,
2015
, “
A Universal Model for the Load–Displacement Relation in an Elastic Coated Spherical Contact
,”
Wear
,
322–323
, pp.
126
132
.
10.
Bhushan
,
B.
, ed.,
2010
,
Springer Handbook of Nanotechnology
,
Springer, Berlin
.
11.
Bhushan
,
B.
,
2007
, “
Nanotribology and Nanomechanics of MEMS/NEMS and BioMEMS/BioNEMS Materials and Devices
,”
Microelectron. Eng.
,
84
(
3
), pp.
387
412
.
12.
Greer
,
J. R.
, and
Nix
,
W. D.
,
2005
, “
Size Dependence of Mechanical Properties of Gold at the Sub-Micron Scale
,”
Appl. Phys. A
,
80
(
8
), pp.
1625
1629
.
13.
Mordehai
,
D.
,
Kazakevich
,
M.
,
Srolovitz
,
D. J.
, and
Rabkin
,
E.
,
2011
, “
Nanoindentation Size Effect in Single-Crystal Nanoparticles and Thin Films: A Comparative Experimental and Simulation Study
,”
Acta Mater.
,
59
(
6
), pp.
2309
2321
.
14.
Uchic
,
M. D.
,
Dimiduk
,
D. M.
,
Florando
,
J. N.
, and
Nix
,
W. D.
,
2004
, “
Sample Dimensions Influence Strength and Crystal Plasticity
,”
Science
,
305
(
5686
), pp.
986
989
.
15.
Montemayor
,
L. C.
, and
Greer
,
J. R.
,
2015
, “
Mechanical Response of Hollow Metallic Nanolattices: Combining Structural and Material Size Effects
,”
ASME J. Appl. Mech.
,
82
(
7
), p.
071012
.
16.
Yang
,
L.
,
Bian
,
J. J.
,
Zhang
,
H.
,
Niu
,
X. R.
, and
Wang
,
G. F.
,
2015
, “
Size-Dependent Deformation Mechanisms in Hollow Silicon Nanoparticles
,”
AIP Adv.
,
5
(
7
), p.
077162
.
17.
Luan
,
B.
, and
Robbins
,
M. O.
,
2005
, “
The Breakdown of Continuum Models for Mechanical Contacts
,”
Nature
,
435
(
7044
), pp.
929
932
.
18.
Luan
,
B.
, and
Robbins
,
M. O.
,
2006
, “
Contact of Single Asperities With Varying Adhesion: Comparing Continuum Mechanics to Atomistic Simulations
,”
Phys. Rev. E
,
74
(
2
), p.
026111
.
19.
Wang
,
G.
,
Bian
,
J.
,
Feng
,
J.
, and
Feng
,
X.
,
2015
, “
Compressive Behavior of Crystalline Nanoparticles With Atomic-Scale Surface Steps
,”
Mater. Res. Express
,
2
(
1
), p.
015006
.
20.
Ramisetti
,
S. B.
,
Anciaux
,
G.
, and
Molinari
,
J.-F.
,
2015
, “
MD/FE Multiscale Modeling of Contact
,”
Fundamentals of Friction and Wear on the Nanoscale
,
E.
Gnecco
, and
E.
Meyer
, eds.,
Springer
,
Berlin
, pp.
289
312
.
21.
Luan
,
B. Q.
,
Hyun
,
S.
,
Molinari
,
J. F.
,
Bernstein
,
N.
, and
Robbins
,
M. O.
,
2006
, “
Multiscale Modeling of Two-Dimensional Contacts
,”
Phys. Rev. E
,
74
(
4
), p.
046710
.
22.
Plimpton
,
S.
,
1995
, “
Fast Parallel Algorithms for Short-Range Molecular Dynamics
,”
J. Comput. Phys.
,
117
(
1
), pp.
1
19
.
23.
Mishin
,
Y.
,
2004
, “
Atomistic Modeling of the γ and γ′-Phases of the Ni–Al System
,”
Acta Mater.
,
52
(
6
), pp.
1451
1467
.
24.
Polak
,
E.
, and
Ribiere
,
G.
,
1969
, “
Note Sur la Convergence de Méthodes de Directions Conjuguées
,”
Rev. Fr. Inf. Rech. Opér.
,
3
(
1
), pp.
35
43
.
25.
Allen
,
M. P.
, and
Tildesley
,
D. J.
,
1989
,
Computer Simulation of Liquids
,
Clarendon Press
,
Oxford, UK
.
26.
Stukowski
,
A.
,
2010
, “
Visualization and Analysis of Atomistic Simulation Data With OVITO—The Open Visualization Tool
,”
Model. Simul. Mater. Sci. Eng.
,
18
(
1
), p.
015012
.
27.
Mordehai
,
D.
,
Lee
,
S.-W.
,
Backes
,
B.
,
Srolovitz
,
D. J.
,
Nix
,
W. D.
, and
Rabkin
,
E.
,
2011
, “
Size Effect in Compression of Single-Crystal Gold Microparticles
,”
Acta Mater.
,
59
(
13
), pp.
5202
5215
.
28.
Kositski
,
R.
, and
Mordehai
,
D.
,
2015
, “
Depinning-Controlled Plastic Deformation During Nanoindentation of BCC Iron Thin Films and Nanoparticles
,”
Acta Mater.
,
90
, pp.
370
379
.
29.
Gerberich
,
W. W.
,
Mook
,
W. M.
,
Chambers
,
M. D.
,
Cordill
,
M. J.
,
Perrey
,
C. R.
,
Carter
,
C. B.
,
Miller
,
R. E.
,
Curtin
,
W. A.
,
Mukherjee
,
R.
, and
Girshick
,
S. L.
,
2006
, “
An Energy Balance Criterion for Nanoindentation-Induced Single and Multiple Dislocation Events
,”
ASME J. Appl. Mech.
,
73
(
2
), pp.
327
334
.
30.
Li
,
L.
,
Lee
,
M.-G.
, and
Anderson
,
P. M.
,
2012
, “
Probing the Relation Between Dislocation Substructure and Indentation Characteristics Using Quantized Crystal Plasticity
,”
ASME J. Appl. Mech.
,
79
(
3
), p.
031009
.
31.
Bower
,
A. F.
,
2010
,
Applied Mechanics of Solids
, CRC Press, Boca Raton, FL.
32.
Thompson
,
A. P.
,
Plimpton
,
S. J.
, and
Mattson
,
W.
,
2009
, “
General Formulation of Pressure and Stress Tensor for Arbitrary Many-Body Interaction Potentials Under Periodic Boundary Conditions
,”
J. Chem. Phys.
,
131
(
15
), p.
154107
.
33.
Voronoi
,
G.
,
1908
, “
Nouvelles Applications des Paramètres Continus à la Théorie des Formes Quadratiques
,”
J. Reine Angew. Math.
,
133
, pp.
97
102
.
34.
Admal
,
N. C.
, and
Tadmor
,
E. B.
,
2010
, “
A Unified Interpretation of Stress in Molecular Systems
,”
J. Elast.
,
100
(
1–2
), pp.
63
143
.
35.
Olsson
,
P. A. T.
, and
Park
,
H. S.
,
2012
, “
On the Importance of Surface Elastic Contributions to the Flexural Rigidity of Nanowires
,”
J. Mech. Phys. Solids
,
60
(
12
), pp.
2064
2083
.
36.
Tadmor
,
E. B.
,
Ortiz
,
M.
, and
Phillips
,
R.
,
1996
, “
Quasicontinuum Analysis of Defects in Solids
,”
Philos. Mag. A
,
73
(
6
), pp.
1529
1563
.
37.
Tadmor
,
E. B.
,
Phillips
,
R.
, and
Ortiz
,
M.
,
1996
, “
Mixed Atomistic and Continuum Models of Deformation in Solids
,”
Langmuir
,
12
(
19
), pp.
4529
4534
.
38.
Mordehai
,
D.
,
Rabkin
,
E.
, and
Srolovitz
,
D. J.
,
2011
, “
Pseudoelastic Deformation During Nanoscale Adhesive Contact Formation
,”
Phys. Rev. Lett.
,
107
(
9
), p.
096101
.
39.
Seely
,
F. B.
, and
Smith
,
J. O.
,
1952
,
Advanced Mechanics of Materials
,
Wiley
,
New York
.
40.
Barber
,
J. R.
,
1990
, “
Contact Problems for the Thin Elastic Layer
,”
Int. J. Mech. Sci.
,
32
(
2
), pp.
129
132
.
You do not currently have access to this content.