A robust algorithm for configurational-force-driven brittle crack propagation with R-adaptive mesh alignment

International Journal for Numerical Methods in Engineering

Volumn 72, Issue 2, 2007, Pages 127-155

  Miehe, Christian ^a   Gurses E ^a  

^a UNIVERSITY OF STUTTGART   (Germany)

Author keywords

Configurational forces; Crack simulations; Energy minimization; Finite elements; Fracture

Indexed keywords

ALGORITHMS; BRITTLE FRACTURE; COMPUTATIONAL GEOMETRY; COMPUTER SIMULATION; CRACK PROPAGATION; ELASTICITY; ENERGY RELEASE RATE;

CLAUSIUS-PLANCK INEQUALITY; ENERGY MINIMIZATION; GRIFFITH CRITERION;

FINITE ELEMENT METHOD;

ALGORITHMS; BRITTLE FRACTURE; COMPUTATIONAL GEOMETRY; COMPUTER SIMULATION; CRACK PROPAGATION; ELASTICITY; ENERGY RELEASE RATE; FINITE ELEMENT METHOD;

EID: 34948823349     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.1999     Document Type: Article

References (56)

1. Griffith AA. The phenomena of rupture and flow in solids. Philosophical Transactions of the Royal Society of London 1921; 221:163-198.
2. Griffith AA. The theory of rupture. In Proceedings of the First International Congress for Applied Mechanics, Biezeno CB, Burgers JM (eds). Delft, 1924; 55-63.
3. Irwin GR. Elasticity and plasticity: fracture. In Encyclopedia of Physics, Flügge S (ed.), vol. 6. Springer: Berlin, 1958; 551-590.
4. Barenblatt GI. Mathematical theory of equilibrium cracks in brittle fracture. Advances in Applied Mechanics 1962; 7:55-129.
5. Stumpf H, Le KC. Variational principles of nonlinear fracture mechanics. Acta Mechanica 1990; 83:25-37.
6. Maugin GA, Trimarco C. Pseudomomentum and material forces in nonlinear elasticity: variational formulations and applications to brittle fracture. Acta Mechanica 1992; 94:1-28.
7. Eshelby JD. The force on an elastic singularity. Philosophical Transactions of the Royal Society London A 1951; 224:87-112.
8. Eshelby JD. Energy relations and the energy-momentum tensor in continuum mechanics. In Inelastic Behavior of Solids, Kanninen MF et al. (eds). 1970; 77-115.
9. Rice JR. A path independent integral and the approximate analysis of strain concentration by notches and cracks. Journal of Applied Mechanics 1968; 35:379-386.
10. Maugin GA. Material Inhomogeneities in Elasticity. Chapman & Hall: London, 1993.
11. Gurtin ME. On the energy release rate in quasistatic elastic crack propagation. Journal of Elasticity 1979; 9:187-195.
12. Gurtin ME. Configurational Forces as Basic Concepts of Continuum Physics. Springer: New York, 2000.
13. Kienzler R, Herrmann G. Mechanics in Material Space with Applications to Defect and Fracture Mechanics. Springer: Berlin, Heidelberg, 2000.
14. Gurtin ME, Podio-Guidugli P. Configurational forces and the basic laws for crack propagation. Journal of the Mechanics and Physics of Solids 1996; 44:905-927.
15. Gurtin ME, Podio-Guidugli P. Configurational forces and a constitutive theory for crack propagation that allows for kinking and curving. Journal of the Mechanics and Physics of Solids 1998; 46:1343-1378.
16. Steinmann P, Maugin GA (eds). Mechanics of Material Forces. Springer: Berlin, 2005.
17. Francfort GA, Marigo JJ. Revisiting brittle fracture as an energy minimization problem. Journal of the Mechanics and Physics of Solids 1998; 46:1319-1342.
18. Dal Maso G, Toader R. A model for the quasistatic growth of brittle fractures: existence and approximation results. Archive for Rational Mechanics and Analysis 2002; 162:101-135.
19. Bourdin B, Francfort GA, Marigo JJ. Numerical experiments in revisited brittle fracture. Journal of the Mechanics and Physics of Solids 2000; 48:797-826.
20. Dugdale DS. Yielding of steel sheets containing slits. Journal of the Mechanics and Physics of Solids 1960; 8:100-104.
21. Hillerborg A, Modeer M, Petersson PE. Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements. Cement and Concrete Research 1976; 6:773-782.
22. Xu XP, Needleman A. Void nucleation by inclusion debonding in a crystal matrix. Modelling and Simulation in Materials Science and Engineering 1993; 1:111-132.
23. Ortiz M, Pandolfi A. Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis. International Journal for Numerical Methods in Engineering 1999; 44:1267-1282.
24. Simo JC, Oliver J, Armero F. An analysis of strong discontinuities induced by strain-softening in rate-independent inelastic solids. Computational Mechanics 1993; 12:277-296.
25. Oliver J. Modelling strong discontinuities in solid mechanics via strain softening constitutive equations. Part1: fundamentals. International Journal for Numerical Methods in Engineering 1996; 39:3575-3600.
26. Oliver J. Modelling strong discontinuities in solid mechanics via strain softening constitutive equations. Part2: numerical simulation. International Journal for Numerical Methods in Engineering 1996; 39:3601-3623.
27. Belytschko T, Black T. Elastic crack growth in finite element with minimal remeshing. International Journal for Numerical Methods in Engineering 1999; 45:601-620.
28. 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.
29. Wells GN, Sluys LJ. A new method for modeling cohesive cracks using finite elements. International Journal for Numerical Methods in Engineering 2001; 50:2667-2682.
30. Gasser TC, Holzapfel GA. Modelling 3D crack propagation in unreinforced concrete using PUFEM. Computer Methods in Applied Mechanics and Engineering 2005; 194:2859-2896.
31. Oliver J, Huespe AE, Sanchez PJ. A comperative study on finite elements for capturing strong discontinuities: E-FEM vs. X-FEM. Computer Methods in Applied Mechanics and Engineering 2006, in press.
32. Hansbo A, Hansbo P. An unfitted finite element method, based on Nitsche's method, for elliptic interface problems. Computer Methods in Applied Mechanics and Engineering 2002; 191:5537-5552.
33. Hansbo A, Hansbo P. A finite element method for the simulation of strong and weak discontinuities in solid mechanics. Computer Methods in Applied Mechanics and Engineering 2004; 193:3523-3540.
34. Steinmann P, Ackermann D, Barth FJ. Application of material forces to hyperelastostatic fracture mechanics. II. Computational setting. International Journal of Solids and Structures 2001; 38:5509-5526.
35. Denzer R, Barth FJ, Steinmann P. Studies in elastic fracture mechanics based on the material force method. International Journal for Numerical Methods in Engineering 2003; 58:1817-1835.
36. Mueller R, Maugin GA. On material forces and finite element discretization. Computational Mechanics 2002; 29:52-60.
37. Mueller R, Kolling S, Gross D. On configurational forces in the context of the finite element method. International Journal for Numerical Methods in Engineering 2002; 53:1557-1574.
38. Heintz P, Larsson F, Hansbo P, Runesson K. Adaptive strategies and error control for computing material forces in fracture mechanics. International Journal for Numerical Methods in Engineering 2004; 60:1287-1299.
39. Larsson R, Fagerström M. A framework for fracture modelling based on the material forces concept with XFEM kinematics. International Journal for Numerical Methods in Engineering 2005; 62:1763-1788.
40. Fagerström M, Larsson R. Theory and numerics for finite deformation fracture modelling using strong discontinuities. International Journal for Numerical Methods in Engineering 2006; 66:911-948.
41. Heintz P. On the numerical modelling of quasi-static crack growth in linear elastic fracture mechanics. International Journal for Numerical Methods in Engineering 2006; 65:174-189.
42. Negri M. A finite element approximation of the Griffith's model in fracture mechanics. Numerische Mathematik 2003; 95:653-687.
43. Coleman B, Gurtin ME. Thermodynamics with internal state variables. The Journal of Chemical Physics 1967; 47:597-613.
44. Pandolfi A, Ortiz M. An efficient adaptive procedure for three-dimensional fragmentation simulations. Engineering with Computers 2002; 18:148-159.
45. Xu XP, Needleman A. Numerical simulations of fast crack growth in brittle solids. Journal of the Mechanics and Physics of Solids 1994; 42:1397-1434.
46. Pandolfi A, Krysl P, Ortiz M. Finite element simulation of ring expansion and fragmentation: the capturing of length and time scales through cohesive models of fracture. International Journal of Fracture 1999; 95:279-297.
47. Pandolfi A, Guduru PR, Ortiz M, Rosakis AJ. Three-dimensional cohesive elements analysis and experiments of dynamic fracture in C300 steels. International Journal of Solids and Structures 2000; 37:3733-3760.
48. Ruiz G, Ortiz M, Pandolfi A. Three dimensional finite element simulation of the dynamic Brazilian test on concrete cylinders. International Journal for Numerical Methods in Engineering 2000; 48:963-994.
49. Ruiz G, Pandolfi A, Ortiz M. Three dimensional cohesive modeling of dynamic mix-mode fracture. International Journal for Numerical Methods in Engineering 2001; 52:97-120.
50. Rooke DP, Cartwright DJ. Compendium of Stress Intensity Factors. Hillingdon Press: Uxbridge, 1976.
51. Barsoum RS. On the use of isoparemetric finite elements linear fracture mechanics. International Journal for Numerical Methods in Engineering 1976; 10:25-37.
52. Barsoum RS. Triangular quarter point elements as elastic and perfectly-plastic crack tip elements. International Journal for Numerical Methods in Engineering 1977; 11: 85-98.
53. Henshell RD, Shaw KG. Crack tip finite elements are unnecessary. International Journal for Numerical Methods in Engineering 1975; 9:495-507.
54. Li FZ, Shih CF, Needleman A. A comparison methods for calculating energy release rates. Engineering Fracture Mechanics 1985; 21:405-421.
55. Bittencourt TN, Wawrzynek PA, Ingraffea AR, Sousa JL. Quasi-automatic simulation of crack propagation for 2D LEFM problems. Engineering Fracture Mechanics 1996; 55:321-334.
56. Phongthanapanich S, Dechaumphai P. Adaptive delaunay triangulation with object-oriented programming for crack propagation analysis. Finite Elements in Analysis and Design 2004; 40:1753-1771.