An implicit gradient model by a reproducing kernel strain regularization in strain localization problems

Computer Methods in Applied Mechanics and Engineering

Volumn 193, Issue 27-29, 2004, Pages 2827-2844

  Chen, Jiun Shyan ^a   Zhang, Xinwei ^a   Belytschko, Ted ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b Northwestern University   (United States)

Author keywords

Damage mechanics; Gradient reproducing conditions; Implicit gradient model; Strain localization; Strain regularization

Indexed keywords

APPROXIMATION THEORY; BOUNDARY CONDITIONS; GRADIENT METHODS; MATHEMATICAL MODELS; SPECTRUM ANALYSIS; STRAIN;

LOCALIZATION PROBLEMS; NON-LOCAL ENERGY; REPRODUCING KERNAL STRAIN REGULARIZATION (RKSR);

MECHANICS;

BOUNDARY CONDITION; DAMAGE MECHANICS; MATHEMATICAL ANALYSIS; NUMERICAL MODEL; STRAIN;

EID: 2442541015     PISSN: 00457825     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cma.2003.12.057     Document Type: Article

References (28)

1. Askes H. Sluys L.J. A classification of higher-order strain gradient models in damage mechanics Arch. Appl. Mech. 72 2002 171-188
2. Askes H. Pamin J. de Borst R. Dispersion analysis and element-free Galerkin solutions of second and fourth-order gradient-enhanced damage models Int. J. Numer. Methods Engrg. 49 6 2000 811-832
3. Bazant Z.P. Cabot P.G. Nonlocal continuum damage, localization instability and convergence ASME, J. Appl. Mech. 55 1988 287-293
4. Bazant Z.P. Belytscko T. Chang T.-P. Continuum model for strain softening J. Engrg. Mech. 110 1984 1666-1692
5. Bazant Z.P. Jirasek M. Nonlocal integral formulations of plasticity and damage: Survey of progress J. Engrg. Mech. ASCE 128 2002 1119-1149
6. Belytschko T. Bazant Z.P. Hyun Y.-W. Chang T.-P. Strain-softening materials and finite-element solutions Comput. Struct. 23 1986 163-180
7. Belytschko T. Krongauz Y. Organ D. Fleming M. Krysl P. Meshless methods: An overview and recent development Comput. Methods Appl. Mech. Engrg. 139 1996 3-49
8. Belytschko T. Lu Y.Y. Gu L. Element-free Galerkin methods Int. J. Numer. Methods Engrg. 37 1994 229-256
9. Chen J.S. Wu C.T. Belytschko T. Regularization of material instabilities by meshfree approximations with intrinsic length scales Int. J. Numer. Methods Engrg. 47 2000 1301-1322
10. Chen J.S. Wang H.P. New boundary condition treatments for meshless computation of contact problems Comput. Methods Appl. Mech. Engrg. 187 1998 441-468
11. Chen J.S. Pan C. Wu C.T. Liu W.K. Reproducing kernel particle methods for large deformation analysis of nonlinear structures Comput. Methods Appl. Mech. Engrg. 139 1996 195-227
12. de Borst R. Muhlhaus H.B. Gradient-dependent plasticity: Formulation and algorithmic aspects Int. J. Numer. Methods Engrg. 35 1992 521-539
13. de Borst R. Pamin J. Gradient plasticity in numerical simulation of concrete cracking Eur. J. Mech., A/Solids 15 1996 295-320
14. de Borst R. Pamin R.H. Peerlings R.H.J. Sluys L.J. On gradient-enhanced damage and plasticity models for failure in quasi-brittle and frictional materials Comput. Mech. 17 1996 130-141
15. Feng J. Wen K. Tian X. Chen Z. Nonlocal softening model and its application to engineering excavation Engrg. Mech. (Chinese Journal) 16 6 1999 36-43
16. Fusao O. Toshihisa A. Atsushi Y. A strain localization analysis using a viscoplastic softening model for clay Int. J. Plast. 11 1995 523-545
17. Krongauz Y. Belytschko T. Consistent pseudo-derivatives in the meshless methods Comput. Methods Appl. Mech. Engrg. 146 1997 371-386
18. Lade P.V. Wang Q. Analysis of shear banding in true triaxial tests on sand J. Engrg. Mech. 127 8 2001 762-768
19. Lasry D. Belytschko T. Localization limiters in transient problems Int. J. Solids Struct. 24 1988 581-597
20. Lemaitre J. A continuous damage mechanics model for ductile fracture J. Engrg. Mater. Tech. 107 1985 83-89
21. Liu W.K. Jun S. Li S. Adee J. Belytschko T. Reproducing kernel particle methods for structural dynamics Int. J. Numer. Methods Engrg. 38 1995 1655-1679
22. Liu W.K. Jun S. Zhang Y. Reproducing kernel particle methods Int. J. Numer. Methods Fluids 20 1995 1081-1106
23. Mühlhaus H.B. Vardoulakis I. The thickness of shear band in granular materials Geotechnique 37 1987 271-283
24. Needleman A. Material rate dependence and mesh sensitivity in localization problems Comput. Methods Appl. Engrg. 67 1988 69-85
25. 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. Methods Engrg. 39 1996 3391-3403
26. Simo J.C. Hughes T.J.R. On the variational foundations of assumed strain methods ASME J. Appl. Mech. 53 1986 51-54
27. Simo J.C. Ju J.W. Strain- and stress-based continuum damage models--I. Formulation Int. J. Solids Struct. 23 1987 821-840
28. L.J. Sluys, Wave propagation, localization and dispersion in softening solids, Ph.D. Thesis, Civil Engineering Department of Delft University of Technology, 1992