Issues related to the construction of continuum theories of strain gradient plasticity which have emerged in recent years are reviewed and brought to bear on the formulation of the most basic theories. Elastic loading gaps which can arise at initial yield or under imposition of nonproportional incremental boundary conditions are documented and analytical methods for dealing with them are illustrated. The distinction between unrecoverable (dissipative) and recoverable (energetic) stress quantities is highlighted with respect to elastic loading gaps, and guidelines for eliminating the gaps are presented. An attractive gap-free formulation that generalizes the classical J2 flow theory is identified and illustrated.

References

References
1.
Fleck
,
N. A.
,
Hutchinson
,
J. W.
, and
Willis
,
J. R.
,
2014
, “
Strain Gradient Plasticity Under Non-Proportional Loading
,”
Proc. R. Soc., A
,
470
(2170), p.
20140267
.10.1098/rspa.2014.0267
2.
Bardella
,
L.
, and
Panteghini
,
A.
,
2015
, “
Modelling the Torsion of Thin Metal Wires by Distortion Gradient Plasticity
,”
J. Mech. Phys. Solids
,
78
, pp.
467
492
.10.1016/j.jmps.2015.03.003
3.
Gurtin
,
M. E.
,
2003
, “
On a Framework for Small-Deformation Viscoplasticity: Free Energy, Microforces, Strain Gradients
,”
Int. J. Plast.
,
19
(1), pp.
47
90
.10.1016/S0749-6419(01)00018-3
4.
Gudmundson
,
P. A.
,
2004
, “
A Unified Treatment of Strain Gradient Plasticity
,”
J. Mech. Phys. Solids
,
52
(6), pp.
1379
1406
.10.1016/j.jmps.2003.11.002
5.
Gurtin
,
M. E.
, and
Anand
,
L.
,
2005
, “
A Theory of Strain-Gradient Plasticity for Isotropic, Plastically Irrotational Materials. Part I: Small Deformations
,”
J. Mech. Phys. Solids
,
53
(7), pp.
1624
1649
.10.1016/j.jmps.2004.12.008
6.
Fleck
,
N. A.
, and
Hutchinson
,
J. W.
,
1997
, “
Strain Gradient Plasticity
,”
Adv. Appl. Mech.
,
33
, pp.
295
361
.10.1016/S0065-2156(08)70388-0
7.
Muhlhaus
,
H. B.
, and
Aifantis
,
E. C.
,
1991
, “
A Variational Principle for Gradient Plasticity
,”
Int. J. Solids Struct.
,
28
(
7
), pp.
845
857
.10.1016/0020-7683(91)90004-Y
8.
Fleck
,
N. A.
, and
Willis
,
J. R.
,
2009
,“
A Mathematical Basis for Strain Gradient Plasticity Theory. Part I: Scalar Plastic Multiplier. Part II: Tensorial Plastic Multiplier
,”
J. Mech. Phys. Solids
,
57
(
1
), pp.
161
177
.10.1016/j.jmps.2008.09.010
9.
Hutchinson
,
J. W.
,
2012
, “
Generalizing J2 Flow Theory: Fundamental Issues in Strain gradient Plasticity
,”
Acta Mech. Sin.
,
28
(
4
), pp.
1078
1086
.10.1007/s10409-012-0089-4
10.
Forest
,
S.
, and
Sievert
,
R.
,
2003
, “
Elastoviscoplastic Constitutive Frameworks for Generalized Continua
,”
Acta Mech.
,
160
(
12
), pp.
71
111
.10.1007/s00707-002-0975-0
11.
Danas
,
K.
,
Deshpande
,
V. S.
, and
Fleck
,
N. A.
,
2010
, “
Compliant Interfaces: A Mechanism for Relaxation of Dislocation Pile-Ups in a Sheared Single Crystal
,”
Int. J. Plast.
,
26
(
12
), pp.
1792
1805
.10.1016/j.ijplas.2010.03.008
12.
Fleck
,
N. A.
,
Muller
,
G. M.
,
Ashby
,
M. F.
, and
Hutchinson
,
J. W.
,
1994
, “
Strain Gradient Plasticity: Theory and Experiment
,”
Acta Metall. Mater.
,
42
(
2
), pp.
475
487
.10.1016/0956-7151(94)90502-9
13.
Nix
,
W. D.
, and
Gao
,
H.
,
1998
, “
Indentation Size Effects in Crystalline Materials: A Law for Strain Gradient Plasticity
,”
J. Mech. Phys. Solids
,
46
(
3
), pp.
411
425
.10.1016/S0022-5096(97)00086-0
14.
Niordson
,
C. N.
, and
Legarth
,
B. N.
,
2010
, “
Strain Gradient Effects in Cyclic Plasticity
,”
J. Mech. Phys. Solids
,
58
(4), pp.
542
557
.10.1016/j.jmps.2010.01.007
15.
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
,
51
(
2
), pp.
281
310
.10.1016/S0022-5096(02)00081-9
16.
Ohno
,
N.
, and
Okumura
,
D.
,
2007
, “
Higher-Order Stress and Grain Size Effects Due to Self-Energy of Geometrically Necessary Dislocations
,”
J. Mech. Phys. Solids
,
55
(
9
), pp.
1879
1898
.10.1016/j.jmps.2007.02.007
17.
Evans
,
A. G.
, and
Hutchinson
,
J. W.
,
2009
, “
A Critical Assessment of Theories of Strain Gradient Plasticity
,”
Acta Mater.
,
57
(
5
), pp.
1675
1688
.10.1016/j.actamat.2008.12.012
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