A classification of higher-order strain-gradient models in damage mechanics

Archive of Applied Mechanics

Volumn 73, Issue 5-6, 2003, Pages 448-465

  Askes, H ^a   Sluys, L J ^a  

^a DELFT UNIVERSITY OF TECHNOLOGY   (Netherlands)

Author keywords

Damage; Higher order continuum; Microstructure; Stability; Strain gradient model; Wave dispersion

Indexed keywords

COMPUTER SIMULATION; DISPERSION (WAVES); DUCTILITY; ELASTICITY; GRADIENT METHODS; INTEGRATION; MICROSTRUCTURE; STRAIN;

DAMAGE MECHANICS;

CONTINUUM MECHANICS;

EID: 0344826666     PISSN: 09391533     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00419-003-0296-3     Document Type: Article

References (36)

1. Aifantis, E.C.: On the microstructural origin of certain inelastic models. ASME J Eng Mat Tech 106 (1984) 326-330
2. Aifantis, B.C.: The physics of plastic deformation. Int J Plasticity 3 (1987) 211-247
3. Aifantis, E.C.: Gradient deformation models at nano, micro, and macro scales. ASME J Eng Mat Tech 121 (1999) 189-202
4. Aifantis, E.C.: Strain gradient interpretation of size effects. Int J Fracture 95 (1999) 299-314
5. Altan, B.S.; Aifantis, E.C.: On some aspects in the special theory of gradient elasticity. J Mech Behavior Mat 8 (1997) 231-282
6. 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 Eng 49 (2000) 811-832
7. Askes, H.; Sluys, L.J.: Explicit and implicit gradient series in damage mechanics. Eur J Mech A/Solids 21 (2002) 379-390
8. Askes, H.; Suiker, A.S.J.; Sluys, L.J.: Dispersion analysis and element-free Galerkin simulations of higher-order strain gradient models. Mat Physics Mech 3 (2001) 12-20. Also available at http://www.ipme.ru
9. Askes, H.; Suiker, A.S.J.; Slays, L.J.: A classification of higher-order strain gradient models - linear analysis. Arch Appl Mech 72 (2002) 171-188
10. Bazant, Z.P.; Pijaudier-Cabot, G.: Measurement of characteristic length of nonlocal continuum. ASCE J Eng Mech 115 (1989) 755-767
11. Belytschko, T.; Krongauz, Y.; Organ, D.; Fleming, M.; Krysl, P.: Meshless methods: an overview and recent developments. Comput Methods Appl Mech Eng 139 (1996) 3-47
12. Belytschko, T.; Lu, Y.Y.; Gu, L.: Element-free Galerkin methods. Int J Numer Methods Eng 37 (1994) 229-256
13. Chang, C.S.; Gao, J.: Second-gradient constitutive theory for granular material with random packing structure. Int J Solids Struct 32 (1995) 2279-2293
14. Comi, C.; Driemeier, L.: On gradient regularization for numerical analysis in the presence of damage. In: de Borst, R.; van der Giessen, E. (Eds.) Material instabilities in solids, pp. 425-440. Chichester, Wiley 1998
15. de Borst, R.; Heeres, O.M.; Benallal, A.: A gradient enhanced damage model: theory and computation. In: Owen, D.R.J.; Oñate, E., Hinton, E. (Eds.) Computational plasticity, fundamentals and applications, pp. 373-380. Barcelona, CIMNE 1997
16. Gutkin, M.Y.: Nanoscopics of dislocations and disclinations in gradient elasticity. Reviews on Advanced Materials Science, 1 (2000) 27-60. Also available at http://www.ipme.ru
17. Gutkin, M.Y.; Aifantis, E.C.: Dislocations in the theory of gradient elasticity. Scripta Materialia 40 (1999) 559-566
18. Hughes, T.J.R.: The finite element method - linear static and dynamic finite element analysis. London, Prentice - Hall 1987
19. Mühlhaus, H.-B.; Aifantis, E.C.: A variational principle for gradient plasticity. Int J Solids Struct 28 (1991) 845-857
20. Mühlhaus, H.-B.; Oka, F.: Dispersion and wave propagation in discrete and continuous models for granular materials. Int J Solids Struct 33 (1996) 271-283
21. Mühlhaus, H.-B.; Vardoulakis, I.: The thickness of shear bands in granular materials. Géotechnique 37 (1987) 271-283
22. Pamin, J.: Gradient-dependent plasticity in numerical simulation of localization phenomena. Diss. Delft University of Technology, 1994
23. Pamin, J.; Askes, H.; de Borst, R.: Two gradient plasticity theories discretized with the element-free Galerkin method. Comput Meth Appl Mech Eng 192 (2003) 2377-2403
24. 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 Eng 39 (1996) 3391-3403
25. Peerlings, R.H.J.; de Borst, R.; Brekelmans, W.A.M.; de Vree, J.H.P.; Spee, I.: Some observations on localisation in non-local and gradient damage models. Eur J Mech A/Solids 15 (1996) 937-953
26. Peerlings, R.H.J.; de Borst, R.; Brekelmans, W.A.M.; Geers, M.G.D.: Gradient-enhanced damage modeling of concrete fracture. Mech Cohesive-Frictional Mat 3 (1998) 323-342
27. Schreyer, H.L.; Chen, Z.: One-dimensional softening with localization. ASME J Appl Mech 53 (1986) 791-797
28. Sluys, L.J.: Wave propagation, localisation and dispersion in softening solids. Diss. Delft University of Technology 1992
29. Suiker, A.S.J.; Askes, H.; Sluys, L.J.: Micro-mechanically based 1-D gradient damage models. In: Onate, E.; Bugeda, G.; Suárez, B. (Eds.) European Congress on Comptational Methods in Applied Sciences and Engineering, Barcelona, CIMNE 2000
30. Suiker, A.S.J.; de Borst, R.; Chang, C.S.: Micro-mechanical modeling of granular material I: Derivation of a second-gradient micro-polar constitutive theory. Acta Mech 149 (2001) 161-180
31. Suiker, A.S.J.; de Borst, R.; Chang, C.S.: Micro-mechanical modeling of granular material II: Plane wave propagation in infinite media. Acta Mech 149 (2001) 181-200
32. Triantafyllidis, N.; Aifantis, E.C.: A gradient approach to localization of deformation. I: Hyperelastic materials. J Elast 16 (1986) 225-237
33. Tsagrakis, I.: The role of gradients in elasticity and plasticity, analytical and numerical applications. Diss. Aristotle University of Thessaloniki, 2001
34. Unger, D.J.; Aifantis, E.C.: Strain gradient elasticity theory for antiplane shear cracks I: Oscillatory displacements. Theor Appl Fracture Mech 34 (2000) 243-252
35. Unger, D.J.; Aifantis, E.C.: Strain gradient elasticity theory for antiplane shear cracks II: Monotonic displacements. Theor Appl Fracture Mech 34 (2000) 253-265
36. Zbib, H.M.: Instabilities and size effects in plasticity: continuum and dislocation approaches. In: de Borst, R.; van der Giessen, E. (Eds.) Material instabilities in solids, pp. 473-487. Chichester, Wiley 1998