A constitutive model for finite elastoplastic deformations is presented. This model incorporates two novel features: first, a strain-hardening law that is applicable to complex loading paths and histories; and second, an objective stress-rate measure that is based on the spin of an orthogonal triad of material unit vectors which instantaneously coincides with the principal directions of the stress tensor. Problems of shear superposed on triaxial tension, cyclic shear deformation, and biaxial nonproportional loading are studied. It is shown that realistic predictions for the aforementioned problems are obtained by using the proposed constitutive model.
Issue Section:
Technical Papers
1.
Bell
J. F.
1983
, “Continuum Plasticity at Finite Strain for Stress Path of Arbitrary Composition and Direction
,” Archive for Rational Mechanics and Analysis
, Vol. 84
, pp. 139
–170
.2.
Bell
J. F.
1990
, “Material Objectivity in an Experimentally Based Incremental Theory of Large Finite Plastic Strain
,” International Journal of Plasticity
, Vol. 6
, pp. 293
–314
.3.
Chaboche
J. L.
1989
, “Constitutive Equations for Cyclic Plasticity and Cyclic Viscoplasticity
,” International Journal of Plasticity
, Vol. 5
, pp. 247
–302
.4.
Dafalias, Y. F., 1985a, “A Missing Link in the Macroscopic Constitutive Formulation of Large Plastic Deformation,” Plasticity Today, Modelling, Methods and Application, A. Sawczuk and G. Bianchi, eds., Elsevier, London, pp. 135–151.
5.
Dafalias
Y. F.
1985
b, “The Plastic Spin
,” ASME JOURNAL OF APPLIED MECHANICS
, Vol. 52
, pp. 865
–871
.6.
Dafalias
Y. F.
Popov
E. P.
1976
, “Plastic Internal Variables Formalism of Cyclic Plasticity
,” ASME JOURNAL OF APPLIED MECHANICS
, Vol. 43
, pp. 645
–651
.7.
Dienes
J. K.
1979
, “On the Analysis of Rotation and Stress Rate in Deforming Bodies
,” Acta Mechanica
, Vol. 32
, pp. 217
–232
.8.
EI-Rafei, A. M., 1980, “Etude experimentale et comparative des aciers ecourissables soumis a des deformation finies,” M.Sc. thesis, IV-258, Universite´ de Sherbrooke, Sherbrooke, PQ, Canada.
9.
Ellyin
F.
Xia
Z.
1989
, “A Rate-Independent Constitutive Model for Transient Nonproportional Loading
,” Journal of Mechanics and Physics of Solids
, Vol. 37
, pp. 71
–91
.10.
Ellyin
F.
Xia
Z.
1991
, “A Rate-Dependent Inelastic Constitutive Model—Part I: Elastic-Plastic Flow
,” ASME Journal of Engineering Materials and Technology
, Vol. 113
, pp. 314
–323
.11.
Green
A. E.
Naghdi
P. M.
1965
, “A General Theory of an Elastic-Plastic Continuum
,” Archive for Rational Mechanics and Analysis
, Vol. 18
, pp. 251
–281
.12.
Harren
S.
Lowe
T. C.
Asaro
R. J.
Needleman
A.
1989
, “Analysis of Large-Strain Shear in Rate-Dependent Face-Centred Cubic Polycrystals: Correlation of Micro- and Macromechanics
,” Philosophical Transactions of Royal Society of London
, Vol. A328
, pp. 493
–500
.13.
Krempl
E.
McMahon
J. J.
Yao
D.
1986
, “Viscoplasticity Based on Overstress with a Differential Growth Law for the Equilibrium Stress
,” Mechanics of Materials
, Vol. 5
, pp. 35
–48
.14.
Lee, E. H., and Wertheimer, T. B., 1983, “Deformation Analysis of Simple Shear Loading with Anisotropic Hardening in Finite Deformation Plasticity,” Recent Developments in Computing Methods for Nonlinear Solids and Structural Mechanics, ASME Applied Mechanics Div. Symp., June 20–22, pp. 297–310.
15.
Masing, G., 1926, “Eigenspannungen und Verfestigung beim Messing,” Proceedings of 2nd International Congress of Applied Mechanics, Zurich, pp. 332–335.
16.
McDowell
D. L.
1985
, “A Two Surface Model for Transient Nonproportional Cyclic Plasticity: Part I—Development of Appropriate Equations; Part II—Comparison of Theory with Experiments
,” ASME JOURNAL OF APPLIED MECHANICS
, Vol. 52
, pp. 298
–308
.17.
Miller
A. K.
1976
, “An Inelastic Constitutive Model for Monotonic, Cyclic and Creep Deformation: Part I—Equations Development and Analytical Procedures
,” ASME Journal of Engineering Materials and Technology
, Vol. 99
, pp. 97
–105
.18.
Moosbrugger
J. C.
McDowell
D. L.
1990
, “A Rate-Dependent Bounding Surface Model with a Generalized Image Point for Cyclic Nonproportional Viscoplasticity
,” Journal of Mechanics and Physics of Solids
, Vol. 38
, pp. 627
–656
.19.
Mroz
Z.
1967
, “An Attempt to Describe the Behaviour of Metals under Cyclic Loads Using a More General Work Hardening Model
,” Acta Mechanica
, Vol. 7
, pp. 199
–212
.20.
Nagtegall, J. C., and de Jong, J. E., 1982, “Some Aspects of Non-Isotropic Work-Hardening in Finite Strain Plasticity,” Proceedings of the Workshop on Plasticity of Metals at Finite Strain: Theory, Experiment and Computation, E. H. Lee and R. L. Mallet, eds., R.P.I., Troy, NY, pp. 65–102.
21.
Paulun
J. E.
Pecherski
R. B.
1985
, “Study of Corotational Rates for Kinematic Hardening in Finite Deformation Plasticity
,” Archives of Mechanics
, Vol. 37
, pp. 661
–667
.22.
Wang
C. C.
1970
, “A New Representation Theorem for Isotropic Functions: An Answer to Professor G. F. Smith’s Criticism of My Paper on Representations for Isotropic Functions
,” Archive for Rational Mechanics and Analysis
, Vol. 36
, pp. 198
–223
.23.
Wineman
A.
Gandhi
M.
1984
, “On Local and Global Universal Relations in Elasticity
,” Journal of Elasticity
, Vol. 14
, pp. 97
–102
.24.
Xia
Z.
Ellyin
F.
1993
, “A Stress Rate Measure for Finite Elastic Plastic Deformation
,” Acta Mechanica
, Vol. 98
, pp. 1
–14
.25.
Ziegler
H.
1959
, “A Modification of Prager’s Hardening Rule
,” Quarterly Journal of Applied Mathematics
, Vol. 17
, pp. 55
–65
.
This content is only available via PDF.
Copyright © 1995
by The American Society of Mechanical Engineers
You do not currently have access to this content.
