A multiscale projection method for macro/microcrack simulations

International Journal for Numerical Methods in Engineering

Volumn 71, Issue 12, 2007, Pages 1466-1482

  Loehnert, Stefan ^a   Belytschko, Ted ^a  

^a Northwestern University   (United States)

Author keywords

Cracks XFEM; Multiscale

Indexed keywords

CRACK INITIATION; CRACK PROPAGATION; FINITE ELEMENT METHOD;

COARSE SCALE FORMULATION; CRACK SHIELDING; EXTENDED FINITE ELEMENT METHOD; MULTISCALE METHOD;

MICROCRACKS;

CRACK INITIATION; CRACK PROPAGATION; FINITE ELEMENT METHOD; MICROCRACKS;

EID: 34548683907     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.2001     Document Type: Article

References (30)

1. Hughes TJR. Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods. Computer Methods in Applied Mechanics and Engineering 1995; 127:387-401.
2. Zohdi TI, Oden JT, Rodin GJ. Hierarchical modeling of heterogeneous bodies. Computer Methods in Applied Mechanics and Engineering 1996; 138:273-298.
3. Oden JT, Zohdi TI. Analysis and adaptive modeling of highly heterogeneous elastic structures. Computer Methods in Applied Mechanics and Engineering 1997; 148:367-391.
4. 2 multiscale approach for modelling the elastoviscoplastic behaviour of long fibre sic/ti composite materials. Computer Methods in Applied Mechanics and Engineering 2000; 183:309-330.
5. Farhat C. A Lagrange multiplier based divide and conquer finite element algorithm. Journal of Computers in System Engineering 1991; 2:149-156.
6. Xiao SP, Belytschko T. A bridging domain method for coupling continua with molecular dynamics. Computer Methods in Applied Mechanics and Engineering 2004; 193:1645-1669.
7. Ben Dhia H, Rateau G. The Arlequin method as a flexible engineering design tool. International Journal for Numerical Methods in Engineering 2005; 62:1442-1462.
8. Terada K, Kikuchi N. A class of general algorithms for multi-scale analyses of heterogeneous media. Computer Methods in Applied Mechanics and Engineering 2001; 190:5427-5464.
9. Karpov EG, Wagner GJ, Liu WK. A Green's function approach to deriving non-reflecting boundary condition in molecular dynamics simulations. International Journal for Numerical Methods in Engineering 2005; 62: 1250-1262.
10. Fish J, Markolefas S, Guttal R, Nayak P. On adaptive multilevel superposition of finite-element meshes for linear elastostatics. Applied Numerical Mathematics 1994; 14:135-164.
11. 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.
12. Moës N, Dolbow J, Belytschko T. A finite element method for crack growth without remeshing. International Journal for Numerical Methods in Engineering 1999; 46(1):131-150.
13. Budyn E, Zi G, Moës N, Belytschko T. A method for multiple crack growth in brittle materials without remeshing. International Journal for Numerical Methods in Engineering 2004; 61:1741-1770.
14. Guidault PA, Allix O, Champeney L, Cornault C. A multiscale extended finite element method for crack propagation. Computer Methods in Applied Mechanics and Engineering 2006, in press.
15. Stolarska M, Chopp DL, Moës N, Belytschko T. Modelling crack growth by level sets in the extended finite element method, International Journal for Numerical Methods in Engineering 2001; 51:943-960.
16. Belytschko T, Moës N, Usui S, Parimi C. Arbitrary discontinuities in finite elements. International Journal for Numerical Methods in Engineering 2001; 50:993-1013.
17. Xiao QZ, Karihaloo BL. Improving the accuracy of XFEM crack tip fields using higher order quadrature and statically admissible stress recovery. International Journal for Numerical Methods in Engineering 2006; 66: 1378-1410.
18. Laborde P, Pommier J, Renard Y, Salaün M. Higher-order extended finite element method for cracked domains. International Journal for Numerical Methods in Engineering 2005; 64:354-381.
19. 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.
20. 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.
21. Areias PMA, Belytschko T. Analysis of three-dimensional crack initiation and propagation using the extended finite element method. International Journal for Numerical Methods in Engineering 2005; 63:760-788.
22. Areias PMA, Belytschko T. Two-scale shear band evolution by local partition of unity. International Journal for Numerical Methods in Engineering 2006; 66:878-910.
23. Samaniego E, Belytschko T. A continuum-discontinuum modelling of shear bands. International Journal for Numerical Methods in Engineering 2005; 62:1857-1872.
24. Ventura G, Moran B, Belytschko T. Dislocations by partition of unity. International Journal for Numerical Methods in Engineering 2005; 62:1463-1487.
25. Gracie R, Ventura G, Belytsehko T. A new fast finite element method for dislocations based on interior discontinuities, International Journal for Numerical Methods in Engineering 2006. DOI: 10.1002/nme.1896
26. Bao G, Suo Z. Remarks on crack bridging concepts. Applied Mechanics Reviews 1992; 45:355-366.
27. 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.
28. Bellec J, Dolbow J. A note on enrichment functions for modelling crack nucleation. Communications in Numerical Methods in Engineering 2003; 19:921-932.
29. Moran B, Shih CF. Crack tip and associated domain integrals from momentum and energy balance. Engineering Fracture Mechanics 1987; 27(6):615-642.
30. Rose LRF. Microcrack interaction with a main crack, International Journal of Fracture 1986; 31:233-242.