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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