Thin film technology is pervasive in many applications, including microelectronics, optics, magnetic, hard and corrosion resistant coatings, micromechanics, etc. Therefore, basic research activities will be necessary in the future to increase knowledge and understanding and to develop predictive capabilities for relating fundamental physical and chemical properties to the microstructure and performance of thin films in various applications. In basic research, special model systems are needed for quantitative investigation of the relevant and fundamental processes in thin film material science. Because of the diversity of the subject and the sheer volume of the publications, a complete a review of the area of the current study is focused particularly on the experimental and theoretical investigations for the inelastic behavior of the micro-/nanostructured thin films.

1.
Wagner
,
T.
, and
Blank
,
E.
, 2004,
Characterizations of Thin Film and Coatings
,
Wiley
,
New York
.
2.
Alexopoulos
,
P. S.
, and
O’Sullivan
,
T. C.
, 1990, “
Mechanical Properties of Thin Films
,”
Annu. Rev. Mater. Sci.
0084-6600,
20
, pp.
391
420
.
3.
Vinci
,
R. P.
, and
Vlassak
,
J. J.
, 1996, “
Mechanical Behavior of Thin Films
,”
Annu. Rev. Mater. Sci.
0084-6600,
26
, pp.
431
462
.
4.
Ashby
,
M. F.
, 1970, “
Deformation of Plastically Non-Homogeneous Materials
,”
Philos. Mag.
0031-8086,
21
(
170
), pp.
399
424
.
5.
Frost
,
H. J.
, and
Ashby
,
M. F.
, 1971, “
Motion of a Dislocation Acted on by a Viscous Drag Through an Array of Discrete Obstacles
,”
J. Appl. Phys.
0021-8979,
42
(
13
), p.
5273
.
6.
Murakami
,
M.
,
Kuan
,
T. S.
, and
Blech
,
I. A.
, 1982, “
Strain Relaxation Mechanisms of Lead and Lead Alloy Thin-Films on Silicon Substrates
,”
Thin Solid Films
0040-6090,
89
(
2
), pp.
165
173
.
7.
Vinci
,
R. P.
,
Zielinski
,
E. M.
, and
Bravman
,
J. C.
, 1995, “
Thermal Strain and Stress in Copper Thin-Films
,”
Thin Solid Films
0040-6090,
262
(
1–2
), pp.
142
153
.
8.
Keller-Flaig
,
R. M.
,
Legros
,
M.
,
Sigle
,
W.
,
Gouldstone
,
A.
,
Hemker
,
K. J.
,
Suresh
,
S.
, and
Arzt
,
E.
, 1999, “
In Situ Transmission Electron Microscopy Investigation of Threading Dislocation Motion in Passivated Thin Aluminum Films
,”
J. Mater. Res.
0884-2914,
14
(
12
), pp.
4673
4676
.
9.
Fayad
,
W. R.
,
Kobrinsky
,
M. J.
, and
Thompson
,
C. V.
, 2000, “
Analytic Model for the Development of Bamboo Microstructures in Thin Film Strips Undergoing Normal Grain Growth
,”
Phys. Rev. B
0163-1829,
62
(
8
), pp.
5221
5227
.
10.
Freund
,
I.
,
Shvartsman
,
N.
, and
Freilikher
,
V.
, 1993, “
Optical Dislocation Networks in Highly Random-Media
,”
Opt. Commun.
0030-4018,
101
(
3–4
), pp.
247
264
.
11.
Freund
,
L. B.
, 1992, “
Dislocation Mechanisms of Relaxation in Strained Epitaxial-Films
,”
MRS Bull.
0883-7694,
17
(
7
), pp.
52
60
.
12.
Kraft
,
O.
,
Freund
,
L. B.
,
Phillips
,
R.
, and
Arzt
,
E.
, 2002, “
Dislocation Plasticity in Thin Metal Films
,”
MRS Bull.
0883-7694,
27
(
1
), pp.
30
37
.
13.
Nix
,
W. D.
, 1989, “
Mechanical-Properties of Thin-Films
,”
Metall. Trans. A
0360-2133,
20
(
11
), pp.
2217
2245
.
14.
Saha
,
R.
,
Xue
,
Z. Y.
,
Huang
,
Y.
, and
Nix
,
W. D.
, 2001, “
Indentation of a Soft Metal Film on a Hard Substrate: Strain Gradient Hardening Effects
,”
J. Mech. Phys. Solids
0022-5096,
49
(
9
), pp.
1997
2014
.
15.
Muhlhaus
,
H. B.
, and
Aifantis
,
E. C.
, 1991, “
A Variational Principle for Gradient Plasticity
,”
Int. J. Solids Struct.
0020-7683,
28
(
7
), pp.
845
857
.
16.
Aifantis
,
E. C.
, 2003, “
Update on a Class of Gradient Theories
,”
Mech. Mater.
0167-6636,
35
(
3–6
), pp.
259
280
.
17.
Aifantis
,
E. C.
, 1999, “
Gradient Deformation Models at Nano, Micro, and Macro Scales
,”
ASME J. Eng. Mater. Technol.
0094-4289,
121
(
2
), pp.
189
202
.
18.
1995,
Constitutive Modeling for Nanostructured Materials
,
W. W.
Miligan
,
S. A.
Hackney
, and
E. C.
Aifantis
, eds.,
Wiley
,
New York
.
19.
Nilsson
,
C.
, 1998, “
On Nonlocal Rate-Independent Plasticity
,”
Int. J. Plast.
0749-6419,
14
(
6
), pp.
551
575
.
20.
Stromberg
,
L.
, and
Ristinmaa
,
K.
, 1996, “
FE-Formulation of a Nonlocal Plasticity Theory
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
136
, pp.
127
144
.
21.
Eringen
,
A. C.
, and
Edelen
,
D. G. B.
, 1972, “
Nonlocal Elasticity
,”
Int. J. Eng. Sci.
0020-7225,
10
, pp.
233
248
.
22.
De Borst
,
R.
, and
Mühlhaus
,
H. B.
, 1992, “
Gradient Dependent Plasticity: Formulation and Algorithm Aspects
,”
Int. J. Numer. Methods Eng.
0029-5981,
35
, pp.
521
539
.
23.
de Borst
,
R.
, 2001, “
Some Recent Issues in Computational Failure Mechanics
,”
Int. J. Numer. Methods Eng.
0029-5981,
52
(
1–2
), pp.
63
95
.
24.
Kratochvil
,
J.
, and
Dillon
,
O. W.
, 1970, “
Thermodynamics of Crystalline Elastic-Visco-Plastic Materials
,”
J. Appl. Phys.
0021-8979,
41
(
4
), p.
1470
.
25.
Kratochvil
,
J.
, and
Dillon
,
O. W.
, 1969, “
Thermodynamics of Elastic-Plastic Materials as Theory With Internal State Variables
,”
J. Appl. Phys.
0021-8979,
40
, pp.
3207
3320
.
26.
Zbib
,
H. M.
, and
Aifantis
,
E. C.
, 1988, “
On the Localization and Postlocalization Behavior of Plastic-Deformation.1. On the Initiation of Shear Bands
,”
Res. Mech.
0143-0084,
23
(
2–3
), pp.
261
277
.
27.
Voyiadjis
,
G. Z.
, and
Ju
,
J. W. W.
, 2000, “
Special Issue: Advances in Computational Methods for Fracture Mechanics and Localization—Preface
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
183
(
1–2
), pp.
1
155
.
28.
Rajagopal
,
K. R.
, and
Málek
,
J.
, 2006, “
On the Modeling of Inhomogeneous Incompressible Fluid-Like Bodies
,”
Mech. Mater.
0167-6636,
38
, pp.
233
242
.
29.
Rajagopal
,
K. R.
, and
Srinivasa
,
A. R.
, 2008, “
On the Development of Fluid Models of the Differential Type Within a New Thermodynamic Framework
,”
Mech. Res. Commun.
0093-6413,
35
, pp.
483
489
.
30.
Faciu
,
C.
, and
Molinari
,
A.
, 1998, “
A Non-Local Rate-Type Viscoplastic Approach to Patterning of Deformation
,”
Acta Mech.
0001-5970,
126
(
1–4
), pp.
71
99
.
31.
Faciu
,
C.
, and
Molinari
,
A.
, 1996, “
Evolution of Layered Structures in a Gradient-Dependent Viscoplastic Material
,”
J. Phys. IV
1155-4339,
6
(C1), pp.
C1
-45–C1-
54
.
32.
Faciu
,
C.
,
Molinari
,
A.
,
Dablij
,
M.
, and
Zeghloul
,
A.
, 1998, “
A New Rate-Type Gradient-Dependent Viscoplastic Approach for Stop-and-Go Strain Band Propagation. Numerical vs. Physical Experiments
,”
J. Phys. IV
1155-4339,
8
, pp.
Pr8
-143–Pr8-
150
.
33.
Borg
,
U.
, and
Fleck
,
N. A.
, 2007, “
Strain Gradient Effect in Surface Roughing
,”
Modell. Simul. Mater. Sci. Eng.
0965-0393,
15
, pp.
S1
S12
.
34.
Fleck
,
N. A.
, and
Hutchinson
,
J. W.
, 2001, “
A Reformulation of Strain Gradient Plasticity
,”
J. Mech. Phys. Solids
0022-5096,
49
(
10
), pp.
2245
2271
.
35.
Fleck
,
N. A.
, and
Hutchinson
,
J. W.
, 1997, “
Strain Gradient Plasticity
,”
Adv. Appl. Mech.
0065-2156,
33
(
33
), pp.
295
361
.
36.
Fleck
,
N. A.
, and
Hutchinson
,
J. W.
, 1993, “
A Phenomenological Theory for Strain Gradient Effects in Plasticity
,”
J. Mech. Phys. Solids
0022-5096,
41
(
12
), pp.
1825
1857
.
37.
Fleck
,
N. A.
,
Muller
,
G. M.
,
Ashby
,
M. F.
, and
Hutchinson
,
J. W.
, 1994, “
Strain Gradient Plasticity—Theory and Experiment
,”
Acta Metall. Mater.
0956-7151,
42
(
2
), pp.
475
487
.
38.
Fleck
,
N. A.
, and
Willis
,
J. R.
, 2008, “
A Mathematical Basis for Strain Gradient Plasticity Theory—Part I: Scalar Plastic Multiplier
,”
J. Mech. Phys. Solids
0022-5096,
57
, pp.
161
177
.
39.
Abu Al-Rub
,
R. K.
,
Voyiadjis
,
G. Z.
, and
Bammann
,
D. J.
, 2007, “
A Thermodynamic Based Higher-Order Gradient Theory for Size Dependent Plasticity
,”
Int. J. Solids Struct.
0020-7683,
44
(
9
), pp.
2888
2923
.
40.
Voyiadjis
,
G.
, and
Deliktas
,
B.
, 2009, “
Formulation of Strain Gradient Plasticity With Interface Energy in a Consistent Thermodynamic Framework
,”
Int. J. Plast.
0749-6419, in press; doi:10.1016/j.ijplas.2008.12.014.
41.
Acharya
,
A.
, 2000, “
A Nonlinear Generalization of the Koiter–Sanders–Budiansky Bending Strain Measure
,”
Int. J. Solids Struct.
0020-7683,
37
(
39
), pp.
5517
5528
.
42.
Acharya
,
A.
, and
Beaudoin
,
A. J.
, 2000, “
Grain Size Effect in Viscoplastic Polycrystal at Moderate Strains
,”
J. Mech. Phys. Solids
0022-5096,
48
, pp.
2213
2230
.
43.
Acharya
,
A.
,
Tang
,
H.
,
Saigal
,
S.
, and
Bassani
,
J. L.
, 2004, “
On Boundary Conditions and Plastic Strain-Gradient Discontinuity in Lower-Order Gradient Plasticity
,”
J. Mech. Phys. Solids
0022-5096,
52
(
8
), pp.
1793
1826
.
44.
Niordson
,
C. F.
, and
Hutchinson
,
J. W.
, 2003, “
On Lower Order Strain Gradient Plasticity Theories
,”
Eur. J. Mech. A/Solids
0997-7538,
22
(
6
), pp.
771
778
.
45.
Volokh
,
K. Y.
, and
Hutchinson
,
J. W.
, 2002, “
Are Lower Order Gradient Theories of Plasticity Really Lower Order?
ASME Trans. J. Appl. Mech.
0021-8936,
69
, pp.
862
864
.
46.
Gao
,
H.
,
Huang
,
Y.
,
Nix
,
W. D.
, and
Hutchinson
,
J. W.
, 1999, “
Mechanism-Based Strain Gradient Plasticity—I. Theory
,”
J. Mech. Phys. Solids
0022-5096,
47
(
6
), pp.
1239
1263
.
47.
Mindlin
,
R. D.
, 1964, “
Micro-Structure in Linear Elasticity
,”
Arch. Ration. Mech. Anal.
0003-9527,
16
(
1
), pp.
51
78
.
48.
Aifantis
,
E. C.
, 1987, “
The Physics of Plastic-Deformation
,”
Int. J. Plast.
0749-6419,
3
(
3
), pp.
211
247
.
49.
Aifantis
,
E. C.
, 1984, “
On the Microstructural Origin of Certain Inelastic Models
,”
ASME J. Eng. Mater. Technol.
0094-4289,
106
(
4
), pp.
326
330
.
50.
Zbib
,
H. M.
, and
Aifantis
,
E. C.
, 1992, “
On the Gradient-Dependent Theory of Plasticity and Shear Banding
,”
Acta Mech.
0001-5970,
92
(
1–4
), pp.
209
225
.
51.
Nye
,
J. F.
, 1953, “
Some Geometrical Relations in Dislocated Crystals
,”
Acta Metall.
0001-6160,
1
(
2
), pp.
153
162
.
52.
Chen
,
S. H.
, and
Wang
,
T. C.
, 2002, “
A New Deformation Theory With Strain Gradient Effects
,”
Int. J. Plast.
0749-6419,
18
(
8
), pp.
971
995
.
53.
Stolken
,
J. S.
, and
Evans
,
A. G.
, 1998, “
A Microbend Test Method for Measuring the Plasticity Length Scale
,”
Acta Mater.
1359-6454,
46
(
14
), pp.
5109
5115
.
54.
Xiang
,
Y.
,
Tsui
,
T. Y.
, and
Vlassak
,
J. J.
, 2006, “
The Mechanical Properties of Freestanding Electroplated Cu Thin Films
,”
J. Mater. Res.
0884-2914,
21
(
6
), pp.
1607
1618
.
55.
Huang
,
Y.
,
Gao
,
H.
,
Nix
,
W. D.
, and
Hutchinson
,
J. W.
, 2000, “
Mechanism-Based Strain Gradient Plasticity—II. Analysis
,”
J. Mech. Phys. Solids
0022-5096,
48
(
1
), pp.
99
128
.
56.
Huang
,
H. C.
,
Ghoniem
,
N.
,
de la Rubia
,
T. D.
,
Rhee
,
M.
,
Zbib
,
H.
, and
Hirth
,
J.
, 1999, “
Stability of Dislocation Short-Range Reactions in BCC Crystals
,”
ASME J. Eng. Mater. Technol.
0094-4289,
121
(
2
), pp.
143
150
.
57.
Huang
,
Y.
,
Qu
,
S.
,
Hwang
,
K. C.
,
Li
,
M.
, and
Gao
,
H.
, 2004, “
A Conventional Theory of Mechanism-Based Strain Gradient Plasticity
,”
Int. J. Plast.
0749-6419,
20
, pp.
753
782
.
58.
Taylor
,
G. I.
, 1934, “
The Mechanism of Plastic Deformation of Crystals. Part I. Theoretical
,”
Proc. R. Soc. London, Ser. A
0950-1207,
145
, pp.
362
387
.
59.
Taylor
,
G. I.
, 1938, “
Plastic Strain in Metals
,”
J. Inst. Met.
0020-2975,
62
, pp.
307
324
.
60.
McElhaney
,
K. W.
,
Vlassak
,
J. J.
, and
Nix
,
W. D.
, 1998, “
Determination of Indenter Tip Geometry and Indentation Contact Area for Depth-Sensing Indentation Experiments
,”
J. Mater. Res.
0884-2914,
13
(
5
), pp.
1300
1306
.
61.
Xue
,
Z.
,
Huang
,
Y.
,
Hwang
,
K. C.
, and
Li
,
M.
, 2002, “
The Influence of Indenter Tip Radius on the Micro-Indentation Hardness
,”
ASME J. Eng. Mater. Technol.
0094-4289,
124
(
3
), pp.
371
379
.
62.
Shi
,
M. X.
,
Huang
,
Y.
, and
Hwang
,
K. C.
, 2000, “
Plastic Flow Localization in Mechanism-Based Strain Gradient Plasticity
,”
Int. J. Mech. Sci.
0020-7403,
42
(
11
), pp.
2115
2131
.
63.
Lu
,
T.
,
Shi
,
T. W.
, and
Jiang
,
J. P.
, 2000, “
Residual Stress Distributions and Plastic Zones in Heterogeneous Welded Plates With a Transverse Crack
,”
Int. J. Pressure Vessels Piping
0308-0161,
77
(
9
), pp.
549
553
.
64.
Jiang
,
Y. Y.
, 2001, “
An Experimental Study of Inhomogeneous Cyclic Plastic Deformation
,”
ASME J. Eng. Mater. Technol.
0094-4289,
123
(
3
), pp.
274
280
.
65.
Shi
,
X. H.
, and
Gao
,
Y. G.
, 2001, “
Generalization of Response Number for Dynamic Plastic Response of Shells Subjected to Impulsive Loading
,”
Int. J. Pressure Vessels Piping
0308-0161,
78
(
6
), pp.
453
459
.
66.
Gurtin
,
M. E.
, 2004, “
A Gradient Theory of Small-Deformation Isotropic Plasticity That Accounts for the Burgers Vector and for Dissipation Due to Plastic Spin
,”
J. Mech. Phys. Solids
0022-5096,
52
(
11
), pp.
2545
2568
.
67.
Anand
,
L.
,
Gurtin
,
M. E.
,
Lele
,
S. P.
, and
Gething
,
C.
, 2005, “
A One-Dimensional Theory of Strain-Gradient Plasticity: Formulation, Analysis, Numerical Results
,”
J. Mech. Phys. Solids
0022-5096,
53
(
8
), pp.
1789
1826
.
68.
Estrin
,
Y.
,
Kubin
,
L. P.
, and
Aifantis
,
E. C.
, 1993, “
Introductory Remarks to the Viewpoint Set on Propagative Plastic Instabilities
,”
Scr. Metall. Mater.
0956-716X,
29
(
9
), pp.
1147
1150
.
69.
Baaser
,
H.
, and
Tvergaard
,
V.
, 2003, “
A New Algorithmic Approach Treating Nonlocal Effects at Finite Rate-Independent Deformation Using the Rousselier Damage Model
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
192
(
1–2
), pp.
107
124
.
70.
Benallal
,
A.
, and
Tvergaard
,
V.
, 1995, “
Nonlocal Continuum Effects on Bifurcation in the Plane-Strain Tension—Compression Test
,”
J. Mech. Phys. Solids
0022-5096,
43
(
5
), pp.
741
770
.
71.
Kuroda
,
M.
, and
Tvergaard
,
V.
, 2008, “
A Finite Deformation Theory of Higher-Order Gradient Crystal Plasticity
,”
J. Mech. Phys. Solids
0022-5096,
56
(
8
), pp.
2573
2584
.
72.
Kuroda
,
M.
,
Tvergaard
,
V.
, and
Ohashi
,
T.
, 2007, “
Simulations of Micro-Bending of Thin Foils Using a Scale Dependent Crystal Plasticity Model
,”
Modell. Simul. Mater. Sci. Eng.
0965-0393,
15
(
1
), pp.
S13
S22
.
73.
Mikkelsen
,
L. P.
, and
Tvergaard
,
V.
, 1999, “
A Nonlocal Two-Dimensional Analysis of Instabilities in Tubes Under Internal Pressure
,”
J. Mech. Phys. Solids
0022-5096,
47
(
4
), pp.
953
969
.
74.
Molinari
,
A.
, and
Moufki
,
A.
, 2005, “
A New Thermomechanical Model of Cutting Applied to Turning Operations. Part I. Theory
,”
Int. J. Mach. Tools Manuf.
0890-6955,
45
(
2
), pp.
166
180
.
75.
Molinari
,
A.
,
Pellizzari
,
M.
,
Tremea
,
A.
,
Biggi
,
A.
, and
Corbo
,
G.
, 2005, “
Effect of Matrix Microhardness on Thermal Fatigue Behaviour of Spincast High Speed Steels for Hot Rolls
,”
Mater. Sci. Technol.
0267-0836,
21
(
3
), pp.
352
356
.
76.
Molinari
,
A.
, and
Ravichandran
,
G.
, 2005, “
Constitutive Modeling of High-Strain-Rate Deformation in Metals Based on the Evolution of an Effective Microstructural Length
,”
Mech. Mater.
0167-6636,
37
(
7
), pp.
737
752
.
77.
Molinari
,
A.
, and
Wright
,
T. W.
, 2005, “
A Physical Model for Nucleation and Early Growth of Voids in Ductile Materials Under Dynamic Loading
,”
J. Mech. Phys. Solids
0022-5096,
53
(
7
), pp.
1476
1504
.
78.
Ravichandran
,
G.
, and
Molinari
,
A.
, 2005, “
Analysis of Shear Banding in Metallic Glasses Under Bending
,”
Acta Mater.
1359-6454,
53
(
15
), pp.
4087
4095
.
79.
Shu
,
J. Y.
,
Fleck
,
N. A.
,
Van der Giessen
,
E.
, and
Needleman
,
A.
, 2001, “
Boundary Layers in Constrained Plastic Flow: Comparison of Nonlocal and Discrete Dislocation Plasticity
,”
J. Mech. Phys. Solids
0022-5096,
49
(
6
), pp.
1361
1395
.
80.
Devincre
,
B.
,
Veyssiere
,
P.
,
Kubin
,
L. P.
, and
Saada
,
G.
, 1997, “
A Simulation of Dislocation Dynamics and of the Flow Stress Anomaly in L1(2) Alloys
,”
Philos. Mag. A
0141-8610,
75
(
5
), pp.
1263
1286
.
81.
Zbib
,
H. M.
,
de la Rubia
,
T. D.
, and
Bulatov
,
V.
, 2002, “
A Multiscale Model of Plasticity Based on Discrete Dislocation Dynamics
,”
ASME J. Eng. Mater. Technol.
0094-4289,
124
(
1
), pp.
78
87
.
82.
Nicola
,
L.
,
Van der Giessen
,
E.
, and
Needleman
,
A.
, 2003, “
Discrete Dislocation Analysis of Size Effects in Thin Films
,”
J. Appl. Phys.
0021-8979,
93
(
10
), pp.
5920
5928
.
83.
Benzerga
,
A. A.
, and
Shaver
,
N. F.
, 2006, “
Scale Dependence of Mechanical Properties of Single Crystals Under Uniform Deformation
,”
Scr. Mater.
1359-6462,
54
(
11
), pp.
1937
1941
.
84.
Shizawa
,
K.
, and
Zbib
,
H. M.
, 1999, “
A Thermodynamical Theory of Plastic Spin and Internal Stress With Dislocation Density Tensor
,”
ASME J. Eng. Mater. Technol.
0094-4289,
121
(
2
), pp.
247
253
.
85.
Shen
,
C.
, and
Wang
,
Y.
, 2003, “
Phase Field Model of Dislocation Networks
,”
Acta Mater.
1359-6454,
51
(
9
), pp.
2595
2610
.
86.
Schiotz
,
J.
, 2004, “
Atomic-Scale Modeling of Plastic Deformation of Nanocrystalline Copper
,”
Scr. Mater.
1359-6462,
51
(
8
), pp.
837
841
.
87.
Wolf
,
D.
,
Yamakov
,
V.
,
Phillpot
,
S. R.
,
Mukherjee
,
A.
, and
Gleiter
,
H.
, 2005, “
Deformation of Nanocrystalline Materials by Molecular-Dynamics Simulation: Relationship to Experiments?
,”
Acta Mater.
1359-6454,
53
(
1
), pp.
1
40
.
88.
Lidorikis
,
E.
,
Bachlechner
,
M. E.
,
Kalia
,
R. K.
,
Nakano
,
A.
,
Vashishta
,
P.
, and
Voyiadjis
,
G. Z.
, 2001, “
Coupling Length Scales for Multiscale Atomistics-Continuum Simulations: Atomistically Induced Stress Distributions in Si/Si3N4 Nanopixels
,”
Phys. Rev. Lett.
0031-9007,
87
(
8
), p.
086104
.
89.
Nakano
,
A.
,
Bachlechner
,
M. E.
,
Kalia
,
R. K.
,
Lidorikis
,
E.
,
Vashishta
,
P.
,
Voyiadjis
,
G. Z.
,
Campbell
,
T. J.
,
Ogata
,
S.
, and
Shimojo
,
F.
, 2001, “
Multiscale Simulation of Nanosystems
,”
Comput. Sci. Eng.
1521-9615,
3
(
4
), pp.
56
66
.
90.
Aifantis
,
K. E.
,
Kolesnikova
,
A. L.
, and
Romanov
,
A. E.
, 2007, “
Nucleation of Misfit Dislocations and Plastic Deformation in Core/Shell Nanowires
,”
Philos. Mag.
1478-6435,
87
(
30
), pp.
4731
4757
.
91.
Cholevas
,
K.
,
Liosatos
,
N.
,
Romanov
,
A. E.
,
Zaiser
,
M.
, and
Aifantis
,
E. C.
, 1998, “
Misfit Dislocation Patterning in Thin Films
,”
Phys. Status Solidi B
0370-1972,
209
(
2
), pp.
295
304
.
92.
Gryaznov
,
V. G.
,
Polonsky
,
I. A.
,
Romanov
,
A. E.
, and
Trusov
,
L. I.
, 1991, “
Size Effects of Dislocation Stability in Nanocrystals
,”
Phys. Rev. B
0163-1829,
44
(
1
), pp.
42
46
.
93.
Gutkin
,
M. Y.
,
Romanov
,
A. E.
, and
Aifantis
,
E. C.
, 1995, “
Nonuniform Misfit Dislocation Distributions in Nanoscale Thin Layers
,”
Nanostruct. Mater.
0965-9773,
6
(
5–8
), pp.
771
774
.
94.
Kolesnikova
,
A. L.
,
Ovid’ko
,
I. A.
, and
Romanov
,
A. E.
, 2007, “
Dislocation-Disclination Transformations and the Reverse Hall–Petch Effect in Nanocrystalline Materials
,”
Tech. Phys. Lett.
1063-7850,
33
(
8
), pp.
641
644
.
95.
Nazarov
,
A. A.
,
Romanov
,
A. E.
, and
Valiev
,
R. Z.
, 1990, “
On the Hierarchy of Dislocation Descriptions of Grain-Boundary Structures
,”
Phys. Status Solidi A
0031-8965,
122
(
2
), pp.
495
502
.
96.
Romanov
,
A. E.
, 2002, “
Fundamentals of Disclination Theory: Development of Disclination-Dislocation Structures in Deformed Materials
,”
Local Lattice Rotations and Disclinations in Microstructures of Distorted Crystalline Materials
,
Solid State Phenomena
, Vol.
87
,
Trans Tech Publications
,
Switzerland
, pp.
47
56
.
97.
Van der Giessen
,
E.
,
Deshpande
,
V. S.
,
Cleveringa
,
H. H. M.
, and
Needleman
,
A.
, 2001, “
Discrete Dislocation Plasticity and Crack Tip Fields in Single Crystals
,”
J. Mech. Phys. Solids
0022-5096,
49
(
9
), pp.
2133
2153
.
98.
Balint
,
D. S.
,
Deshpande
,
V. S.
,
Needleman
,
A.
, and
Van der Giessen
,
E.
, 2006, “
Discrete Dislocation Plasticity Analysis of the Wedge Indentation of Films
,”
J. Mech. Phys. Solids
0022-5096,
54
(
11
), pp.
2281
2303
.
99.
Toupin
,
R. A.
, 1962, “
Elastic Materials With Coupled Stresses
,”
Arch. Ration. Mech. Anal.
0003-9527,
11
, pp.
385
414
.
100.
Berdichevski
,
V. L.
, and
Sedov
,
L. I.
, 1967, “
Dynamic Theory of Continuously Distributed Dislocations. Its Relation to Plasticity Theory
,”
J. Appl. Math. Mech.
0021-8928,
31
, pp.
981
1000
.
101.
Bilby
,
B. A.
,
Bullough
,
R.
, and
Smith
,
E.
, 1955, “
Continuous Distributions of Dislocations: A New Application of the Methods of Non-Riemannian Geometry
,”
Proc. R. Soc. London, Ser. A
0950-1207,
231
, pp.
263
273
.
102.
Teodosiu
,
C.
, 1967, “
Contribution to the Continuum Theory of Dislocations and Initial Stresses
,”
Rev. Roum. Sci. Tech., Ser. Mec. Appl.
0035-4074,
12
, pp.
961
977
.
103.
Cermelli
,
P.
, and
Gurtin
,
M. E.
, 2002, “
Geometrically Necessary Dislocations in Viscoplastic Single Crystal and Bicrystals Undergoing Small Deformation
,”
Int. J. Solids Struct.
0020-7683,
39
, pp.
6281
6309
.
104.
Clayton
,
J. D.
,
Bammann
,
D. J.
, and
McDowell
,
D. L.
, 2005, “
A Geometric Framework for the Kinematics of Crystals With Defects
,”
Philos. Mag.
1478-6435,
85
, pp.
3983
4010
.
105.
Bammann
,
D. J.
, 2001, “
A Model of Crystal Plasticity Containing a Natural Length Scale
,”
Mater. Sci. Eng., A
0921-5093,
309-310
, pp.
406
410
.
106.
Reguerio
,
R. A.
,
Bammann
,
D. J.
,
Marin
,
E. B.
, and
Garikipati
,
K.
, 2002, “
A Nonlocal Phenomenological Anisotropic Finite Deformation Plasticity Model Accounting for Dislocation Defects
,”
ASME J. Eng. Mater. Technol.
0094-4289,
124
, pp.
38
87
.
107.
Aifantis
,
E. C.
, 2000, “
Gradient Aspects of Crystal Plasticity at Micro and Macro Scales
,”
Key Eng. Mater.
1013-9826,
177
, pp.
805
809
.
108.
Aifantis
,
E. C.
, 1992, “
On the Role of Gradients in the Localization of Deformation and Fracture
,”
Int. J. Eng. Sci.
0020-7225,
30
(
10
), pp.
1279
1299
.
109.
Aifantis
,
E. C.
, 1999, “
Strain Gradient Interpretation of Size Effects
,”
Int. J. Fract.
0376-9429,
95
(
1–4
), pp.
299
314
.
110.
Charalambakis
,
N.
,
Rigatos
,
A.
, and
Aifantis
,
E. C.
, 1991, “
The Stabilizing Role of Higher-Order Strain Gradients in Nonlinear Thermoviscoplasticity
,”
Acta Mech.
0001-5970,
86
(
1–4
), pp.
65
81
.
111.
Aifantis
,
E. C.
, 1995, “
Pattern-Formation in Plasticity
,”
Int. J. Eng. Sci.
0020-7225,
33
(
15
), pp.
2161
2178
.
112.
Hutchinson
,
J. W.
, 2000, “
Plasticity at the Micron Scale
,”
Int. J. Solids Struct.
0020-7683,
37
(
1–2
), pp.
225
238
.
113.
Ma
,
Q.
, and
Clarke
,
D. R.
, 1995, “
Size-Dependent Hardness of Silver Single-Crystals
,”
J. Mater. Res.
0884-2914,
10
(
4
), pp.
853
863
.
114.
Smyshlyaev
,
V. P.
, and
Fleck
,
N. A.
, 1995, “
Bounds and Estimates for the Overall Plastic Behaviour of Composites With Strain Gradient Effects
,”
Proc. R. Soc. London, Ser. A
0950-1207,
451
(
1943
), pp.
795
810
.
115.
Begley
,
M. R.
, and
Hutchinson
,
J. W.
, 1999, “
Plasticity in Fretting of Coated Substrates
,”
Eng. Fract. Mech.
0013-7944,
62
(
2–3
), pp.
14
64
.
116.
Teskey
,
G. C.
,
Hutchinson
,
J. E.
, and
Kolb
,
B.
, 1999, “
Sex Differences in Cortical Plasticity and Behavior Following Anterior Cortical Kindling in Rats
,”
Cereb. Cortex
1047-3211,
9
(
7
), pp.
675
682
.
117.
Volokh
,
K. Y.
, and
Hutchinson
,
J. W.
, 2002, “
Are Lower-Order Gradient Theories of Plasticity Really Lower Order?
,”
ASME J. Appl. Mech.
0021-8936,
69
(
6
), pp.
862
864
.
118.
Wei
,
Y.
, and
Hutchinson
,
J. W.
, 2008, “
Toughness of Ni/Al2O3
Interfaces as Dependent on Micron-Scale Plasticity and Atomistic-Scale Separation,”
Philos. Mag.
1478-6435,
88
(
30–32
), pp.
3841
3859
.
119.
Shu
,
J. Y.
, and
Fleck
,
N. A.
, 1999, “
Strain Gradient Crystal Plasticity: Size-Dependent Deformation of Bicrystals
,”
J. Mech. Phys. Solids
0022-5096,
47
(
2
), pp.
297
324
.
120.
Shu
,
J. Y.
,
King
,
W. E.
, and
Fleck
,
N. A.
, 1999, “
Finite Elements for Materials With Strain Gradient Effects
,”
Int. J. Numer. Methods Eng.
0029-5981,
44
(
3
), pp.
373
391
.
121.
Buehler
,
M. J.
,
Gao
,
H. J.
, and
Huang
,
Y. G.
, 2004, “
Atomistic and Continuum Studies of Stress and Strain Fields Near a Rapidly Propagating Crack in a Harmonic Lattice
,”
Theor. Appl. Fract. Mech.
0167-8442,
41
(
1–3
), pp.
21
42
.
122.
Chen
,
J. Y.
,
Wei
,
Y.
,
Huang
,
Y.
,
Hutchinson
,
J. W.
, and
Hwang
,
K. C.
, 1999, “
The Crack Tip Fields in Strain Gradient Plasticity: The Asymptotic and Numerical Analyses
,”
Eng. Fract. Mech.
0013-7944,
64
(
5
), pp.
625
648
.
123.
Nix
,
W. D.
,
Greer
,
J. R.
,
Feng
,
G.
, and
Lilleodden
,
E. T.
, 2007, “
Deformation at the Nanometer and Micrometer Length Scales: Effects of Strain Gradients and Dislocation Starvation
,”
Thin Solid Films
0040-6090,
515
(
6
), pp.
3152
3157
.
124.
Voyiadjis
,
G. Z.
,
Abu Al-Rub
,
R. K.
, and
Palazotto
,
A. N.
, 2003, “
Non-Local Coupling of Viscoplasticity and Anisotropic Viscodamage for Impact Problems Using the Gradient Theory
,”
Arch. Mech.
0373-2029,
55
(
1
), pp.
39
89
.
125.
1965,
The Nonlinear Field Theories of Mechanics
,
C.
Truesdell
and
W.
Noll
, eds.,
Springer-Verlag
,
Berlin
.
126.
Maugin
,
G. A.
, and
Inoue
,
T.
, 1999, “
Progress of Phase Boundaries and Walls in Thermo-Deformable Solids: A Canonical Approach
,”
J. Phys. IV
1155-4339,
9
, pp.
Pr9
-351–Pr9-
360
.
127.
Maugin
,
G. A.
, 1990, “
Internal Variables and Dissipative Structures
,”
J. Non-Equilib. Thermodyn.
0340-0204,
15
(
2
), pp.
173
192
.
128.
Maugin
,
G. A.
, and
Drouot
,
R.
, 1983, “
Internal Variables and the Thermodynamics of Macromolecule Solutions
,”
Int. J. Eng. Sci.
0020-7225,
21
(
7
), pp.
705
724
.
129.
Drouot
,
R.
, and
Maugin
,
G. A.
, 2001, “
Application of Diffusive Internal Variables in Complex Fluids
,”
J. Non-Newtonian Fluid Mech.
0377-0257,
96
(
1–2
), pp.
31
43
.
130.
Engelbrecht
,
J.
, and
Maugin
,
G. A.
, 1996, “
Deformation Waves in Thermoelastic Media and the Concept of Internal Variables
,”
Arch. Appl. Mech.
0939-1533,
66
(
3
), pp.
200
207
.
131.
Engelbrecht
,
J.
,
Vendelin
,
M.
, and
Maugin
,
G. A.
, 2000, “
Hierarchical Internal Variables Reflecting Microstructural Properties: Application to Cardiac Muscle Contraction
,”
J. Non-Equilib. Thermodyn.
0340-0204,
25
(
2
), pp.
119
130
.
132.
Lazar
,
M.
,
Maugin
,
G. A.
, and
Aifantis
,
E. C.
, 2006, “
Dislocations in Second Strain Gradient Elasticity
,”
Int. J. Solids Struct.
0020-7683,
43
(
6
), pp.
1781
1817
.
133.
Maugin
,
G. A.
, and
Muschik
,
W.
, 1994, “
Thermodynamics With Internal Variables.1. General Concepts
,”
J. Non-Equilib. Thermodyn.
0340-0204,
19
(
3
), pp.
217
249
.
134.
Maugin
,
G. A.
, and
Muschik
,
W.
, 1994, “
Thermodynamics With Internal Variables.1. Applications
,”
J. Non-Equilib. Thermodyn.
0340-0204,
19
(
3
), pp.
250
289
.
135.
Valanis
,
K. C.
, 1996, “
A Gradient Theory of Internal Variables
,”
Acta Mech.
0001-5970,
116
(
1–4
), pp.
1
14
.
136.
Borino
,
G.
, and
Polizzotto
,
C.
, 2003, “
Paper: ‘Higher-Order Strain/Higher-Order Stress Gradient Models Derived From a Discrete Microstructure, With Application to Fracture,’ by C.S Chang, H. Askes and L.J. Sluys; Engineering Fracture Mechanics 69 (2002), 1907–1924
,”
Eng. Fract. Mech.
0013-7944,
70
(
9
), pp.
1219
1221
.
137.
Borino
,
G.
, and
Polizzotto
,
C.
, 1999, “
Comments on ‘Nonlocal Strain Softening Bar Revisited’ by Christer Nilsson [International Journal of Solids and Structures 34 (1997) 4399–4419]
,”
Int. J. Solids Struct.
0020-7683,
36
(
20
), pp.
3085
3091
.
138.
Polizzotto
,
C.
, 2007, “
Strain-Gradient Elastic-Plastic Material Models and Assessment of the Higher Order Boundary Conditions
,”
Eur. J. Mech. A/Solids
0997-7538,
26
(
2
), pp.
189
211
.
139.
Polizzotto
,
C.
,
Fuschi
,
P.
, and
Pisano
,
A. A.
, 2004, “
A Strain-Difference-Based Nonlocal Elasticity Model
,”
Int. J. Solids Struct.
0020-7683,
41
(
9–10
), pp.
2383
2401
.
140.
Gurtin
,
M. E.
, 2003, “
On a Framework for Small-Deformation Viscoplasticity: Free Energy, Microforces, Strain Gradient
,”
Int. J. Plast.
0749-6419,
19
, pp.
47
90
.
141.
Bardella
,
L.
, 2006, “
A Deformation Theory of Strain Gradient Crystal Plasticity That Accounts for Geometrically Necessary Dislocations
,”
J. Mech. Phys. Solids
0022-5096,
54
(
1
), pp.
128
160
.
142.
Bardella
,
L.
, 2007, “
Some Remarks on the Strain Gradient Crystal Plasticity, With Particular Reference to the Material Length Scales Involved
,”
Int. J. Plast.
0749-6419,
23
, pp.
296
322
.
143.
Gudmundson
,
P.
, 2004, “
A Unified Treatment of Strain Gradient Plasticity
,”
J. Mech. Phys. Solids
0022-5096,
52
(
6
), pp.
1379
1406
.
144.
Clayton
,
J. D.
, and
Chung
,
P. W.
, 2006, “
An Atomistic-to-Continuum Framework for Nonlinear Crystal Mechanics Based on Asymptotic Homogenization
,”
J. Mech. Phys. Solids
0022-5096,
54
, pp.
1604
1639
.
145.
Voyiadjis
,
G. Z.
, and
Abu Al-Rub
,
R. K.
, 2007, “
Nonlocal Gradient-Dependent Thermodynamics for Modeling Scale-Dependent Plasticity
,”
Int. J. Multiscale Comp. Eng.
1543-1649,
5
(
3–4
), pp.
295
323
.
146.
Bittencourt
,
E.
,
Needleman
,
A.
,
Gurtin
,
M. E.
, and
Van der Giessen
,
E.
, 2003, “
A Comparison of Nonlocal Continuum and Discrete Dislocation Plasticity Predictions
,”
J. Mech. Phys. Solids
0022-5096,
51
, pp.
281
310
.
147.
Barney
,
M. M.
,
Campbell
,
G. H.
,
Stolken
,
J. S.
,
Schwatz
,
A. J.
,
Plitzko
,
J.
,
King
,
W. E.
, and
Morris
,
J. W.
, 2000, “
Experimental Assessment of Gradient Plasticity
,”
Materials Research Society Fall 2000 Meeting
, Boston, MA.
148.
Reddy
,
B. D.
,
Ebobisse
,
F.
, and
McBride
,
A.
, 2008, “
Well-Posedness of a Model of Strain Gradient Plasticity for Plastically Irrotational Materials
,”
Int. J. Plast.
0749-6419,
24
, pp.
55
73
.
149.
Phillips
,
M. A.
,
Clemens
,
B. M.
, and
Nix
,
W. D.
, 2003, “
Microstructure and Nanoindentation Hardness of Al/Al3Sc Multilayers
,”
Acta Mater.
1359-6454,
51
(
11
), pp.
3171
3184
.
150.
Qu
,
S.
,
Huang
,
Y.
,
Nix
,
W. D.
,
Jiang
,
H.
,
Zhang
,
F.
, and
Hwang
,
K. C.
, 2004, “
Indenter Tip Radius Effect on the Nix–Gao Relation in Micro- and Nanoindentation Hardness Experiments
,”
J. Mater. Res.
0884-2914,
19
(
11
), pp.
3423
3434
.
151.
Saha
,
R.
, and
Nix
,
W. D.
, 2002, “
Effects of the Substrate on the Determination of Thin Film Mechanical Properties by Nanoindentation
,”
Acta Mater.
1359-6454,
50
(
1
), pp.
23
38
.
152.
Feng
,
G.
,
Nix
,
W. D.
,
Yoon
,
Y.
, and
Lee
,
C. J.
, 2006, “
A Study of the Mechanical Properties of Nanowires Using Nanoindentation
,”
J. Appl. Phys.
0021-8979,
99
(
7
), p.
074304
.
153.
Mustre de León
,
J.
,
Espinosa
,
F. J.
,
Perez
,
V. A.
,
Jimenez-Sandoval
,
S.
,
Lopez-Lopez
,
S.
, and
Montano
,
P. A.
, 2000, “
Local Atomic Environment of Cu:CdTe Thin Film Alloys
,”
Microelectron. J.
0026-2692,
31
(
6
), pp.
429
431
.
154.
Espinosa
,
H. D.
, and
Peng
,
B.
, 2005, “
A New Methodology to Investigate Fracture Toughness of Freestanding MEMS and Advanced Materials in Thin Film Form
,”
J. Microelectromech. Syst.
1057-7157,
14
(
1
), pp.
153
159
.
155.
Espinosa
,
J.
,
Shi
,
H.
, and
Lederman
,
D.
, 2006, “
In Situ Measurements of Cobalt Thin-Film Surface Roughening Upon Annealing
,”
J. Appl. Phys.
0021-8979,
99
(
2
), p.
023516
.
156.
Xiang
,
Y.
,
Chen
,
X.
,
Tsui
,
T. Y.
,
Jang
,
J. I.
, and
Vlassak
,
J. J.
, 2006, “
Mechanical Properties of Porous and Fully Dense Low-Kappa Dielectric Thin Films Measured by Means of Nanoindentation and the Plane-Strain Bulge Test Technique
,”
J. Mater. Res.
0884-2914,
21
(
2
), pp.
386
395
.
157.
Haque
,
M. A.
, and
Saif
,
M. T. A.
, 2004, “
Deformation Mechanisms in Free-Standing Nanoscale Thin Films: A Quantitative In Situ Transmission Electron Microscope Study
,”
Proceedings of the National Academy of Science of the United State of America
.
158.
Pant
,
P.
,
Schwarz
,
K. W.
, and
Baker
,
S. P.
, 2003, “
Dislocation Interactions in Thin FCC Metal Films
,”
Acta Mater.
1359-6454,
51
(
11
), pp.
3243
3258
.
159.
Groh
,
S.
,
Devincre
,
B.
,
Kubin
,
L. P.
,
Roos
,
A.
,
Feyel
,
F.
, and
Chaboche
,
J. L.
, 2003, “
Dislocations and Elastic Anisotropy in Heteroepitaxial Metallic Thin Films
,”
Philos. Mag. Lett.
0950-0839,
83
(
5
), pp.
303
313
.
160.
Ghoniem
,
N. M.
,
Busso
,
E. P.
,
Kioussis
,
N.
, and
Huang
,
H. C.
, 2003, “
Multiscale Modelling of Nanomechanics and Micromechanics: An Overview
,”
Philos. Mag.
1478-6435,
83
(
31–34
), pp.
3475
3528
.
161.
Han
,
X.
,
Ghoniem
,
N. M.
, and
Wang
,
Z.
, 2004, “
Parametric Dislocation Dynamics of Anisotropic Crystals
,”
Philos. Mag.
1478-6435,
83
(
31–34
), pp.
3705
3721
.
162.
Hartmaier
,
A.
,
Buehler
,
M. J.
, and
Gao
,
H. J.
, 2005, “
Two-Dimensional Discrete Dislocation Models of Deformation in Polycrystalline Thin Metal Films on Substrates
,”
Mater. Sci. Eng., A
0921-5093,
400-401
, pp.
260
263
.
163.
Nicola
,
L.
,
Van der Giessen
,
E.
, and
Gurtin
,
M. E.
, 2005, “
Effect of Defect Energy on Strain-Gradient Predictions of Confined Single-Crystal Plasticity
,”
J. Mech. Phys. Solids
0022-5096,
53
(
6
), pp.
1280
1294
.
164.
Gerberich
,
W. W.
,
Kramer
,
D. E.
,
Tymiak
,
N. I.
,
Volinsky
,
A. A.
,
Bahr
,
D. F.
, and
Kriese
,
M. D.
, 1999, “
Nanoindentation-Induced Defect-Interface Interactions: Phenomena, Methods and Limitations
,”
Acta Mater.
1359-6454,
47
(
15–16
), pp.
4115
4123
.
165.
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.
0021-8936,
73
(
2
), pp.
327
334
.
166.
Grunlan
,
J. C.
,
Xia
,
X. Y.
,
Rowenhorst
,
D.
, and
Gerberich
,
W. W.
, 2001, “
Preparation and Evaluation of Tungsten Tips Relative to Diamond for Nanoindentation of Soft Materials
,”
Rev. Sci. Instrum.
0034-6748,
72
(
6
), pp.
2804
2810
.
167.
Karapanagiotis
,
I.
,
Evans
,
D. F.
, and
Gerberich
,
W. W.
, 2002, “
Dynamics of the Leveling Process of Nanoindentation Induced Defects on Thin Polystyrene Films
,”
Polymer
0032-3861,
43
(
4
), pp.
1343
1348
.
168.
Karapanagiotis
,
I.
,
Gerberich
,
W. W.
, and
Evans
,
D. F.
, 2001, “
Early Dewetting Stages of Thin Polymer Films Initiated by Nanoindentation
,”
Langmuir
0743-7463,
17
(
8
), pp.
2375
2379
.
169.
Li
,
M.
,
Carter
,
C. B.
,
Hillmyer
,
M. A.
, and
Gerberich
,
W. W.
, 2001, “
Adhesion of Polymer-Inorganic Interfaces by Nanoindentation
,”
J. Mater. Res.
0884-2914,
16
(
12
), pp.
3378
3388
.
170.
Volinsky
,
A. A.
,
Moody
,
N. R.
, and
Gerberich
,
W. W.
, 2004, “
Nanoindentation of Au and Pt/Cu Thin Films at Elevated Temperatures
,”
J. Mater. Res.
0884-2914,
19
(
9
), pp.
2650
2657
.
171.
Voyiadjis
,
G. Z.
,
Abu Al-Rub
,
R. K.
, and
Palazotto
,
A. N.
, 2004, “
Thermodynamic Framework for Coupling of Non-Local Viscoplasticity and Non-Local Anisotropic Viscodamage for Dynamic Localization Problems Using Gradient Theory
,”
Int. J. Plast.
0749-6419,
20
(
6
), pp.
981
1038
.
172.
Nix
,
W. D.
, and
Gao
,
H.
, 1998, “
Indentation Size Effects in Crystalline Materials: A Law for Strain Gradient Plasticity
,”
J. Mech. Phys. Solids
0022-5096,
46
, pp.
411
425
.
173.
Voyiadjis
,
G. Z.
, and
Abu Al-Rub
,
R. K.
, 2005, “
Gradient Plasticity Theory With a Variable Length Scale Parameter
,”
Int. J. Solids Struct.
0020-7683,
42
(
14
), pp.
3998
4029
.
174.
Voyiadjis
,
G. Z.
, and
Almasri
,
A. H.
, 2008, “
A Physically Based Constitutive Model for Fee Metals With Applications to Dynamic Hardness
,”
Mech. Mater.
0167-6636,
40
(
6
), pp.
549
563
.
175.
Arsenlis
,
A.
, and
Parks
,
D. M.
, 1999, “
Crystallographic Aspects of Geometrically-Necessary and Statistically-Stored Dislocation Density
,”
Acta Mater.
1359-6454,
47
(
5
), pp.
1597
1611
.
176.
Voyiadjis
,
G. Z.
, and
Abed
,
F. H.
, 2006, “
A Coupled Temperature and Strain Rate Dependent Yield Function for Dynamic Deformations of bcc Metals
,”
Int. J. Plast.
0749-6419,
22
(
8
), pp.
1398
1431
.
177.
Abu Al-Rub
,
R. K.
, and
Voyiadjis
,
G. Z.
, 2003, “
On the Coupling of Anisotropic Damage and Plasticity Models for Ductile Materials
,”
Int. J. Solids Struct.
0020-7683,
40
(
11
), pp.
2611
2643
.
178.
Abu Al-Rub
,
R. K.
, and
Voyiadjis
,
G. Z.
, 2004, “
Analytical and Experimental Determination of the Material Intrinsic Length Scale of Strain Gradient Plasticity Theory From Micro- and Nano-Indentation Experiments
,”
Int. J. Plast.
0749-6419,
20
(
6
), pp.
1139
1182
.
179.
Gracio
,
J. J.
, 1994, “
The Double Effect of Grain Size on the Work Hardening Behavior of Polycrystalline Copper
,”
Scr. Metall. Mater.
0956-716X,
31
, pp.
487
489
.
180.
Begley
,
M. R.
, and
Hutchinson
,
J. W.
, 1998, “
The Mechanics of Size Dependent Indentation
,”
J. Mech. Phys. Solids
0022-5096,
46
, pp.
2049
2068
.
181.
Ibach
,
H.
, 1999, “
The Role of Surface Stress in Reconstruction, Epitaxial Growth and Stabilization of Mesoscopic Structures
,”
Surf. Sci. Rep.
0167-5729,
35
(
1–2
), pp.
71
73
.
182.
Ibach
,
H.
, 1997, “
The Role of Surface Stress in Reconstruction, Epitaxial Growth and Stabilization of Mesoscopic Structures
,”
Surf. Sci. Rep.
0167-5729,
29
(
5–6
), pp.
195
263
.
183.
Bahadur
,
H.
,
Samanta
,
S. B.
,
Srivastava
,
A. K.
,
Sood
,
K. N.
,
Kishore
,
R.
,
Sharma
,
R. K.
,
Basu
,
A.
,
Rashmi
,
Kar
,
M.
,
Pal
,
P.
,
Bhatt
,
V.
, and
Chandra
,
S.
, 2006, “
Nano and Micro Structural Studies of Thin Films of ZnO
,”
J. Mater. Sci.
0022-2461,
41
(
22
), pp.
7562
7570
.
184.
Sharma
,
P.
, and
Ganti
,
S.
, 2005, “
Size-Dependent Eshelby’s Tensor for Embedded Nano-Inclusions Incorporating Surface/Interface Energies
,”
ASME J. Appl. Mech.
0021-8936,
72
(
4
), pp.
628
628
.
185.
Sharma
,
P.
, and
Ganti
,
S.
, 2004, “
Size-Dependent Eshelby’s Tensor for Embedded Nano-Inclusions Incorporating Surface/Interface Energies
,”
ASME J. Appl. Mech.
0021-8936,
71
(
5
), pp.
663
671
.
186.
Sharma
,
P.
, and
Wheeler
,
L. T.
, 2007, “
Size-Dependent Elastic State of Ellipsoidal Nano-Inclusions Incorporating Surface/Interface Tension
,”
ASME J. Appl. Mech.
0021-8936,
74
(
3
), pp.
447
454
.
187.
Fredriksson
,
P.
, and
Gudmundson
,
P.
, 2005, “
Size-Dependent Yield Strength of Thin Films
,”
Int. J. Plast.
0749-6419,
21
(
9
), pp.
1834
1854
.
188.
Fredriksson
,
P.
, and
Gudmundson
,
P.
, 2007, “
Competition Between Interface and Bulk Dominated Plastic Deformation in Strain Gradient Plasticity
,”
Modell. Simul. Mater. Sci. Eng.
0965-0393,
15
(
1
), pp.
S61
S69
.
189.
Noor
,
A. K.
, 1986, “
Global Local Methodologies and Their Applications to Nonlinear Analysis
,”
Finite Elem. Anal. Des.
,
2
, pp.
333
346
. 0168-874X
190.
S. B.
Dong
, 1983, “
Global-Local Finite Element Methods
,”
State of the Art Surveys on Finite Element Technology
,
A. K.
Noor
and
W. D.
Pilkey
, eds.,
ASME
,
New York
, pp.
451
474
.
191.
Belytschko
,
T.
,
Fish
,
J.
, and
Engelmann
,
B. E.
, 1988, “
A Finite-Element With Embedded Localization Zones
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
70
(
1
), pp.
59
89
.
192.
Belytschko
,
T.
, and
Lasry
,
D.
, 1989, “
A Study of Localization Limiters for Strain-Softening in Statics and Dynamics
,”
Comput. Struct.
0045-7949,
33
(
3
), pp.
707
715
.
193.
Belytschko
,
T.
, and
Tabbara
,
M.
, 1993, “
H-Adaptive Finite-Element Methods for Dynamic Problems, With Emphasis on Localization
,”
Int. J. Numer. Methods Eng.
0029-5981,
36
(
24
), pp.
4245
4265
.
194.
Armero
,
F.
, and
Garikipati
,
K.
, 1996, “
An Analysis of Strong Discontinuities in Multiplicative Finite Strain Plasticity and Their Relation With Numerical Simulation of Strain Localization
,”
Int. J. Solids Struct.
0020-7683,
33
, pp.
2863
2885
.
195.
Hughes
,
T. C. R.
, 1995, “
Multiscale Phenomena: Green’s Functions, the Dirichlet to Neumann Formulation, Subgrid Scale Models, Bubbles and the Origin of Stabilized Methods
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
127
, pp.
387
401
.
196.
1975,
Homogenization and Application
,
I.
Babuska
, ed.,
Academic
,
New York
.
197.
Guedes
,
J. M.
, and
Kikuchi
,
N.
, 1990, “
Preprocessing and Postprocessing for Materials Based on the Homogenization Method With Adaptive Finite Element Methods
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
83
, pp.
143
198
.
198.
Abraham
,
F. F.
,
Schneider
,
D.
,
Land
,
B.
,
Lifka
,
D.
,
Skovira
,
J.
,
Gerner
,
J.
, and
Rosenkrantz
,
M.
, 1997, “
Instability Dynamics in Three-Dimensional Fracture: An Atomistic Simulation
,”
J. Mech. Phys. Solids
0022-5096,
45
(
9
), pp.
1461
1471
.
199.
Abraham
,
F. F.
,
Tsai
,
N. H.
, and
Pound
,
G. M.
, 1978, “
Computer-Simulation of an Amorphous Thin-Film on a Crystalline Substrate
,”
Surf. Sci.
0039-6028,
78
(
1
), pp.
181
190
.
200.
Broughton
,
J. Q.
,
Abraham
,
F. F.
,
Bernstein
,
N.
, and
Kaxiras
,
E.
, 1999, “
Concurrent Coupling of Length Scale Methodology and Application
,”
Phys. Rev. B
0163-1829,
60
, pp.
2391
2403
.
201.
Liu
,
W. K.
,
Karpov
,
E. G.
,
Zhang
,
K.
, and
Park
,
H. S.
, 2004, “
An Introduction to Computational Mechanics and Materials
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
193
, pp.
1529
1578
.
202.
Liu
,
W. K.
,
Park
,
H. S.
,
Qian
,
D.
,
Karpov
,
E. G.
,
Kadowaki
,
H.
, and
Wagner
,
G. J.
, 2006, “
Bridging Scale Methods for Nanomechanics and Materials
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
195
, pp.
1407
1421
.
203.
Shilkort
,
L. E.
,
Curtin
,
W. A.
, and
Miller
,
R. E.
, 2002, “
A Coupled Atomistic/Continuum Model of Defects in Solids
,”
J. Mech. Phys. Solids
0022-5096,
50
, pp.
2085
2106
.
204.
Qia
,
D.
,
Wagner
,
G. J.
, and
Lui
,
W. K.
, 2006, “
A Multi Scale Projection Method for the Analysis of Carbon Nanotubes
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
193
, pp.
1579
2601
.
205.
Miller
,
R.
,
Ortiz
,
M.
,
Phillips
,
R.
,
Shenoy
,
V.
, and
Tadmor
,
E. B.
, 1998, “
Quasicontinuum Models of Fracture and Plasticity
,”
Eng. Fract. Mech.
0013-7944,
61
(
3–4
), pp.
427
444
.
206.
Medyanik
,
S. N.
,
Karpov
,
E. G.
, and
Lui
,
W. K.
, 2006, “
Domain Reduction Method for Atomistic Simulation
,”
J. Comput. Phys.
0021-9991,
218
, pp.
836
859
.
207.
Horstemeyer
,
M. F.
,
Baskes
,
M. I.
, and
Plimpton
,
S. J.
, 2001, “
Computational Nanoscale Plasticity Simulations Using Embedded Atom Potentials
,”
Theor. Appl. Fract. Mech.
0167-8442,
37
(
1–3
), pp.
49
98
.
208.
Horstemeyer
,
M. F.
,
Baskes
,
M. I.
,
Prantil
,
V. C.
,
Philliber
,
J.
, and
Vonderheide
,
S.
, 2003, “
A Multiscale Analysis of Fixed-End Simple Shear Using Molecular Dynamics, Crystal Plasticity, and a Macroscopic Internal State Variable Theory
,”
Modell. Simul. Mater. Sci. Eng.
0965-0393,
11
(
3
), pp.
265
286
.
209.
Karpov
,
E. G.
,
Yu
,
H.
,
Park
,
H. S.
,
Liu
,
W. K.
,
Jane
,
Q.
, and
Qian
,
D.
, 2006, “
Multiscale Boundary Conditions in Crystalline Solids: Theory and Application to Nanoindentation
,”
Int. J. Solids Struct.
0020-7683,
43
, pp.
6359
6379
.
210.
Park
,
H. S.
,
Karpov
,
E. G.
,
Lui
,
W. K.
, and
Klein
,
P. A.
, 2005, “
The Bridging Scale Method for Two Dimensional Atomistic/Continuum Coupling
,”
Philos. Mag.
1478-6435,
85
, pp.
79
113
.
211.
de Borst
,
R.
,
Pamin
,
J.
,
Peerlings
,
R. H. J.
, and
Sluys
,
L. J.
, 1995, “
On Gradient-Enhanced Damage and Plasticity Models for Failure in Quasi-Brittle and Frictional Materials
,”
Comput. Mech.
0178-7675,
17
(
1–2
), pp.
130
141
.
212.
Peerlings
,
R. H. J.
,
Geers
,
M. G. D.
,
de Borst
,
R.
, and
Brekelmans
,
W. A. M.
, 2001, “
A Critical Comparison of Nonlocal and Gradient-Enhanced Softening Continua
,”
Int. J. Solids Struct.
0020-7683,
38
(
44–45
), pp.
7723
7746
.
213.
Sluys
,
L. J.
, and
Deborst
,
R.
, 1994, “
Dispersive Properties of Gradient-Dependent and Rate-Dependent Media
,”
Mech. Mater.
0167-6636,
18
(
2
), pp.
131
149
.
214.
Bayliss
,
A.
,
Belytschko
,
T.
,
Kulkarni
,
M.
, and
Lottcrumpler
,
D. A.
, 1994, “
On the Dynamics and the Role of Imperfections for Localization in Thermoviscoplastic Materials
,”
Modell. Simul. Mater. Sci. Eng.
0965-0393,
2
(
5
), pp.
941
964
.
215.
Chen
,
J. S.
,
Zhang
,
X. W.
, and
Belytschko
,
T.
, 2004, “
An Implicit Gradient Model by a Reproducing Kernel Strain Regularization in Strain Localization Problems
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
193
(
27–29
), pp.
2827
2844
.
216.
Lasry
,
D.
, and
Belytschko
,
T.
, 1988, “
Localization Limiters in Transient Problems
,”
Int. J. Solids Struct.
0020-7683,
24
(
6
), pp.
581
597
.
217.
Liu
,
W. K.
,
Hao
,
S.
,
Belytschko
,
T.
,
Li
,
S. F.
, and
Chang
,
C. T.
, 1999, “
Multiple Scale Meshfree Methods for Damage Fracture and Localization
,”
Comput. Mater. Sci.
0927-0256,
16
(
1–4
), pp.
197
205
.
218.
Chen
,
Z.
, and
Schreyer
,
H. L.
, 1990, “
A Numerical-Solution Scheme for Softening Problems Involving Total Strain Control
,”
Comput. Struct.
0045-7949,
37
(
6
), pp.
1043
1050
.
219.
Schreyer
,
H. L.
, 1990, “
Analytical Solutions for Nonlinear Strain-Gradient Softening and Localization
,”
ASME J. Appl. Mech.
0021-8936,
57
(
3
), pp.
522
528
.
220.
Schreyer
,
H. L.
, and
Chen
,
Z.
, 1986, “
One-Dimensional Softening With Localization
,”
ASME J. Appl. Mech.
0021-8936,
53
(
4
), pp.
791
797
.
221.
Oka
,
F.
,
Yashima
,
A.
,
Sawada
,
K.
, and
Aifantis
,
E. C.
, 2000, “
Instability of Gradient-Dependent Elastoviscoplastic Model for Clay and Strain Localization Analysis
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
183
(
1–2
), pp.
67
86
.
222.
Wang
,
W. M.
,
Askes
,
H.
, and
Sluys
,
L. J.
, 1998, “
Gradient Viscoplastic Modelling of Material Instabilities in Metals
,”
Met. Mater. Int.
1598-9623,
4
(
3
), pp.
537
542
.
223.
Ramaswamy
,
A.
,
Barzegar
,
F.
, and
Voyiadjis
,
G. Z.
, 1995, “
Study of Layering Procedures in Finite-Element Analysis of RC Flexural and Torsional Elements
,”
J. Struct. Eng.
0733-9445,
121
(
12
), pp.
1773
1783
.
224.
Bodin
,
D.
,
Pijaudier-Cabot
,
G.
,
de La Roche
,
C.
,
Piau
,
J. M.
, and
Chabot
,
A.
, 2004, “
Continuum Damage Approach to Asphalt Concrete Fatigue Modeling
,”
J. Eng. Mech.
0733-9399,
130
(
6
), pp.
700
708
.
225.
Haidar
,
K.
,
Pijaudier-Cabot
,
G.
,
Dube
,
J. F.
, and
Loukili
,
A.
, 2005, “
Correlation Between the Internal Length, the Fracture Process Zone and Size Effect in Model Materials
,”
Mater. Struct.
1359-5997,
38
(
276
), pp.
201
210
.
226.
Le Bellego
,
C.
,
Dubé
,
L. F.
,
Pijaudier-Cabot
,
G.
, and
Gerard
,
B.
, 2003, “
Calibration of Nonlocal Damage Model From Size Effect Tests
,”
Eur. J. Mech. A/Solids
0997-7538,
22
(
1
), pp.
33
46
.
227.
Pijaudier-Cabot
,
G.
,
Haidar
,
K.
, and
Dubé
,
J. F.
, 2004, “
Non-Local Damage Model With Evolving Internal Length
,”
Int. J. Numer. Analyt. Meth. Geomech.
0363-9061,
28
(
7–8
), pp.
633
652
.
228.
Tinga
,
T.
,
Brekelmans
,
W. A. M.
, and
Geers
,
M. G. D.
, 2008, “
Incorporating Strain Gradient Effects in a Multiscale Constitutive Framework for Nickel-Base Superalloys
,”
Philos. Mag.
1478-6435,
88
(
30–32
), pp.
3793
3825
.
229.
Bayley
,
C. J.
,
Brekelmans
,
W. A. M.
, and
Geers
,
M. G. D.
, 2006, “
A Comparison of Dislocation Induced Back Stress Formulations in Strain Gradient Crystal Plasticity
,”
Int. J. Solids Struct.
0020-7683,
43
(
24
), pp.
7268
7286
.
230.
Engelen
,
R. A. B.
,
Geers
,
M. G. D.
, and
Baaijens
,
F. P. T.
, 2003, “
Nonlocal Implicit Gradient-Enhanced Elasto-Plasticity for the Modelling of Softening Behaviour
,”
Int. J. Plast.
0749-6419,
19
(
4
), pp.
403
433
.
231.
Geers
,
M. G. D.
, 2004, “
Finite Strain Logarithmic Hyperelasto-Plasticity With Softening: A Strongly Non-Local Implicit Gradient Framework
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
193
(
30–32
), pp.
3377
3401
.
232.
Geers
,
M. G. D.
,
de Borst
,
R.
,
Brekelmans
,
W. A. M.
, and
Peerlings
,
R. H. J.
, 1999, “
Validation and Internal Length Scale Determination for a Gradient Damage Model: Application to Short Glass-Fibre-Reinforced Polypropylene
,”
Int. J. Solids Struct.
0020-7683,
36
(
17
), pp.
2557
2583
.
233.
Peerlings
,
R. H. J.
,
Massart
,
T. J.
, and
Geers
,
M. G. D.
, 2004, “
A Thermodynamically Motivated Implicit Gradient Damage Framework and Its Application to Brick Masonry Cracking
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
193
(
30–32
), pp.
3403
3417
.
234.
Benallal
,
A.
, and
Comi
,
C.
, 2005, “
On Interfacial Properties in Gradient Damaging Continua
,”
C. R. Mec.
1631-0721,
333
(
4
), pp.
319
324
.
235.
Comi
,
C.
, 1999, “
Computational Modelling of Gradient-Enhanced Damage in Quasi-Brittle Materials
,”
Mech. Cohesive-Frict. Mater.
1082-5010,
4
(
1
), pp.
17
36
.
236.
Comi
,
C.
, and
Corigliano
,
A.
, 1996, “
On Uniqueness of the Dynamic Finite-Step Problem in Gradient-Dependent Softening Plasticity
,”
Int. J. Solids Struct.
0020-7683,
33
(
26
), pp.
3881
3902
.
237.
Comi
,
C.
, and
Perego
,
U.
, 1996, “
A Generalized Variable Formulation for Gradient Dependent Softening Plasticity
,”
Int. J. Numer. Methods Eng.
0029-5981,
39
(
21
), pp.
3731
3755
.
238.
Dorgan
,
R. J.
, and
Voyiadjis
,
G. Z.
, 2007, “
Nonlocal Coupled Damage-Plasticity Model Incorporating Functional Forms of Hardening State Variables
,”
AIAA J.
0001-1452,
45
(
2
), pp.
337
346
.
239.
Dorgan
,
R. J.
, and
Voyiadjis
,
G. Z.
, 2006, “
A Mixed Finite Element Implementation of a Gradient-Enhanced Coupled Damage-Plasticity Model
,”
Int. J. Damage Mech.
1056-7895,
15
(
3
), pp.
201
235
.
240.
Voyiadjis
,
G. Z.
, and
Dorgan
,
R. J.
, 2004, “
Bridging of Length Scales Through Gradient Theory and Diffusion Equations of Dislocations
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
193
(
17–20
), pp.
1671
1692
.
241.
Fremond
,
M.
, and
Nedjar
,
B.
, 1996, “
Damage, Gradient of Damage and Principle of Virtual Power
,”
Int. J. Solids Struct.
0020-7683,
33
(
8
), pp.
1083
1103
.
242.
Aluru
,
N. R.
, and
White
,
J.
, 1999, “
A Multilevel Newton Method for Mixed-Energy Domain Simulation of MEMS
,”
J. Microelectromech. Syst.
1057-7157,
8
(
3
), pp.
299
308
.
243.
Aluru
,
N. R.
, and
White
,
J.
, 1997, “
An Efficient Numerical Technique for Electromechanical Simulation of Complicated Microelectromechanical Structures
,”
Sens. Actuators, A
0924-4247,
58
(
1
), pp.
1
11
.
244.
Aluru
,
R.
,
Keefe
,
M.
, and
Advani
,
S.
, 2001, “
Simulation of Injection Molding Into Rapid-Prototyped Molds
,”
Rapid Prototyping J.
1355-2546,
7
(
1
), pp.
42
51
.
245.
Chatterjee
,
A. N.
, and
Aluru
,
N. R.
, 2005, “
Combined Circuit/Device Modeling and Simulation of Integrated Microfluidic Systems
,”
J. Microelectromech. Syst.
1057-7157,
14
(
1
), pp.
81
95
.
246.
Chatterjee
,
A. N.
,
Cannon
,
D. M.
,
Gatimu
,
E. N.
,
Sweedler
,
J. V.
,
Aluru
,
N. R.
, and
Bohn
,
P. W.
, 2005, “
Modeling and Simulation of Ionic Currents in Three-Dimensional Microfluidic Devices With Nanofluidic Interconnects
,”
J. Nanopart. Res.
1388-0764,
7
(
4–5
), pp.
507
516
.
247.
Joseph
,
S.
, and
Aluru
,
N. R.
, 2006, “
Hierarchical Multiscale Simulation of Electrokinetic Transport in Silica Nanochannels at the Point of Zero Charge
,”
Langmuir
0743-7463,
22
(
21
), pp.
9041
9051
.
248.
Qiao
,
R.
, and
Aluru
,
N. R.
, 2005, “
Atomistic Simulation of KCl Transport in Charged Silicon Nanochannels: Interfacial Effects
,”
Colloids Surf., A
0927-7757,
267
(
1–3
), pp.
103
109
.
249.
Wang
,
X.
,
Kanapka
,
J.
,
Ye
,
W. J.
,
Aluru
,
N. R.
, and
White
,
J.
, 2006, “
Algorithms in FastStokes and Its Application to Micromachined Device Simulation
,”
IEEE Trans. Comput.-Aided Des.
0278-0070,
25
(
2
), pp.
248
257
.
250.
Phillips
,
R.
,
Rodney
,
D.
,
Shenoy
,
V.
,
Tadmor
,
E.
, and
Ortiz
,
M.
, 1999, “
Hierarchical Models of Plasticity: Dislocation Nucleation and Interaction
,”
Modell. Simul. Mater. Sci. Eng.
0965-0393,
7
(
5
), pp.
769
780
.
251.
Tadmor
,
E. B.
,
Miller
,
R.
,
Phillips
,
R.
, and
Ortiz
,
M.
, 1999, “
Nanoindentation and Incipient Plasticity
,”
J. Mater. Res.
0884-2914,
14
(
6
), pp.
2233
2250
.
252.
Lill
,
J. V.
, and
Broughton
,
J. Q.
, 2000, “
Molecular Dynamics Simulation of a Glissile Dislocation Interface Propagating a Martensitic Transformation
,”
Phys. Rev. Lett.
0031-9007,
84
(
25
), pp.
5784
5787
.
253.
Mullins
,
M.
, 1982, “
Molecular-Dynamics Simulation of Propagating Cracks
,”
Scr. Metall.
0036-9748,
16
(
6
), pp.
663
666
.
254.
Broughton
,
J. Q.
,
Bonissent
,
A.
, and
Abraham
,
F. F.
, 1981, “
The Fcc (111) and (100) Crystal-Melt Interfaces—A Comparison by Molecular-Dynamics Simulation
,”
J. Chem. Phys.
0021-9606,
74
(
7
), pp.
4029
4039
.
255.
Buehler
,
M. J.
,
Hartmaier
,
A.
,
Duchaineau
,
M. A.
,
Abraham
,
F. R.
, and
Gao
,
H. J.
, 2005, “
The Dynamical Complexity of Work-Hardening: A Large-Scale Molecular Dynamics Simulation
,”
Acta Mech. Sin.
0459-1879,
21
(
2
), pp.
103
111
.
256.
Buehler
,
M. J.
,
Hartmaier
,
A.
,
Gao
,
H. J.
,
Duchaineau
,
M.
, and
Abraham
,
F. F.
, 2004, “
Atomic Plasticity: Description and Analysis of a One-Billion Atom Simulation of Ductile Materials Failure
,”
Comput. Methods Appl. Mech. Eng.
0045-7825,
193
(
48–51
), pp.
5257
5282
.
257.
Lidorikis
,
E.
,
Bachlechner
,
M. E.
,
Kalia
,
R. K.
,
Nakano
,
A.
, and
Vashishta
,
P.
, 2005, “
Coupling Atomistic and Continuum Length Scales in Heteroepitaxial Systems: Multiscale Molecular-Dynamics/Finite-Element Simulations of Strain Relaxation in Si/Si3N4 Nanopixels
,”
Phys. Rev. B
0163-1829,
72
(
11
), p.
115338
.
258.
Koh
,
S. J. A.
, and
Lee
,
H. P.
, 2006, “
Molecular Dynamics Simulation of Size and Strain Rate Dependent Mechanical Response of FCC Metallic Nanowires
,”
Nanotechnology
0957-4484,
17
(
14
), pp.
3451
3467
.
259.
Koh
,
S. J. A.
,
Lee
,
H. P.
,
Lu
,
C.
, and
Cheng
,
Q. H.
, 2005, “
Molecular Dynamics Simulation of a Solid Platinum Nanowire Under Uniaxial Tensile Strain: Temperature and Strain-Rate Effects
,”
Phys. Rev. B
0163-1829,
72
(
8
), p.
085414
.
260.
Ling
,
X. W.
,
Horstemeyer
,
M. F.
, and
Potirniche
,
G. P.
, 2005, “
On the Numerical Implementation of 3D Rate-Dependent Single Crystal Plasticity Formulations
,”
Int. J. Numer. Methods Eng.
0029-5981,
63
(
4
), pp.
548
568
.
261.
Potirniche
,
G. P.
,
Horstemeyer
,
M. F.
, and
Ling
,
X. W.
, 2007, “
An Internal State Variable Damage Model in Crystal Plasticity
,”
Mech. Mater.
0167-6636,
39
(
10
), pp.
941
952
.
262.
Groh
,
S.
,
Marin
,
E. B.
,
Horstemeyer
,
M. F.
, and
Xbib
,
H. M.
, 2008, “
Multiscale Modeling of the Plasticity in an Aluminum Single Crystal
,”
Int. J. Plast.
0749-6419,
25
, pp.
1456
1473
.
263.
Ogata
,
S.
,
Lidorikis
,
E.
,
Shimojo
,
F.
,
Nakano
,
A.
,
Vashishta
,
P.
, and
Kalia
,
R. K.
, 2001, “
Hybrid Finite-Element/Molecular-Dynamics/Electronic-Density-Functional Approach to Materials Simulations on Parallel Computers
,”
Comput. Phys. Commun.
0010-4655,
138
(
2
), pp.
143
154
.
264.
Bachlechner
,
M. E.
,
Omeltchenko
,
A.
,
Nakano
,
A.
,
Kalia
,
R. K.
,
Vashishta
,
P.
,
Ebbsjo
,
I.
,
Madhukar
,
A.
, and
Messina
,
P.
, 1998, “
Multimillion-Atom Molecular Dynamics Simulation of Atomic Level Stresses in Si(111)/Si3N4(0001) Nanopixels
,”
Appl. Phys. Lett.
0003-6951,
72
(
16
), pp.
1969
1971
.
265.
Bachlechner
,
M. E.
,
Srivastava
,
D.
,
Owens
,
E. T.
,
Schiffbauer
,
J.
,
Anderson
,
J. T.
,
Burky
,
M. R.
,
Ducatman
,
S. C.
,
Gripper
,
A. M.
,
Guffey
,
E. J.
, and
Ramos
,
F. S.
, 2006, “
Mechanisms of Pit Formation at Strained Crystalline Si(111)/Si3N4(0001) interfaces: Molecular-Dynamics Simulations
,”
Phys. Rev. B
0163-1829,
74
(
7
), p.
075327
.
266.
Bachlechner
,
M. E.
,
Zhang
,
J.
,
Wang
,
Y.
,
Schiffbauer
,
J.
,
Knudsen
,
S. R.
, and
Korakakis
,
D.
, 2005, “
Molecular Dynamics Simulations of the Mechanical Strength of Si/Si3N4 Interfaces
,”
Phys. Rev. B
0163-1829,
72
(
9
), p.
094115
.
267.
Donev
,
A.
,
Torquato
,
S.
, and
Stillinger
,
F. H.
, 2005, “
Neighbor List Collision-Driven Molecular Dynamics Simulation for Nonspherical Hard Particles. II. Applications to Ellipses And Ellipsoids
,”
J. Comput. Phys.
0021-9991,
202
(
2
), pp.
765
793
.
268.
Stillinger
,
F. H.
, and
Weber
,
T. A.
, 1988, “
Molecular-Dynamics Simulation for Chemically Reactive Substances—Fluorine
,”
J. Chem. Phys.
0021-9606,
88
(
8
), pp.
5123
5133
.
269.
Stillinger
,
F. H.
, and
Weber
,
T. A.
, 1978, “
Study of Melting and Freezing in Gaussian Core Model by Molecular-Dynamics Simulation
,”
J. Chem. Phys.
0021-9606,
68
(
8
), pp.
3837
3844
.
270.
Stillinger
,
F. H.
, and
Weber
,
T. A.
, 1981, “
Computer-Simulation of Proton Hydration Dynamics
,”
Chem. Phys. Lett.
0009-2614,
79
(
2
), pp.
259
260
.
271.
Bachlechner
,
M. E.
,
Kalia
,
R. K.
,
Nakano
,
A.
,
Omeltchenko
,
A.
,
Vashishta
,
P.
,
Ebbsjo
,
I.
,
Madhukar
,
A.
, and
Zhao
,
G. L.
, 1999, “
Structural Correlations at Si/Si3N4 Interface and Atomic Stresses in Si/Si3N4 Nanopixel-10 Million-Atom Molecular Dynamics Simulation on Parallel Computers
,”
J. Eur. Ceram. Soc.
0955-2219,
19
(
13–14
), pp.
2265
2272
.
272.
Fan
,
J. D.
,
Zhao
,
G. L.
,
Edis
,
T.
, and
Malozovsky
,
Y. M.
, 1997, “
Molecular-Dynamics-Simulation Study of the Two-Dimensional Lattice Structure of the Cu-1 Plane in YBa2Cu3O6+x
,”
Phys. Rev. B
0163-1829,
56
(
17
), pp.
10747
10750
.
273.
Ackbarow
,
T.
, and
Buehler
,
M. J.
, 2007, “
Superelasticity, Energy Dissipation and Strain Hardening of Vimentin Coiled-Coil Intermediate Filaments: Atomistic and Continuum Studies
,”
J. Mater. Sci.
0022-2461,
42
(
21
), pp.
8771
8787
.
274.
Buehler
,
M. J.
, 2006, “
Mechanics of Protein Crystals: Atomistic Modeling of Elasticity and Fracture
,”
J. Comput. Theor. Nanosci.
1546-1955,
3
(
5
), pp.
670
683
.
275.
Buehler
,
M. J.
, 2006, “
Atomistic and Continuum Modeling of Mechanical Properties of Collagen: Elasticity, Fracture, and Self-Assembly
,”
J. Mater. Res.
0884-2914,
21
(
8
), pp.
1947
1961
.
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