Abstract

Throughout his career, Zbib was innovative, originating models in seminal papers that anticipated areas of subsequent increased interest. These include strain-gradient plasticity, discrete dislocation dynamics, multiscale modeling, arrays of Somigliana ring dislocations and nanoscale plasticity. We comment here on these aspects of his work. Many of the papers in this volume represent applications of these ideas.

References

1.
Zbib
,
H. M.
, and
Aifantis
,
E. C.
,
1988
, “
On the Concept of Relative and Plastic Spins and its Implications to Large Deformation Theories. Part I: Hypoelasticity and Vertex-Type Plasticity
,”
Acta Mech.
,
75
(
1–4
), pp.
15
33
.
2.
Zbib
,
H. M.
, and
Aifantis
,
E. C.
,
1988
, “
On the Concept of Relative and Plastic Spins and Its Implications to Large Deformation Theories. Part II: Anisotropic Hardening Plasticity
,”
Acta Mech.
,
75
(
1–4
), pp.
35
56
.
3.
Fleck
,
N. A.
,
Muller
,
G. M.
,
Ashby
,
M. F.
, and
Hutchinson
,
J. W.
,
1994
, “
Gradient Plasticity Theory and Experiment
,”
Acta Metall.
,
42
(
2
), pp.
475
487
.
4.
Gao
,
H.
,
Huang
,
Y.
,
Nix
,
W. D.
, and
Hutchinson
,
J. W.
,
1999
, “
Mechanism Based Strain Gradient Plasticity
,”
J. Mech. Phys. Solids
,
47
(
6
), pp.
1239
1263
.
5.
Zbib
,
H. M.
,
1988
, “
Deformations of Materials Exhibiting Noncoaxiality and Finite Rotations
,”
Scr. Metall.
,
23
(
5
), pp.
789
794
.
6.
Zbib
,
H. M.
,
1991
, “
On the Mechanics of Large Inelastic Deformations: Noncoaxiality, Axial Effects in Torsion and Localization
,”
Acta Mech.
,
87
(
3–4
), pp.
179
196
.
7.
Akarapu
,
S.
, and
Hirth
,
J. P.
,
2013
, “
Dislocation Pile-Ups in Stress Gradients Revisited
,”
Acta Mater.
,
61
(
10
), pp.
3621
3629
.
8.
Zbib
,
H. M.
,
1988
, “
Strain Gradients and Size Effects in Nonhomogeneous Plastic Deformation
,”
Scr. Metall. Mater.
,
30
(
9
), pp.
1223
1226
.
9.
Zbib
,
H. M.
,
1991
, “
On the Mechanics of Large Inelastic Deformations: Kinematics and Constitutive Modeling
,”
Acta Mech.
,
96
(
1–4
), pp.
119
138
.
10.
Zbib
,
H. M.
, and
Aifantis
,
E. C.
,
1988
, “
On the Structure and Width of Shear Bands
,”
Scr. Metall.
,
22
(
5
), pp.
703
708
.
11.
Zhu
,
H. T.
, and
Zbib
,
H. M.
,
1995
, “
On the Role of Strain Gradients in Adiabatic Shear Banding
,”
Acta Mech.
,
111
(
1–2
), pp.
111
124
.
12.
Rhee
,
M.
,
Hirth
,
J. P.
, and
Zbib
,
H. M.
,
1994
, “
A Superdislocation Model for the Strengthening of Metal Matrix Composites and the Initiation and Propagation of Shear Bands
,”
Acta Metall. Mater.
,
42
(
8
), pp.
2645
2655
.
13.
Khraishi
,
T. A.
,
Zbib
,
H. M.
, and
De La Rubia
,
T. D.
,
2001
, “
The Treatment of Traction-Free Boundary Condition in Three-Dimensional Dislocation Dynamic Using Generalized Image Stress Analysis
,”
Mater. Sci. Eng. A
,
309
(
3
), pp.
283
287
.
14.
Rhee
,
M.
,
Stolken
,
J. S.
,
Bulatov
,
V. V.
,
De La Rubia
,
T. D.
,
Zbib
,
H. M.
, and
Hirth
,
J. P.
,
2001
, “
Dislocation Stress Fields for Dynamic Codes Using Anisotropic Elasticity: Methodology and Analysis
,”
Mater. Sci. Eng. A
,
309
(
3
), pp.
288
293
.
15.
Khraishi
,
T. A.
, and
Zbib
,
H. M.
,
2002
, “
Free-Surface Effects in 3D Dislocation Dynamics: Formulation and Modeling
,”
ASME J. Eng. Mater. Technol.
,
124
(
3
), pp.
342
351
.
16.
Alankar
,
A.
,
Field
,
D. P.
, and
Zbib
,
H. M.
,
2012
, “
Explicit Incorporation of Cross-Slip in a Dislocation Density-Based Crystal Plasticity Model
,”
Philos. Mag.
,
92
(
24
), pp.
3084
3100
.
17.
Alankar
,
A.
,
Mastorakos
,
I. N.
,
Field
,
D. P.
, and
Zbib
,
H. M.
,
2012
, “
Determination of Dislocation Interaction Strengths Using Discrete Dislocation Dynamics of Curved Dislocations
,”
ASME J. Eng. Mater. Technol.
,
134
(
4
), p.
021018
.
18.
Zbib
,
H. M.
,
Diaz de la Rubia
,
T.
, and
Bulatov
,
V. V.
,
2002
, “
A Multiscale Model of Plasticity Based on Discrete Dislocation Dynamics
,”
ASME J. Eng. Mater. Technol.
,
124
(
1
), pp.
78
87
.
19.
Groh
,
S.
, and
Zbib
,
H. M.
,
2009
, “
Advances in Discrete Dislocations Dynamics and Multiscale Modeling
,”
ASME J. Eng. Mater. Technol.
,
131
(
4
), p.
041209
.
20.
Anderson
,
P. M.
,
Hirth
,
J. P.
, and
Lothe
,
J.
,
2017
,
Theory of Dislocations
, 3rd ed.,
Cambridge University Press
,
Cambridge
.
21.
Khraisheh
,
M. K.
,
Zbib
,
H. M.
,
Hamilton
,
C. H.
, and
Bayoumi
,
A. E.
,
1997
, “
Constitutive Modeling of Superplastic Deformation. Part I: Theory and Experiments
,”
Int. J. Plast.
,
13
(
1–2
), pp.
143
164
.
22.
Zbib
,
H. M.
, and
Bahr
,
D. F.
,
2011
, “Challenges Below the Grain Scale and Multiscale Models,”
Comput. Meth. Microstr.-Prop. Relation.
,
S
Ghosh
, and
D
Dimiduk
, eds.,
Springer
,
Berlin
, pp.
555
590
.
23.
Hirth
,
J. P.
,
Zbib
,
H. M.
, and
Lothe
,
J.
,
1993
, “
Forces on High Velocity Dislocations
,”
Modell. Simul. Mater. Sci. Eng.
,
6
(
2
), pp.
165
169
.
24.
Shehadeh
,
M. A.
,
Zbib
,
H. M.
, and
Diaz de La Rubia
,
T.
,
2005
, “
Multiscale Dislocation Dynamics Simulations of Shock Compression in Copper Single Crystal
,”
Int. J. Plast.
,
21
(
12
), pp.
2369
2390
.
25.
Demir
,
I.
,
Hirth
,
J. P.
, and
Zbib
,
H. M.
,
1993
, “
The Somigliana Ring Dislocation
,”
J. Elasticity
,
28
(
3
), pp.
223
246
.
26.
Khraishi
,
T. A.
,
Hirth
,
J. P.
,
Zbib
,
H. M.
, and
de La Rubia
,
T. D.
,
2000
, “
The Stress Field of a General Circular Volterra Dislocation Loop: Analytical and Numerical Approaches
,”
Philos. Mag. Lett.
,
80
(
2
), pp.
95
105
.
27.
Demir
,
I.
, and
Zbib
,
H. M.
,
1994
, “
Interface Ring Dislocation in Fiber-Matrix Composites: Approximate Analytical Solution
,”
ASME J. Eng. Mater. Technol.
,
116
(
3
), pp.
279
285
.
28.
Demir
,
I.
, and
Khraishi
,
T. A.
,
2005
, “
The Torsional Dislocation Loop and Mode III Cylindrical Crack
,”
J. Mech.
,
21
(
2
), pp.
109
116
.
29.
Hirth
,
J. P.
, and
Armstrong
,
R. W.
,
2021
, “
Straight and Curved Disclinations and Dislocation Equivalents
,”
Philos. Mag.
,
101
(
1
), pp.
25
37
.
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