A variational multiscale method to model crack propagation at finite strains

International Journal for Numerical Methods in Engineering

Volumn 80, Issue 3, 2009, Pages 269-289

  Mergheim, J ^a  

^a Rheinland Pfälzische Technische Universität Kaiserslautern Landau   (Germany)

Author keywords

Fine scale crack propagation; Finite element method; Hansbo's method; Multiscale; Solids; Variational multiscale method

Indexed keywords

ADAPTIVE SCHEME; DECOUPLED SYSTEM; DEFORMATION MAP; FINE-SCALE CRACK PROPAGATION; FINITE STRAIN; GROWING CRACKS; HANSBO'S METHOD; MULTISCALE; VARIATIONAL MULTISCALE; VARIATIONAL MULTISCALE METHOD; VARIATIONAL MULTISCALE METHODS;

CRACK DETECTION; CRACK PROPAGATION;

FINITE ELEMENT METHOD;

EID: 70349456491     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.2602     Document Type: Article

References (38)

1. Park HS, Liu WK. An introduction and tutorial on multiple-scale analysis in solids. Computer Methods in Applied Mechanics and Engineering 2004; 193:1733-1772.
2. Fish J, Yuan Z. Multiscale enrichment based on partition of unity. International Journal for Numerical Methods in Engineering 2005; 62:1341-1359.
3. Zohdi TI, Wriggers P. Introduction to Computational Micromechanics. Lecture Notes in Applied and Computational Mechanics, vol. 20. Springer: Berlin, 2005.
4. Ghosh S, Lee K, Raghavan P. A multi-level computational model for multi-scale damage analysis in composite and porous materials. International Journal of Solids and Structures 2001; 38:2335-2385.
5. Fish J, Yu Q. Multiscale damage modeling for composite materials: theory and computational framework. International Journal for Numerical Methods in Engineering 2001; 52:161-191.
6. Ladevèze P, Lubineau G. On a damage mesomodel for laminates: micro-meso relationships, possibilities and limits. Composites Science and Technology 2001; 61:2149-2158.
7. Guidault PA, Allix O, Champaney L, Cornuault C. A multiscale extended finite element method for crack propagation. Computer Methods in Applied Mechanics and Engineering 2008; 197:381-399.
8. Ladevèze P, Loiseau O, Dureisseix D. A micro-macro and parallel computational strategy for highly heterogeneous structures. International Journal for Numerical Methods in Engineering 2001; 52:121-138.
9. Loehnert S, Belytschko T. A multiscale projection method for macro/microcrack simulations. International Journal for Numerical Methods in Engineering 2007; 71:1466-1482.
10. Hughes TJR, Feijoo GR, Mazzei L, Quincy JB. The variational multiscale method-a paradigm for computational mechanics. Computer Methods in Applied Mechanics and Engineering 1998; 166:3-24.
11. Garikipati K, Hughes TJR. A study of strain localization in a multiple scale framework-the one-dimensional problem. Computer Methods in Applied Mechanics and Engineering 1998; 159:193-222.
12. Garikipati K, Hughes TJR. A variational multiscale approach to strain localization-formulation for multidimensional problems. Computer Methods in Applied Mechanics and Engineering 2000; 188:39-60.
13. Creighton SL, Regueiro RA, Garikipati K, Klein PA, Marin EB, Bammann DJ. A variational multiscale method to incorporate strain gradients in a phenomenological plasticity model. Computer Methods in Applied Mechanics and Engineering 2004; 193:5453-5475.
14. Yeon JH, Youn SK. Meshfree analysis of softening elastoplastic solids using variational multiscale method. International Journal of Solids and Structures 2005; 42:4030-4057.
15. Masud A, Franca LP. A hierarchical multiscale framework for problems with multiscale source terms. Computer Methods in Applied Mechanics and Engineering 2008; 197:2692-2700.
16. Hund A, Ramm E. Locality constraints within multiscale model for non-linear material behaviour. International Journal for Numerical Methods in Engineering 2007; 70(13):1613-1632.
17. Ibrahimbegović A, Markovič D. Strong coupling methods in multi-phase and multi-scale modeling of inelastic behavior of heterogeneous structures. Computer Methods in Applied Mechanics and Engineering 2003; 192: 3089-3107.
18. Simo J, Oliver J, Armero F. An analysis of strong discontinuities induced by strain softening in rate-independent inelastic solids. Computational Mechanics 1993; 12:277-296.
19. Oliver J. Modelling strong discontinuities in solid mechanics via strain softening constitutive equations part 1: fundamentals. Part 2: numerical simulations. International Journal for Numerical Methods in Engineering 1996; 39:3575-3623.
20. Armero F, Garikipati K. An analysis of strong discontinuities in multiplicative finite strain plasticity and their relation with the numerical simulation of strain localization in solids. International Journal of Solids and Structures 1996; 33:2863-2885.
21. Oliver J, Huespe AE, Pulido MDG, Samaniego E. On the strong discontinuity approach in finite deformation setting. International Journal for Numerical Methods in Engineering 2003; 56:1051-1082.
22. Mosler J, Meschke G. 3D modelling of strong discontinuities in elastoplastic solids: fixed and rotating localization formulations. International Journal for Numerical Methods in Engineering 2003; 57:1553-1576.
23. Babuška I, Melenk JM. The partition of unity method. International Journal for Numerical Methods in Engineering 1997; 40:727-758.
24. Belytschko T, Black T. Elastic crack growth in finite elements with minimal remeshing. International Journal for Numerical Methods in Engineering 1999; 45:601-620.
25. 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.
26. 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.
27. Zi G, Belytschko T. New crack-tip elements for XFEM and applications to cohesive cracks. International Journal for Numerical Methods in Engineering 2003; 57:2221-2240.
28. Wells GN, de Borst R, Sluys LJ. A consistent geometrically non-linear approach for delamination. International Journal for Numerical Methods in Engineering 2002; 54:1333-1355.
29. Hansbo A, Hansbo P. A finite element method for the simulation of strong and weak discontinuities in elasticity. Computer Methods in Applied Mechanics and Engineering 2004; 193:3523-3540.
30. Song JH, Areias PMA, Belytschko T. A method for dynamic crack and shear band propagation with phantom nodes. International Journal for Numerical Methods in Engineering 2006; 67:868-893.
31. Mergheim J, Kuhl E, Steinmann P. A finite element method for the computational modeling of cohesive cracks. International Journal for Numerical Methods in Engineering 2005; 63(2):276-289.
32. Mergheim J, Kuhl E, Steinmann P. Towards the algorithmic treatment of 3D strong discontinuities. Communications in Numerical Methods in Engineering 2007; 23(2):97-108.
33. Hettich T, Hund A, Ramm E. Modeling of failure in composites by X-FEM and level-sets within a multiscale framework. Computer Methods in Applied Mechanics and Engineering 2008; 197:414-424.
34. Farhat C, Roux FX. A method of finite element tearing and interconnecting and its parallel solution. International Journal for Numerical Methods in Engineering 1991; 32:1205-1227.
35. Jäger P, Steinmann P, Kuhl E. Modeling three-dimensional crack propagation-a comparison of crack path tracking strategies. International Journal for Numerical Methods in Engineering 2008; 76:1328-1352.
36. Allix O, Corigliano A. Geometrical and interfacial non-linearities in the analysis of delamination in composites. International Journal of Solids and Structures 1999; 36:2189-2216.
37. de Borst R, Remmers JJC. Computational modelling of delamination. Composites Science and Technology 2006; 66:713-722.
38. Schlangen E. Experimental and numerical analysis of fracture processes in concrete. Ph.D. Thesis, Technische Universiteit Delft, Delft, Nederlands, 1993.