Abstract

In this study, the electrostatic adhesive contact between a smooth indenter with a power-law geometry and an elastic half-space is studied using both a theoretical and numerical approach. Both the indenter and substrate are coated with an electrically insulating layer. The Maxwell stress and hard-wall constraint are applied to describe the interaction between the indenter and elastic counter face. By assuming electrostatic adhesion as a long-range interaction, we derived a theoretical relation between external load and contact radius. We show that the theoretical and numerical results are plausible when the Tabor parameter is small. However, when the Tabor parameter is large, the numerical results get closer to the Johnson–Kendall–Roberts (JKR) limit. The generalized Tabor parameter, which depends on the applied voltage and indenter shape, has been derived by following the technique of dimensional analysis.

References

1.
Johnsen
,
A.
, and
Rahbek
,
K.
,
1923
, “
A Physical Phenomenon and Its Applications to Telegraphy, Telephony, Etc
,”
J. Inst. Electr. Eng.
,
61
(
320
), pp.
713
725
.
2.
Ayyildiz
,
M.
,
Scaraggi
,
M.
,
Sirin
,
O.
,
Basdogan
,
C.
, and
Persson
,
B. N. J.
,
2018
, “
Contact Mechanics Between the Human Finger and a Touchscreen Under Electroadhesion
,”
Proc. Natl. Acad. Sci. U. S. A.
,
115
(
50
), pp.
12668
12673
.
3.
Chen
,
R.
,
Liu
,
F.
,
Wang
,
H.
,
Zhu
,
X.
,
Tao
,
X.
,
Zhang
,
S.
, and
Jiang
,
G.
,
2022
, “
Theoretical and Experimental Analyses of the Dynamic Electroadhesion Force
,”
Extreme Mech. Lett.
,
56
, p.
101892
.
4.
Rajagopalan
,
P.
,
Muthu
,
M.
,
Liu
,
Y.
,
Luo
,
J.
,
Wang
,
X.
, and
Wan
,
C.
,
2022
, “
Advancement of Electroadhesion Technology for Intelligent and Self-Reliant Robotic Applications
,”
Adv. Intell. Syst.
,
4
(
7
), p.
2200064
.
5.
AliAbbasi
,
E.
,
Sormoli
,
M. A.
, and
Basdogan
,
C.
,
2022
, “
Frequency-Dependent Behavior of Electrostatic Forces Between Human Finger and Touch Screen Under Electroadhesion
,”
IEEE Trans. Hapt.
,
15
(
2
), pp.
416
428
.
6.
Huang
,
G.-Y.
, and
Yan
,
J.-F.
,
2017
, “
A Mechanical Model for the Adhesive Contact With Local Sliding Induced by a Tangential Force
,”
Acta Mech. Solida Sin.
,
30
(
4
), pp.
369
373
.
7.
Yan
,
J.-F.
, and
Huang
,
G.-Y.
,
2019
, “
A Double-Hertz Model for Adhesive Contact Between Cylinders Under Inclined Forces
,”
Proc. R. Soc. A: Math., Phys. Eng. Sci.
,
475
(
2221
), p.
20180589
.
8.
Hui
,
C.-Y.
,
Liu
,
T.
,
Salez
,
T.
,
Raphael
,
E.
, and
Jagota
,
A.
,
2015
, “
Indentation of a Rigid Sphere Into an Elastic Substrate With Surface Tension and Adhesion
,”
Proc. R. Soc. A: Math., Phys. Eng. Sci.
,
471
(
2175
), p.
20140727
.
9.
Wang
,
A.
, and
Müser
,
M. H.
,
2022
, “
On the Adhesion Between Thin Sheets and Randomly Rough Surfaces
,”
Front. Mech. Eng.
,
8
, p.
965584
.
10.
Zhu
,
Y.
,
Zheng
,
Z.
,
Zhang
,
Y.
,
Wu
,
H.
, and
Yu
,
J.
,
2021
, “
Adhesion of Elastic Wavy Surfaces: Interface Strengthening/Weakening and Mode Transition Mechanisms
,”
J. Mech. Phys. Solids.
,
151
, p.
104402
.
11.
Xu
,
Y.
,
Scheibert
,
J.
,
Gadegaard
,
N.
, and
Mulvihill
,
D. M.
,
2022
, “
An Asperity-Based Statistical Model for the Adhesive Friction of Elastic Nominally Flat Rough Contact Interfaces
,”
J. Mech. Phys. Solids.
,
164
, p.
104878
.
12.
Persson
,
B. N. J.
,
2018
, “
The Dependency of Adhesion and Friction on Electrostatic Attraction
,”
J. Chem. Phys.
,
148
(
14
), p.
144701
.
13.
Persson
,
B. N. J.
,
2021
, “
General Theory of Electroadhesion
,”
J. Phys.: Condens. Matter.
,
33
(
43
), p.
435001
.
14.
Sirin
,
O.
,
Ayyildiz
,
M.
,
Persson
,
B. N. J.
, and
Basdogan
,
C.
,
2019
, “
Electroadhesion With Application to Touchscreens
,”
Soft Matter
,
15
(
8
), pp.
1758
1775
.
15.
Ciavarella
,
M.
, and
Papangelo
,
A.
,
2020
, “
A Simplified Theory of Electroadhesion for Rough Interfaces
,”
Front. Mech. Eng.
,
6
, p.
27
.
16.
Derjaguin
,
B.
,
Muller
,
V.
, and
Toporov
,
Y.
,
1975
, “
Effect of Contact Deformations on the Adhesion of Particles
,”
J. Colloid. Interface. Sci.
,
53
(
2
), pp.
314
326
.
17.
Papangelo
,
A.
,
Lovino
,
R.
, and
Ciavarella
,
M.
,
2020
, “
Electroadhesive Sphere-Flat Contact Problem: A Comparison Between DMT and Full Iterative Finite Element Solutions
,”
Tribol. Int.
,
152
, p.
106542
.
18.
Argatov
,
I. I.
, and
Borodich
,
F. M.
,
2020
, “
A Macro Model for Electroadhesive Contact of a Soft Finger With a Touchscreen
,”
IEEE Trans. Hapt.
,
13
(
3
), pp.
504
510
.
19.
Johnson
,
K. L.
,
Kendall
,
K.
, and
Roberts
,
A.
,
1971
, “
Surface Energy and the Contact of Elastic Solids
,”
Proc. R. Soc. Lond. A. Math. Phys. Sci.
,
324
(
1558
), pp.
301
313
.
20.
Heß
,
M.
, and
Popov
,
V. L.
,
2019
, “
Voltage-Induced Friction With Application to Electrovibration
,”
Lubricants
,
7
(
12
), p.
102
.
21.
Menga
,
N.
,
Afferrante
,
L.
, and
Carbone
,
G.
,
2016
, “
Effect of Thickness and Boundary Conditions on the Behavior of Viscoelastic Layers in Sliding Contact With Wavy Profiles
,”
J. Mech. Phys. Solids.
,
95
, pp.
517
529
.
22.
Menga
,
N.
,
Afferrante
,
L.
, and
Carbone
,
G.
,
2016
, “
Adhesive and Adhesiveless Contact Mechanics of Elastic Layers on Slightly Wavy Rigid Substrates
,”
Int. J. Solids. Struct.
,
88–89
, pp.
101
109
.
23.
Carbone
,
G.
,
Mangialardi
,
L.
, and
Persson
,
B. N. J.
,
2004
, “
Adhesion Between a Thin Elastic Plate and a Hard Randomly Rough Substrate
,”
Phys. Rev. B
,
70
(
12
), p.
125407
.
24.
Jin
,
F.
,
Yan
,
S.
,
Guo
,
X.
, and
Wang
,
X.
,
2019
, “
On the Contact and Adhesion of a Piezoelectric Half-Space Under a Rigid Punch With an Axisymmetric Power-Law Profile
,”
Mech. Mater.
,
129
, pp.
189
197
.
25.
Zhou
,
Y.
, and
Yang
,
J.
,
2022
, “
How Thickness Affects the Area–Pressure Relation in Line Contacts
,”
Tribol. Lett.
,
70
(
4
), p.
104
.
26.
Müser
,
M. H.
,
2017
, “
On the Linearity of Contact Area and Reduced Pressure
,”
Tribol. Lett.
,
65
(
4
), p.
129
.
27.
Zhou
,
Y.
, and
Müser
,
M. H.
,
2020
, “
Effect of Structural Parameters on the Relative Contact Area for Ideal, Anisotropic, and Correlated Random Roughness
,”
Front. Mech. Eng.
,
6
, p.
59
.
28.
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
(
1
), pp.
47
57
.
29.
Campañá
,
C.
, and
Müser
,
M. H.
,
2006
, “
Practical Green’s Function Approach to the Simulation of Elastic Semi-Infinite Solids
,”
Phys. Rev. B
,
74
(
7
), p.
075420
.
30.
Dapp
,
W. B.
,
Lücke
,
A.
,
Persson
,
B. N. J.
, and
Müser
,
M. H.
,
2012
, “
Self-Affine Elastic Contacts: Percolation and Leakage
,”
Phys. Rev. Lett.
,
108
(
24
), p.
244301
.
31.
Karpov
,
E. G.
,
Wagner
,
G. J.
, and
Liu
,
W. K.
,
2005
, “
A Green’s Function Approach to Deriving Non-reflecting Boundary Conditions in Molecular Dynamics Simulations
,”
Int. J. Numerical Methods Eng.
,
62
(
9
), pp.
1250
1262
.
32.
Venugopalan
,
S. P.
,
Nicola
,
L.
, and
Müser
,
M. H.
,
2017
, “
Green’s Function Molecular Dynamics: Including Finite Heights, Shear, and Body Fields
,”
Modell. Simul. Mater. Sci. Eng.
,
25
(
3
), p.
034001
.
33.
Bitzek
,
E.
,
Koskinen
,
P.
,
Gähler
,
F.
,
Moseler
,
M.
, and
Gumbsch
,
P.
,
2006
, “
Structural Relaxation Made Simple
,”
Phys. Rev. Lett.
,
97
(
17
), p.
170201
.
34.
Zhou
,
Y.
,
Moseler
,
M.
, and
Müser
,
M. H.
,
2019
, “
Solution of Boundary-Element Problems Using the Fast-Inertial-Relaxation-Engine Method
,”
Phys. Rev. B
,
99
(
14
), p.
144103
.
35.
Borodich
,
F. M.
,
2014
, “
The Hertz-Type and Adhesive Contact Problems for Depth-Sensing Indentation
,”
Adv. Appl. Mech.
,
47
, pp.
225
366
.
36.
Galin
,
L. A.
,
1946
, “
Spatial Contact Problems of the Theory of Elasticity for Punches of Circular Shape in Planar Projection
,”
PMM J. Appl. Math. Mech.
,
10
, pp.
425
448
.
37.
Müser
,
M. H.
,
2014
, “
Single-Asperity Contact Mechanics With Positive and Negative Work of Adhesion: Influence of Finite-Range Interactions and a Continuum Description for the Squeeze-Out of Wetting Fluids
,”
Beilstein. J. Nanotechnol.
,
5
, pp.
419
437
.
38.
Zheng
,
Z.
, and
Yu
,
J.
,
2007
, “
Using the Dugdale Approximation to Match a Specific Interaction in the Adhesive Contact of Elastic Objects
,”
J. Colloid Interface Sci.
,
310
(
1
), pp.
27
34
.
39.
Wu
,
J. J.
,
2007
, “
Numerical Analysis on the Adhesive Contact Between a Rigid Power-Law Shaped Axisymmetric Aperity and an Elastic Half-Space
,”
J. Adhes. Sci. Technol.
,
36
(
2
), pp.
195
219
.
40.
Prodanov
,
N.
,
Dapp
,
W. B.
, and
Müser
,
M. H.
,
2013
, “
On the Contact Area and Mean Gap of Rough, Elastic Contacts: Dimensional Analysis, Numerical Corrections, and Reference Data
,”
Tribol. Lett.
,
53
(
2
), pp.
433
448
.
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