Gradient plasticity and damage models: A short comparison

Computational Materials Science

Volumn 32, Issue 3-4, 2005, Pages 472-479

  Pamin, Jerzy ^a  

^a CRACOW UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

Composite; Damage; Gradient enhanced continuum; Localized failure; Plasticity

Indexed keywords

BOUNDARY VALUE PROBLEMS; COMPOSITE MATERIALS; COMPUTER SIMULATION; CRACK INITIATION; FAILURE (MECHANICAL); MATHEMATICAL MODELS; PLASTIC DEFORMATION; PLASTICITY; STRAIN RATE; TENSILE STRENGTH;

DAMAGE; GRADIENT-ENHANCED CONTINUUM; LOCALIZED FAILURE; MESH-SENSITIVITY;

MATERIALS SCIENCE;

EID: 12444331006     PISSN: 09270256     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.commatsci.2004.09.018     Document Type: Conference Paper

References (28)

1. E. Aifantis Gradient deformation models at nano, micro and macro scales ASME J. Engng. Mat. Tech. 121 1999 189 202
2. N. Fleck, and J. Hutchinson Strain gradient plasticity Adv. Appl. Mech. 33 1997 295 361
3. H.-B. Mühlhaus, and E. Aifantis A variational principle for gradient plasticity Int. J. Solids Struct. 28 1991 845 857
4. R. de Borst, and H.-B. Mühlhaus Gradient-dependent plasticity: Formulation and algorithmic aspects Int. J. Numer. Meth. Engng. 35 1992 521 539
5. R. Engelen, M. Geers, and F. Baaijens Nonlocal implicit gradient-enhanced elasto-plasticity for the modelling of softening behaviour Int. J. Plast. 19 4 2003 403 433
6. J. Pamin, H. Askes, and R. de Borst Two gradient plasticity theories discretized with the element-free Galerkin method Comput. Meth. Appl. Mech. Engng. 192 2003 2377 2403
7. R. Peerlings, R. de Borst, W. Brekelmans, and J. de Vree Gradient-enhanced damage for quasi-brittle materials Int. J. Numer. Meth. Engng. 39 1996 3391 3403
8. M. Geers, R. de Borst, W. Brekelmans, and R. Peerlings Strain-based transient-gradient damage model for failure analyses Comput. Meth. Appl. Mech. Engng. 160 1-2 1998 133 153
9. C. Comi Computational modelling of gradient-enhanced damage in quasi-brittle materials Mech. Cohes.-frict. Mater. 4 1 1999 17 36
10. E. Kuhl, E. Ramm, and R. de Borst An anisotropic gradient damage model for quasi-brittle materials Comput. Meth. Appl. Mech. Engng. 183 1-2 2000 87 103
11. R. Peerlings, M. Geers, R. de Borst, and W. Brekelmans A critical comparison of nonlocal and gradient-enhanced softening continua Int. J. Solids Struct. 38 44-45 2001 7723 7746
12. M. Fremond, and B. Nedjar Damage, gradient of damage and principle of virtual power Int. J. Solids Struct. 33 8 1996 1083 1103
13. T. Liebe, P. Steinmann, and A. Benallal Theoretical and computational aspects of a thermodynamically consistent framework for geometrically linear gradient damage Comput. Meth. Appl. Mech. Engng. 190 2001 6555 6576
14. H. Askes, J. Pamin, and R. de Borst Dispersion analysis and element-free Galerkin solutions of second- and fourth-order gradient-enhanced damage models Int. J. Numer. Meth. Engng. 49 2000 811 832
15. R. Mindlin Second gradient of strain and surface-tension in linear elasticity Int. J. Solids Struct. 1 1965 417 438
16. H. Askes, A. Suiker, and L. Sluys A classification of higher-order strain-gradient models-linear analysis Archive Appl. Mech. 72 2-3 2002 171 188
17. C. Chang, H. Askes, and L. Sluys Higher-order strain/higher-order stress gradient models derived from a discrete microstructure, with application to fracture Engng. Fract. Mech. 69 17 2002 1907 1924
18. V. Kouznetsova, M. Geers, and W. Brekelmans Multi-scale constitutive modelling of heterogeneous materials with a gradient-enhanced computational homogenization scheme Int. J. Numer. Meth. Engng. 54 2002 1235 1260
19. J. Pamin, and R. de Borst Simulation of crack spacing using a reinforced concrete model with an internal length parameter Archive Appl. Mech. 68 9 1998 613 625
20. R. de Borst, and J. Pamin Some novel developments in finite element procedures for gradient-dependent plasticity Int. J. Numer. Meth. Engng. 39 1996 2477 2505
21. T. Svedberg, and K. Runesson An algorithm for gradient-regularized plasticity coupled to damage based on a dual mixed FE-formulation Comput. Meth. Appl. Mech. Engng. 161 1-2 1998 49 65
22. S. Ramaswamy, and N. Aravas Finite element implementation of gradient plasticity models. Part I: Gradient-dependent yield functions, Part II: Gradient-dependent evolution equations Comput. Meth. Appl. Mech. Engng. 163 1998 11 32
23. T. Liebe, and P. Steinmann Theory and numerics of a thermodynamically consistent framework for geometrically linear gradient plasticity Int. J. Numer. Meth. Engng. 51 2001 1437 1467
24. G. Maier, and T. Hueckel Nonassociated and coupled flow rules of elastoplasticity for rock-like materials Int. J. Rock Mech. Min. Sci. Geomech. Abstr. 16 1979 77 92
25. R. de Borst, L. Sluys, H.-B. Mühlhaus, and J. Pamin Fundamental issues in finite element analyses of localization of deformation Eng. Comput. 10 1993 99 121
26. J. de Vree, W. Brekelmans, and M. van Gils Comparison of nonlocal approaches in continuum damage mechanics Comput. Struct. 55 4 1995 581 588
27. R. de Borst, J. Pamin, and M. Geers On coupled gradient-dependent plasticity and damage theories with a view to localization analysis Eur. J. Mech. A-Solids 18 6 1999 939 962
28. L. Sluys, R. de Borst, and H.-B. Mühlhaus Wave propagation, localization and dispersion in a gradient-dependent medium Int. J. Solids Struct. 30 1993 1153 1171