Nonlocal implicit gradient-enhanced elasto-plasticity for the modelling of softening behaviour

International Journal of Plasticity

Volumn 19, Issue 4, 2002, Pages 403-433

  Engelen, Roy A B ^a   Geers, Marc G D ^a   Baaijens, Frank P T ^a  

^a EINDHOVEN UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

A. Ductility; B. Elastic plastic material; C. Finite elements; C. Numerical algorithms; Gradient elasto plasticity

Indexed keywords

ALGORITHMS; DUCTILITY; FINITE ELEMENT METHOD; PARTIAL DIFFERENTIAL EQUATIONS; STRAIN;

ELASTIC-PLASTIC MATERIALS;

ELASTOPLASTICITY;

EID: 0036555599     PISSN: 07496419     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0749-6419(01)00042-0     Document Type: Article

References (24)

1. Aifantis E.C. The physics of plastic deformation. Int. J. Plasticity. 3:1987;211-247.
2. Aifantis E.C. On the role of gradients in the localization of deformation and fracture. Int. J. Eng. Sci. 30(10):1992;1279-1300.
3. Aifantis E.C. Strain gradient interpretation of size effects. Int. J. Fracture. 95:1999;299-314.
4. de Borst R., Mühlhaus H.-B. Gradient-dependent plasticity: Formulation and algorithmic aspects. Int J. Numer. Meth. Eng. 35:1992;521-539.
5. de Borst R., Pamin J. Some novel developments in finite element procedures for gradient-dependent plasticity. Int. J. Numer. Meth. Eng. 39(14):1996;2477-2505.
6. de Borst R., Sluys L.J., Mühlhaus H.-B., Pamin J. Fundamental issues in finite element analyses of localization of deformation. Eng. Computation. 10:1999;99-121.
7. Geers M.G.D., de Borst R., Peerlings R.H.J. Validation and internal length scale determination for a gradient damage model. application to short glass-fibre-reinforced polypropylene Int. J. Solids Struct. 36(17):1999;2557-2584.
8. Geers, M.G.D., Ubachs, R.L., Engelen, R.A.B., Brekelmans, W.A.M., 2000. Large deformation gradient-enhanced hyperelasto-plasticity for ductile failure. In: Oñate, O. (Ed.), Proceedings of the European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS 2000, Barcelona, pages on CD-ROM.
9. Li, Z., Wang, C., Chen, C., in press. The evolution of voids in the plasticity strain hardening gradient materials. Int. J. Plasticity.
10. Lorentz E., Andrieux S. A variational formulation for nonlocal damage models. Int. J. Plasticity. 15(2):1999;119-138.
11. 0 finite element in gradient plasticity for localized failure modes analysis. In: Idelsohn, S., Oñate, E., Dvorkin, E., (Eds.), Computational Mechanics: New Trends and Application, Proceedings of the 4th World Congress on Computational Mechanics, Barcelona, pages on CD-ROM.
12. Mühlhaus H.-B., Aifantis E.C. A variational principle for gradient plasticity. Int. J. Solids Struct. 28:1991;845-858.
13. Nilsson C. On nonlocal rate-independent plasticity. Int. J. Plasticity. 14(6):1998;551-576.
14. Pamin, J., 1994. Gradient-Dependent Plasticity in Numerical Simulation of Localization Phenomena. PhD thesis, Delft University of Technology, The Netherlands.
15. Peerlings R.H.J., de Borst R., Brekelmans W.A.M., de Vree J.H.P. Gradient enhanced damage for quasi-brittle materials. Int. J. Numer. Meth. Eng. 17:1996;3391-3403.
16. Peerlings R.H.J., de Borst R., Brekelmans W.A.M., Geers M.G.D. Gradient enhanced damage modelling of concrete fracture. Mech. Cohes-Frict. Mater. 3:1998;323-342.
17. Peerlings, R.H.J., Geers, M.G.D., de Borst, R., Brekelmans, W.A.M., in press. A critical comparison of nonlocal and gradient-enhanced softening continua. Int. J. Solids Struct.
18. Pijaudier-Cabot G., Bažant Z.P. Nonlocal damage theory. J. Eng. Mech. 113:1987;1512-1533.
19. Pijaudier-Cabot G., Bažant Z.P., Tabbara M. Comparison of various models for strain softening. Eng. Computation. 5:1988;141-150.
20. Shu J.Y., Barlow C.Y. Strain gradient effects on microscopic strain field in a metal matrix composite. Int. J. Plasticity. 16(5):2000;563-591.
21. Stolken J.S., Evans A.G. A microbend test method for measuring the plasticity length scale. Acta Mater. 46(14):1998;5109-5116.
22. Strömberg L., Ristinmaa M. FE-formulation of a non-local plasticity theory. Comput. Method. Appl. M. 136:1996;127-144.
23. Zauderer E. Partial differential equations of applied mathematics. 2nd edition:1989;Wiley, Chichester, UK.
24. Zbib H.M., Aifantis E.C. On the gradient-dependent theory of plasticity and shear banding. Acta Mech. 92:1992;209-225.