This work is focused on the comparison between the two strain localization techniques namely, the viscoplasticity and the gradient dependent theory. In the first approach a length-scale parameter is introduced implicitly through viscosity in order to address strain localization and material instability in the (initial) boundary value problems. The second approach is the enhanced nonlocal gradient-dependent theory which formulates a constitutive framework on the continuum level that is used to bridge the gap between the micromechanical theories and the classical (local) continuum. It is successful in explaining the size effects encountered at the micron scale and in preserving the well-posedeness of the (initial) boundary value problems governing the solution of material instability triggering strain localization. This is due to the explicit incorporation of an intrinsic material length scale parameter in the constitutive description. These numerical examples prove the excellent performance of the present frameworks in describing the strain localization problem.

1.
Perzyna, P., 1966 “Fundamental Problems Viscoplasticity,” In: Kuerti, H. (Ed.), Advances in Applied Mechaics, Academic Press, 9, pp. 243–377.
2.
Loret
B.
and
Prevost
H.
,
1990
, “
Dynamics Strain Localization in Elasto-(Visco-)Plastic Solids, Part 1. General Formulation and One-Dimensional Examples
,”
Computer Methods in Applied Mechanics and Engineering
,
83
, pp.
247
273
.
3.
Sluys LJ., 1992, Wave Propagation, Localization and Dispersion in Softening Solids, Ph.D. Thesis, Delft University of Technology, Netherlands.
4.
Needleman
A.
,
1988
, “
Material Rate Dependent and Mesh Sensitivity in Localization Problems
,”
Computer Methods in Applied Mechanics and Engineering
,
67
, pp.
68
85
.
5.
Wang
W. M.
,
Sluys
L. J.
, and
de Borst
R.
,
1996
, “
Interaction Between Material Length Scale and Imperfection size for Localization Phenomena in Viscoplastic Media
,”
European Journal of Mechanics, A/Solids
,
15
, pp.
447
464
.
6.
Abu Al-Rub, R. K., 2004, “Material Length Scales in Gradient-Dependent Plasticity/Damage and Size Effects: Theory and Computation,” Ph.D. Thesis, Louisiana State University, Baton Rouge, LA.
7.
Aifantis
E. C.
,
1984
, “
On the Microstructural Origin of Certain Inelastic Models
,”
J. of Eng. Materials and Tech.
,
106
, pp.
326
330
.
8.
Mu¨hlhaus
H. B.
, and
Aifantis
E. C.
,
1991
, “
A Variational Principle for Gradient Plasticity
,”
Int. J. of Solid and Structures
,
28
, pp.
845
857
.
9.
de Borst
R.
, and
Mu¨hlhaus
H.-B.
,
1992
, “
Gradient-Dependent Plasticity Formulation and Algorithmic Aspects
,”
Int. J. Numer. Methods Engrg.
,
35
, pp.
521
539
.
10.
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
,”
Archives of Mechanics
,
55
, pp.
39
89
.
11.
Voyiadjis
G. Z.
,
Abu Al-Rub
R. K.
,
Palazotto
A. N.
,
2004
, “
Thermodynamic Formulations for Non-Local Coupling of Viscoplasticity and Anisotropic Viscodamage for Dynamic Localization Problems Using Gradient Theory
,”
International Journal of Plasticity
,
20
, pp.
981
1038
.
12.
Abu Al-Rub
R. K.
, and
Voyiadjis
G. Z.
,
2005
, “
A Direct Finite Element Implementation of the Gradient Plasticity Theory
,”
International Journal for Numerical Methods in Engineering
,
63
, pp.
603
629
.
13.
de Borst
R.
, and
Pamin
J.
,
1996
, “
Some Novel Developments in Finite Element Procedures for Gradient-Dependent Plasticity
,”
International Journal for Numerical Methods in Engineering
,
39
, pp.
2477
2505
.
14.
ABAQUS User Manual, Version 6.3, Habbitt, Karlsson and Sorensen, Inc: Providence, RI, 2003.
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