Stress analysis around crack tips in finite strain problems using the eXtended finite element method

International Journal for Numerical Methods in Engineering

Volumn 63, Issue 2, 2005, Pages 290-314

  Legrain, G ^a   Moës, Nicolas ^a   Verron, E ^a  

^a UNIVERSITÉ DE NANTES   (France)

Author keywords

Finite elasticity; Fracture; Partition of unity; Rubber like material; X FEM

Indexed keywords

COMPUTATIONAL METHODS; CRACK PROPAGATION; CRACKS; FRACTURE MECHANICS; FUNCTIONS; MATHEMATICAL MODELS; PROBLEM SOLVING; STRAIN; STRESS ANALYSIS;

CRACK TIPS; FINITE STRAIN PROBLEMS; INCOMPRESSIBILITY; STRAIN FRACTURE;

FINITE ELEMENT METHOD;

CRACK TIP; FINITE ELEMENT METHOD; FRACTURE MECHANICS;

EID: 18544362203     PISSN: 00295981     EISSN: None     Source Type: Journal    
DOI: 10.1002/nme.1291     Document Type: Article

References (36)

1. Charrier P, Kuczynski EO, Verron E, Marckmann G, Gornet L, Chagnon G. Theoretical and numerical limitations for the simulation of crack propagation in natural rubber components. In Constitutive Models for Rubber III, Busfield, Muhr (eds), 2003.
2. Fleming M, Chu YA, Moran B, Belytschko T. Enriched Element-free Galerkin methods for crack tip fields. International Journal for Numerical Methods in Engineering 1997; 40:1483-1504.
3. Babuska I, Melenk JY. The partition of unity finite element method. International Journal for Numerical Methods in Engineering 1997; 40(4):727-758.
4. Belytschko T, Black T. Elastic crack growth in finite elements with minimal remeshing. International Journal for Numerical Methods in Engineering 1999; 45(5):601-620.
5. Moës N, Dolbow J, Belytschko T. A finite element method for crack growth without remeshing. International Journal for Numerical Methods in Engineering 1999; 46:131-150.
6. Dolbow J, Moës N, Belytschko T. An extended finite element method for modelling crack growth with frictional contact. Computer Methods in Applied Mechanics and Engineering 2001; 190:6825-6846.
7. Daux C, Moës N, Dolbow J, Sukumar N, Belytschko T. Arbitrary branched and intersecting cracks with the eXtended finite element method. International Journal for Numerical Methods in Engineering 2000; 48:1741-1760.
8. Moës N, Gravouil A, Belytschko T. Non-planar 3D crack growth by the extended finite element and level sets. Part I: mechanical model. International Journal for Numerical Methods in Engineering 2002; 53:2549-2568.
9. Gravouil A, Moës N, Belytschko T. Non-planar 3d crack growth by the extended finite element and level sets. Part II: level set update. International Journal for Numerical Methods in Engineering 2002; 53:2569-2586.
10. Wells GN, Sluys LJ. A new method for modelling cohesive cracks using finite elements. International Journal for Numerical Methods in Engineering 2001; 50:2667-2682.
11. Moës N, Belytschko T. Extended finite element method for cohesive crack growth. Engineering Fracture Mechanics 2002; 69: 813-834.
12. Sethian JA. Fast marching methods and level sets methods for propagating interfaces.
13. Stolarska M, Chopp DL, Moës N, Belytschko T. Modelling crack growth with level-set and the extended finite element method. International Journal for Numerical Methods in Engineering 2001; 51:943-960.
14. Dolbow JE, Devan A. Enrichment of enhanced assumed strain approximations for representing strong discontinuities: addressing volumetric incompressibility and the discontinuous patch test. International Journal for Numerical Methods in Engineering 2004; 59:47-67.
15. Griffith AA. The phenomena of rupture and flow in solids. Transactions of the Royal Society of London 1920; 221.
16. Rivlin RS, Thomas AG. Rupture of rubber. i. Characteristic energy for tearing. Journal for Polymer Science 1953; 3:291-318.
17. Steinmann P. Application of material forces to hyperelastostatic fracture mechanics. i. Continuum mechanical setting. International Journal of Solids and Structures 2000; 37:7371-7391.
18. Destuynder Ph, Djaoua M, Lescure S. Quelques remarques sur la mecanique de la rupture elastique. Jounrla de Mecnique Theorique et Appliquee 1983; 2(1):113-135.
19. Moran B, Shih CF. Crack tip and associated domain integrals from momentum and energy balance. Engineering Fracture Mechanics 1987; 127:615-642.
20. Stolarska M, Chopp DL, Moës N, Belytschko T. Modelling crack growth by level sets and the extended finite element method. International Journal for Numerical Methods in Engineering 2001; 51 (8):943-960.
21. Dolbow J, Moës N, Belytschko T. Modeling fracture in Mindlin-Reissner plates with the eXtended finite element method. International Journal of Solids and Structures 2000; 37:7161-7183.
22. Goangseup Z, Belytschko T. New crack-tip elements for x-fem and applications to cohesive cracks. International Journal for Numerical Methods in Engineering 2003; 57:2221-2240.
23. Geubelle PH, Knauss WG. Finite strains at the tip of a crack in a sheet of hyperelastic material: I. homogeneous case. Journal of Elasticity 1994; 35:61-98.
24. Geubelle PH, Knauss WG. Finite strains at the tip of a crack in a sheet of hyperelastic material: Ii. Special bimaterial case. Journal of Elasticity 1994; 35:99-137.
25. Geubelle PH, Knauss WG. Finite strains at the tip of a crack in a sheet of hyperelastic material: Iii. General bimaterial case. Journal of Elasticity 1994; 35:139-174.
26. Knowles JK, Sternberg E. An asymptotic finite-deformation analysis of the elastostatic field near the tip of a crack. Journal of Elasticity 1973; 3:67-107.
27. Knowles JK, Sternberg E. Finite-deformation analysis of the elastostatic field near the tip of a crack: reconsideration of higher order results. Journal of Elasticity 1974; 4:201-233.
28. Stephenson RA. The equilibrium field near the tip of a crack for finite plane strain of incompressible elastic materials. Journal of Elasticity 1982; 12:65-99.
29. HKS. Abaqus/Standard User Manual.
30. Rice J. A path independent integral and the approximation analysis of strain concentration by notches and cracks. Journal of Applied Mechanics 1968; 35:379-386.
31. Greensmith HW. Rupture of rubber part 10: The changes in stored energy on making a small cut in a test piece held in simple extension. Journal of Applied Polymer Science 1963; 7:993-1002.
32. Lindley PB. Energy for crack growth in model rubber components. Journal of Strain Analysis 1972; 7:132-140.
33. Treloar LRG. Stress-strain data for vulcanised rubber under various types of deformation. Transactions of Faraday Society 1944; 40:59-70.
34. Lake GJ. Application of fracture mechanics to failure in rubber articles, with particularly reference to groove cracking in tyres. International Conference of Yeld, Deformation and Fracture of Polymers, Cambridge, 1970.
35. Yeoh OH. Relation between crack surface displacement and strain energy release rate in thin rubber sheets. Mechanics of Materials 2002; 32:459-474.
36. Key PL. A relation between crack surface displacement and the strain energy release rate. International Journal of Fracture Mechanics 1969; 5:287-296.