This paper develops a statistically based computational method to rapidly determine stresses in flexible substrates during particle printing processes. Specifically, substrate stresses due to multiple surface particle contact sites are statistically computed by superposing point load solutions for different random particle realizations (sets of random loading sites) within a fixed feature boundary. The approach allows an analyst to rapidly determine the number of particles in a surface feature needed to produce repeatable substrate stresses, thus minimizing the deviation from feature to feature and ensuring consistent production. Three-dimensional examples are provided to illustrate the technique. The utility of the approach is that an analyst can efficiently ascertain the number of particles needed within a feature, without resorting to computationally intensive numerical procedures, such as the finite element method.

References

1.
Gamota
,
D.
,
Brazis
,
P.
,
Kalyanasundaram
,
K.
, and
Zhang
,
J.
,
2004
,
Printed Organic and Molecular Electronics
,
Kluwer Academic Publishers
,
New York
.10.1007/978-1-4419-9074-7
2.
Nakanishi
,
H.
,
Bishop
,
K. J. M.
,
Kowalczyk
,
B.
,
Nitzan
,
A.
,
Weiss
,
E. A.
,
Tretiakov
,
K. V.
,
Apodaca
,
M. M.
,
Klajn
,
R.
,
Stoddart
,
J. F.
, and
Grzybowski
,
B. A.
,
2009
, “
Photoconductance and Inverse Photoconductance in Thin Films of Functionalized Metal Nanoparticles
,”
Nature
,
460
, pp.
371
375
.10.1038/nature08131
3.
Fuller
,
S. B.
,
Wilhelm
,
E. J.
, and
Jacobson
,
J. M.
,
2002
, “
Ink-Jet Printed Nanoparticle Microelectromechanical Systems
,”
J. Microelectromech. Syst.
,
11
(
1
), pp.
54
60
.10.1109/84.982863
4.
Samarasinghe
,
S. R.
,
Pastoriza-Santos
,
I.
,
Edirisinghe
,
M. J.
,
Reece
,
M. J.
, and
Liz-Marzan
,
L. M.
,
2006
, “
Printing Gold Nanoparticles With an Electrohydrodynamic Direct Write Device
,”
Gold Bull.
,
39
(
2
), pp.
48
53
.10.1007/BF03215276
5.
Ahmad
,
Z.
,
Rasekh
,
M.
, and
Edirisinghe
,
M.
,
2010
, “
Electrohydrodynamic Direct Writing of Biomedical Polymers and Composites
,”
Macromol. Mater. Eng.
,
295
(
4
), pp.
315
319
.10.1002/mame.200900396
6.
Sirringhaus
,
H.
,
Kawase
,
T.
,
Friend
,
R. H.
,
Shimoda
,
T.
,
Inbasekaran
,
M.
,
Wu
,
W.
, and
Woo
,
E. P.
,
2000
, “
High-Resolution Inkjet Printing of All-Polymer Transistor Circuits
,”
Science
,
290
(
5499
), pp.
2123
2126
.10.1126/science.290.5499.2123
7.
Wang
,
J. Z.
,
Zheng
,
Z. H.
,
Li
,
H. W.
,
Huck
,
W. T. S.
, and
Sirringhaus
,
H.
,
2004
, “
Dewetting of Conducting Polymer Inkjet Droplets on Patterned Surfaces
,”
Nat. Mater.
,
3
, pp.
171
176
.10.1038/nmat1073
8.
Huang
,
D.
,
Liao
,
F.
,
Molesa
,
S.
,
Redinger
,
D.
, and
Subramanian
,
V.
,
2003
, “
Plastic-Compatible Low-Resistance Printable Gold Nanoparticle Conductors for Flexible Electronics
,”
J. Electrochem. Soc.
,
150
(
7
), pp.
G412
G417
.10.1149/1.1582466
9.
Choi
,
S.
,
Park
,
I.
,
Hao
,
Z.
,
Holman
,
H. Y.
,
Pisano
,
A. P.
, and
Zohdi
,
T. I.
,
2010
, “
Ultra-Fast Self-Assembly of Micro-Scale Particles by Open Channel Flow
,”
Langmuir
,
26
(
7
), pp.
4661
4667
.10.1021/la903492w
10.
Choi
,
S.
,
Stassi
,
S.
,
Pisano
,
A. P.
, and
Zohdi
,
T. I.
,
2010
, “
Coffee-Ring Effect-Based Three Dimensional Patterning of Micro, Nanoparticle Assembly With a Single Droplet
,”
Langmuir
,
26
(
14
), pp.
11690
11698
.10.1021/la101110t
11.
Choi
,
S.
,
Jamshidi
,
A.
,
Seok
,
T. J.
,
Zohdi
,
T. I.
,
Wu
,
M. C.
, and
Pisano
,
A. P.
,
2012
, “
Fast, High-Throughput Creation of Size-Tunable Micro, Nanoparticle Clusters Via Evaporative Self-Assembly in Picoliter-Scale Droplets of Particle Suspension
,”
Langmuir
,
28
(
6
), pp.
3102
3111
.10.1021/la204362s
12.
Choi
,
S.
,
Pisano
,
A. P.
, and
Zohdi
,
T. I.
,
2013
, “
An Analysis of Evaporative Self-Assembly of Micro Particles in Printed Picoliter Suspension Droplets
,”
J. Thin Solid Films
,
537
(
30
), pp.
180
189
.10.1016/j.tsf.2013.04.047
13.
Demko
,
M.
,
Choi
,
S.
,
Zohdi
,
T. I.
, and
Pisano
,
A. P.
,
2012
, “
High Resolution Patterning of Nanoparticles by Evaporative Self-Assembly Enabled by In-Situ Creation and Mechanical Lift-Off of a Polymer Template
,”
Appl. Phys. Lett.
,
99
(
25
), p.
253102
.10.1063/1.3671084
14.
Demko
,
M. T.
,
Cheng
,
J. C.
, and
Pisano
,
A. P.
,
2010
, “
High-Resolution Direct Patterning of Gold Nanoparticles by the Microfluidic Molding Process
,”
Langmuir
,
26
(
22
), pp.
16710
16714
.10.1021/la1022533
15.
Fathi
,
S.
,
Dickens
,
P.
,
Khodabakhshi
,
K.
, and
Gilbert
,
M.
,
2013
, “
Microcrystal Particles Behaviour in Inkjet Printing of Reactive Nylon Materials
,”
ASME J. Manuf. Sci. Eng.
,
135
(
1
), p.
011009
.10.1115/1.4023272
16.
Martin
,
P.
,
2009
,
Handbook of Deposition Technologies for Films and Coatings
, 3rd ed.,
Elsevier
,
Amsterdam, Netherlands
.
17.
Martin
,
P.
,
2011
, “
Introduction to Surface Engineering and Functionally Engineered Materials
,”
J. Vac. Sci. Technol.
,
A2
(
2
), p.
500
.10.1002/9781118171899
18.
Duran
,
J.
,
1997
,
Sands, Powders and Grains—An Introduction to the Physics of Granular Matter
,
Springer Verlag
,
Heidelberg, Germany
.
19.
Zohdi
,
T. I.
,
2003
, “
Genetic Design of Solids Possessing a Random-Particulate Microstructure
,”
Philos. Trans. R. Soc., A
,
361
(
1806
), pp.
1021
1043
.10.1098/rsta.2003.1179
20.
Zohdi
,
T. I.
,
2003
, “
On the compaction of Cohesive Hyperelastic Granules at Finite Strains
,”
Proc. R. Soc.
,
454
(
2034
), pp.
1395
1401
.10.1098/rspa.2003.1117
21.
Zohdi
,
T. I.
,
2004
, “
A Computational Framework for Agglomeration in Thermo-Chemically Reacting Granular Flows
,”
Proc. R. Soc.
,
460
(
2052
), pp.
3421
3445
.10.1098/rspa.2004.1277
22.
Zohdi
,
T. I.
,
2012
, “
Estimation of Electrical-Heating Load-Shares for Sintering of Powder Mixtures
,”
Proc. R. Soc.
,
468
(
2144
), pp.
2174
2190
.10.1098/rspa.2011.0755
23.
Zohdi
,
T. I.
,
2012
,
Dynamics of Charged Particulate Systems: Modeling, Theory and Computation
,
Springer-Verlag
,
Heidelberg, Germany
.
24.
Zohdi
,
T. I.
,
2013
, “
Numerical Simulation of Charged Particulate Cluster-Droplet Impact on Electrified Surfaces
,”
J. Comput. Phys.
,
233
, pp.
509
526
.10.1016/j.jcp.2012.09.012
25.
Zohdi
,
T. I.
,
2014
, “
A Direct Particle-Based Computational Framework for Electrically-Enhanced Thermo-Mechanical Sintering of Powdered Materials
,”
Math. Mech. Solids
,
19
(
1
), pp.
93
113
.10.1177/1081286513505472
26.
Boussinesq
,
J.
,
1885
,
Application des Potentials a l’ etude de l’ equilibre et du mouvement des solides elastiques
,
Gauthier-Villars
,
Paris, France
, Vol.
45
, p.
108
.
27.
Johnson
,
K.
,
1985
,
Contact Mechanics
,
Cambridge University Press
,
Cambridge, UK
.
28.
Kachanov
,
M.
,
Shafiro
,
B.
, and
Tsukrov
,
I.
,
2003
,
Handbook of Elasticity Solutions
,
Kluwer
,
Springer, Verlag
,
Heidelberg, Germany
.10.1007/978-94-017-0169-3
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