Characterization of fracture processes by continuum and discrete modelling

Computational Mechanics

Volumn 50, Issue 3, 2012, Pages 303-320

  Kaliske, M ^a   Dal, H ^a   Fleischhauer, R ^a   Jenkel, C ^a   Netzker, C ^a  

^a DRESDEN UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Cohesive elements; Continuum failure model; Fracture mechanics; Material forces; Uncertainty

Indexed keywords

BEARING CAPACITY; CHARACTERIZATION; CONTINUUM MECHANICS; CRACK PROPAGATION; CRACKS; FIBER REINFORCED PLASTICS; FRACTURE MECHANICS; NUMERICAL METHODS; UNCERTAINTY ANALYSIS;

COHESIVE ELEMENT; CRACK PROPAGATION DIRECTION; DETERMINISTIC MODELLING; FAILURE MODEL; FIBRE REINFORCED COMPOSITES; MATERIAL FORCES; NON-LINEAR STRUCTURAL BEHAVIOURS; UNCERTAINTY;

FRACTURE;

EID: 84871496971     PISSN: 01787675     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00466-011-0578-5     Document Type: Article

References (66)

1. Kaliske M, Netzker C, Näser B (2009) Evaluation of crack driving forces at finite viscoelasticity: Theory and experiments. In: Steinmann P (ed) IUTAM symposium: Progress in the theory and numerics of configurational mechanics. Springer, Dordrecht, pp 193-202
2. Dal H, KaliskeM (2009) Amicro-continuum-mechanical material model for failure of rubber-like materials: Application to ageing induced fracturing. J Mech Phys Solids 57:1340-1356
3. Geißler G, Netzker C, Kaliske M (2010) Discrete crack path prediction by an adaptive cohesive crack model. Eng Frac Mech 77:3541-3557
4. Eshelby JD (1951) The force on an elastic singularity. Philos Trans R Soc Lond Ser A Math Phys Sci 244:87-112
5. EpsteinM (2002) The Eshelby tensor and the theory of continuous distributions of inhomogeneities.Mech Res Commun 29:501-506
6. Maugin GA (2003) Pseudo-plasticity and pseudo-inhomogeneity effects in materials mechanics. J Elast 71:81-103
7. Braun M (1997) Configurational forces induced by finite-element discretization. Proceedings of the Estonian Academy of Sciences, Physics, Mathematics 46:24-31
8. Steinmann P (2000) Application of material force to hyperelastostatic fracture mechanics. I. Continuum mechanical setting. Int J Solids Struct 37:7371-7391
9. Steinmann P, Ackermann D, Barth FJ (2001) Application of material forces to hyperelastostatic fracture mechanics. II. Computational Setting. Int J Solids Struct 38:5509-5526
10. Maugin GA (1993) Material inhomogeneities in elasticity. Chapman & Hall, London
11. Kienzler R, Herrmann G (2000) Mechanics in material space. Springer, Berlin
12. GurtinME (2000) Configurational forces as basic concepts of continuum physics. Springer, New York
13. Eshelby JD (1975) The elastic energy-momentum tensor. J Elast 5:321-335
14. Näser B, Kaliske M (2004) Formulierung materieller Kräfte für elastische und inelastischeMaterialien. LeipzigAnnu Civ Eng Rep 9:433-453
15. Menzel A, Denzer R, Steinmann P (2004) On the comparision of two approaches to compute material forces for inelastic materials. Application to single-slip crystal-plasticity. Comput Methods Appl Mech Eng 193:5411-5428
16. Näser B, Kaliske M, Müller R (2007) Material forces for inelastic models at large strains application to fracture mechanics. Comput Mech 40:1005-1013
17. Näser B, Kaliske M, Mars WV (2010) Fatigue investigation of elastomeric structures. Tire Sci Technol 38:194-212
18. Näser B, Kaliske M (2003) Numerische bruchmechanische Analysen mittels materieller Kräfte. Leipzig Annu Civ Eng Rep 8: 265-280
19. Liebe T, Denzer R, Steinmann P (2003) Application of the material force method to isotropic continuum damage. Comput Mech 30:171-184
20. Mullins L (1969) Softening of rubber by deformation. Rubber Chem Technol 42:339-362
21. Kaliske M, Rothert H (1998) Constitutive approach to rate-independent properties of filled elastomers. Int J Solids Struct 35: 2057-2071
22. Miehe C, Göktepe S, Lulei F (2004) A micro-macro approach to rubber-like materials. Part I. The non-affinemicro-sphere model of rubber elasticity. J Mech Phys Solids 52:2617-2660
23. Kaliske M, Heinrich G (1998) An extended tube-model for rubber elasticity: statistical-mechanical theory and finite element implementation. Rubber Chem Technol 72:602-632
24. Meyer KH, Ferri C (1935) Sur l'élasticité du caoutchouc. Helvetica Chimica Acta 18:570-589
25. Volokh KY (2007) Hyperelasticity with softening for modeling materials failure. J Mech Phys Solids 55:2237-2264
26. Volokh KY (2007) Softening hyperelasticity for modeling materials failure:Analysis of cavitation in hydrostatic tension. Int J Solids Struct 44:5043-5055
27. Gao H, Klein P (1998) Numerical simulation of crack growth in an isotropic solid with randomized internal cohesive bonds. J Mech Phys Solids 46:187-218
28. Morse PM (1929) Diatomic molecules to the wave mechanics. II. Vibrational levels. Physical Review 34:57-64
29. Bažant ZP, Oh BH (1986) Efficient numerical integration on the surface of a sphere. Zeitschrift für angewandte Mathematik und Mechanik 66:37-49
30. Treloar LRG (1944) Stress-strain data for vulcanised rubber under various types of deformation. Trans Faraday Soc 40:59-70
31. Hamdi A, Nait Abdelaziz M, Ait Hocine N, Heuillet P, Benseddiq N (2006) Fracture criterion of rubber-like materials under plane stress conditions. Polym Test 25:994-1005
32. Kawabata S (1973) Fracture and mechanical behavior of rubberlike polymers under finite deformation in biaxial stress field. J Macromol Sci Part B Phys 8:605-630
33. Dugdale DS (1960) Yielding of steel sheets containing slits. J Mech Phys Solids 8:100-104
34. Barenblatt GI (1962) The mathematical theory of equilibrium cracks in brittle fracture. Adv Appl Mech 7:55-129
35. Hillerborg A, Modeer M, Petersson PE (1976) Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cem Concr Res 6:773-781
36. Needleman A (1987) A continuum model for void nucleation by inclusion debonding. J Appl Mech 54:525-531
37. Tvergaard V (1990) Effect of fibre debonding in a whisker-reinforced metal. Mater Sci Eng A 125:203-213
38. Geißler G, KaliskeM (2010) Time-dependent cohesive zone modelling for discrete fracture simulation. Eng Fract Mech 77:153-169
39. Xu XP, Needleman A (1994) Numerical simulations of fast crack growth in brittle solids. J Mech Phys Solids 9:1397-1434
40. Tijssens MG, Sluys BL, Vander Giessen E (2000) Numerical simulation of quasi-brittle fracture using damaging cohesive surfaces. Eur J Mech A/Solids 19:761-780
41. Carpinteri A, Colombo G (1989) Numerical analysis of catastrophic softening behaviour (snap-back instability). Comput Struct 31:607-636
42. Camacho GT, OrtizM (1996) Computational modelling of impact damage in brittle materials. Int J Solids Struct 33:2899-2938
43. Pandolfi A, Ortiz M (1998) Solidmodeling aspects of three-dimensional fragmentation. Eng Comput 14:287-308
44. Pandolfi A, Ortiz M (2002) An efficient adaptive procedure for three-dimensional fragmentation simulations. Eng Comput 18:148-159
45. Pandolfi A, Krysl P, Ortiz M (1999) Finite element simulation of ring expansion and fragmentation. Int J Fract 95:279-297
46. Ruiz G, Ortiz M, Pandolfi A (2000) Three-dimensional finite-element simulation of the dynamic brazilian tests on concrete cylinders. Int J Numer Methods Eng 48:963-994
47. Ruiz G, Pandolfi A, Ortiz M (2001) Three-dimensional cohesive modeling of dynamic mixed-mode fracture. Int J Numer Methods Eng 52:97-120
48. Papoulia KD,Vavasis SA (2003) Time continuity in cohesive finite element modeling. Int J Numer Methods Eng 58:679-701
49. Sam CH, Papoulia KD,Vavasis SA (2005) Obtaining initially rigid cohesive finite element models that are temporally convergent. Eng Fract Mech 72:2247-2267
50. Rice JR (1968) A path independent integral and the approximate analysis of strain concentration by notches and cracks. JAppl Mech 35:379-386
51. Gürses E (2007) Aspects of energy minimization in solid mechanics: evolution of microstructures and brittle crack propagation. Dissertationsschrift, Institut für Mechanik, Universität Stuttgart, Stuttgart
52. Wells G, Sluys LJ (2001) A new method for modelling cohesive cracks using finite elements. Int J Numer Methods Eng 50: 2667-2682
53. Dumstorff P, Meschke G (2004) Investigation of crack growth criteria in the context of the extended finite elementmethod. In: European conference on computational mechancis in applied sciences and engineering. Jyväskylä, Finland
54. Pidaparti R, Yang T, Soedel W (1990) Plane stress finite element prediction of mixed-mode rubber fracture and experimental verification. Int J Fract 45:221-241
55. Miehe C (2001) Strain-driven homogenization of inelastic microstructures and composites based on an incremental variational formulation. Int J Numer Methods Eng 55:1285-1322
56. Miehe C (2003) Computational micro-to-macro transition for discretized micro-structures of heterogeneous materials at finite strains based on the minimization of averaged incremental energy. Comput Methods Appl Mech Eng 192:559-591
57. Frangopol D, Maute K (2003) Life-cycle reliability-based optimization of civil and aerospace structures. Comput Struct 81:397-410
58. Oden J, Belytschko T, Babuska I, Hughes T (2003) Research directions in computational mechanics. Comput Methods Appl Mech Eng 192:913-922
59. Möller B, Beer M (2004) Fuzzy randomness-uncertainty in civil engineering and computational mechanics. Springer, Berlin
60. Viertl R (1996) Statistical methods for non-precise data. CRC Press, New York
61. Spaethe G (1992) Die Sicherheit tragender Baukonstruktionen. Springer, Wien
62. Klir GJ, Folger TA (1988) Fuzzy sets, uncertainty, and information. Prentice Hall, Englewood Cliffs
63. Graf W, Jenkel C, Pannier S, Sickert JU, Steinigen F (2009) Numerical structural monitoring with the uncertainty model fuzzy randomness. Int J Reliab Saf 3:218-234
64. Resch E, Kaliske M (2010) Three-dimensional numerical analyses of load-bearing behavior and failure of multiple double-shear dowel-type connections in timber engineering. Comput Struct 88:165-177
65. Schmidt J (2009) Modellierung und numerische Analyse von Strukturen aus Holz. Habilitationsschrift, Institut für Statik und Dynamik der Tragwerke, TU Dresden
66. Schmidt J, Kaliske M (2009) Models for numerical failure analysis of wooden structures. Eng Struct 31:571-579