Post-necking behaviour modelled by a gradient dependent plasticity theory

International Journal of Solids and Structures

Volumn 34, Issue 35-36, 1997, Pages 4531-4546

  Mikkelsen, Lars Pilgaard ^a  

^a TECHNICAL UNIVERSITY OF DENMARK   (Denmark)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; FINITE ELEMENT METHOD; HARDENING; MATHEMATICAL MODELS; PLASTICITY; STRAIN RATE;

POST NECKING BEHAVIOUR;

SHEET METAL;

EID: 0031365829     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-7683(97)00039-5     Document Type: Article

References (21)

1. Aifantis, E. C. (1984). On the microstructural origin of certain inelastic models. Transactions of the ASME Journal of Engineering Material Technology, 106, 326-330.
2. Aifantis, E. C. (1987). The physics of plastic deformation. International Journal of Plasticity, 3, 211-247.
3. Benallal, A. and Tvergaard, V. (1995). Non-local continuum effects on bifurcation in the plane strain tension-compression test. Journal of Mechanics and Physics of Solids, 43, 741-770.
4. de Borst, R. and Mühlhaus, H.-B. (1992). Gradient-dependent plasticity: formulation and algorithmic aspects. International Journal for Numerical Methods in Engineering, 35, 521-539.
5. Budiansky, B. (1969). Remarks on theories of solid and structural mechanics. In Problems of Hydrodynamics and Continuum Mechanics, eds M. A. Lavrent'ev et al., pp. 77-83. SIAM, Philadelphia.
6. Considére, M. (1885). Annales des Ponts et Chaussées, 9, 574.
7. Eringen, A. C. (1968). Theory of micropolar elasticity. Fracture, an advanced Treatise, ed. H. Leibowitz, pp. 621-729. Academic Press, New York.
8. Fleck, N. A. and Hutchinson, J. W. (1993). A phenomenological theory of strain gradient plasticity. Journal of Mechanics and Physics of Solids, 41, 1825-1857.
9. Fleck, N. A. and Hutchinson, J. W. (1996). Strain gradient plasticity. Advances in Applied Mechanics, 33, 295-361.
10. Hill, R. and Hutchinson, J. W. (1975). Bifurcation phenomena in the plane tension test. International Journal of Solids Structures, 23, 239-264.
11. Hutchinson, J. W. (1973). Finite strain analysis of elastic-plastic solids and structures. In Numerical Solution of Nonlinear Structural Problems, ed. R. F. Hartung, p. 17. ASME, New York.
12. Keeler, S. P. (1968). Understanding sheet metal formability. Machinery and Production Engineering, Part 1-6.
13. Mikkelsen, L. P. (1996). Necking of biaxially stretched thin sheets modeled by a nonlocal plasticity theory. In Proc. of the 3rd Asia-Pacific Symposium on Advances in Engineering Plasticity and its Applications, eds. T. Abe and T. Tsuta, pp. 579-584. Pergamon Elsevier, Hiroshima.
14. Mühlhaus, H.-B. and Aifantis, E. C. (1991). A variational principle for gradient plasticity. International Journal of Solids Structures, 28, 845-856.
15. Mühlhaus, H.-B. and Vardoulakis, I. (1987). The thickness of shear bands in granular materials. Géotechnique, 37, 271-283.
16. Pamin, J. (1994). Gradient-dependent plasticity in numerical simulation of localization phenomena. Dissertation, Delft University of Technology, Delft.
17. Pamin, J. and de Borst, R. (1995). Numerical simulation of localization phenomena using gradient plasticity and finite elements. In Heron, Netherlands School for Advanced Studies in Construction, ed. A. C. W. M. Vrouwenvelder, Vol. 40, pp. 71-92. Delft, The Netherlands.
18. Pijaudier-Cabot, G. and Bazant, Z. P. (1987). Nonlocal damage theory. Journal of Engineering Mechanics ASCE, 113, 1512-1533.
19. Spiegel, M. R. (1959). Theory and Problems of Vector Analysis and an Introduction to Tensor Analysis. Schaum, New York.
20. Tvergaard, V. (1981). Bifurcation and imperfection - sensitivity at necking instabilities. ZAMM, 60, T26-T34.
21. Tvergaard, V. (1993). Necking in tensile bars with rectangular cross-section. Computing Methods in Applied Mechanics and Engineering, 103, 273-290.