Quasi-static crack propagation in plane and plate structures using set-valued traction-separation laws

International Journal for Numerical Methods in Engineering

Volumn 74, Issue 3, 2008, Pages 475-505

  Areias, Pedro M A ^a   Rabczuk, Timon ^b  

^a UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

^b UNIVERSITY OF CANTERBURY   (New Zealand)

Author keywords

Cohesive traction separation law; Complementarity; Crack propagation; Plane problems; Plates

Indexed keywords

ALGORITHMS; BENDING (DEFORMATION); CRACK PROPAGATION; MATHEMATICAL MODELS; PLATE METAL;

COHESIVE TRACTION-SEPARATION LAW; EXTENDED FINITE ELEMENT METHOD;

FINITE ELEMENT METHOD;

ALGORITHMS; BENDING (DEFORMATION); CRACK PROPAGATION; FINITE ELEMENT METHOD; MATHEMATICAL MODELS; PLATE METAL;

EID: 42049114616     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.2182     Document Type: Article

References (40)

1. Barenblatt GI. The mathematical theory of equilibrium of cracks in brittle fracture. Advances in Applied Mechanics 1962; 7:55-129.
2. Planas J, Elices M. Nonlinear fracture of cohesive materials. International Journal of Fracture 1991; 51:139-157.
3. Bažant ZP, Planas J. Fracture and Size Effect in Concrete and Other Quasibrittle Materials. CRC Press: Boca Raton, FL, 1998.
4. Elices M, Guinea GV, Gómez J, Planas J, The cohesive zone model: advantages, limitations and challenges. Engineering Fracture Mechanics 2002; 69:137-163.
5. Planas J, Elices M, Guinea GV, Gómez FJ, Cendón DA, Arbilla I. Generalizations and specializations of cohesive crack models. Engineering Fracture Mechanics 1996; 70:1759-1776.
6. Alfano G, Crisfield MA. Finite element interface models for the delamination analysis of laminated composites: mechanical and computational issues. International Journal for Numerical Methods in Engineering 2001; 50: 1701-1736.
7. Kubair DV, Geubelle PH. Comparative analysis of extrinsic and intrinsic cohesive models of dynamic fracture. International Journal of Solids and Structures 2003; 40:3853-3868.
8. Sam C-H, Papoulia KD, Vavasis SA. Obtaining initially rigid cohesive finite element models that are temporally convergent. Engineering Fracture Mechanics 2005; 72:2247-2267.
9. Papoulia KD, Sam C-H, Vavasis SA. Time continuity in cohesive finite element modeling. International Journal for Numerical Methods in Engineering 2003; 58:679-701.
10. Leine RI, Nijmeijer H. Dynamics and Bifurcations of Non-smooth Mechanical Systems. Springer: Berlin, 2004.
11. Bolzon G, Maier G, Tin-Loi F. On multiplicity of solutions in quasi-brittle fracture computations. Computational Mechanics 1997; 19:511-516.
12. Belytschko T. Private communication, 2003.
13. Huespe AE, Oliver J, Pulido MDG, Blanco S, Linero D. On the fracture models determined by the continuum-strong discontinuity approach. International Journal of Fracture 2006; 137:211-229.
14. Areias PMA, César de Sá JMA, Conceição António CA, Carneiro JASAO, Teixeira VMP. Strong displacement discontinuities and Lagrange multipliers in the analysis of finite displacement fracture problems. Computational Mechanics 2004; 35:54-71.
15. Areias PMA, Song JH, Belytschko T. Analysis of fracture in thin shells by overlapping paired elements. Computer Methods in Applied Mechanics and Engineering 2006; 195(41-43):5343-5360.
16. Pang J-S. Newton's method for B-differentiable equations. Mathematics of Operations Research 1990; 15:311-341.
17. Chen C, Mangasarian OL. A class of smoothing functions for nonlinear and mixed complementarity problems. Computational Optimization and Applications 1996; 5:97-138.
18. Chen B, Harker PT. Smooth approximations to nonlinear complementarity problems. SIAM Journal on Optimization 1997; 7(2):403-420.
19. Areias PMA, Song JH, Belytschko T. Finite-strain quadrilateral shell element based on discrete Kirchhoff-Love constraints. International Journal for Numerical Methods in Engineering 2005; 64(9): 1166-1206.
20. 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.
21. Belytschko T, Black T. Elastic crack growth in finite elements with minimal remeshing. International Journal for Numerical Methods in Engineering 1999; 45:601-620.
22. Belytschko T, Moës N, Usui S, Parimi C. Arbitrary discontinuities in finite elements. International Journal for Numerical Methods in Engineering 2001; 50:993-1013.
23. Barenblatt GI. On some problems of the theory of elasticity arising in investigating the mechanism of hydraulic fracture of an oil-bearing stratum. Prikladnaya Matematika i Mekhanika 1956; 20:475-486 (in Russian).
24. Barenblatt GI. On the equilibrium cracks due to brittle fracture. Doklady AN SSSR 1959; 127:47-50 (in Russian).
25. Goodier JN. Mathematical Theory of Equilibrium Cracks, Volume II of Fracture, Chapter I. Academic Press: New York, 1969; 1-66.
26. Moës N, Belytschko T. Extended finite element method for cohesive crack growth. Engineering Fracture Mechanics 2002; 69:813-833.
27. Eterovic AL, Bathe KJ. On the treatment of inequality constraints arising from contact conditions in finite element analysis. Computers and Structures 1991; 40(2):203-209.
28. Xu X-P, Needleman A. Numerical simulations of fast crack growth in brittle solids. Journal of the Mechanics and Physics of Solids 1994; 42(9):1397-1434.
29. Falk ML, Needleman A, Rice JR. A critical evaluation of dynamic fracture simulations using cohesive surfaces. Journal de Physique IV 2001; 11:43-52.
30. Lanczos C. The Variational Principles of Mechanics (4th edn). Dover: New York, 1986. Reprint from University of Toronto Press, 1970.
31. Tin-Loi F, Tseng P. Efficient computation of multiple solutions in quasibrittle fracture analysis. Computer Methods in Applied Mechanics and Engineering 2003; 192:1377-1388.
32. Tin-Loi F, Que NS. Nonlinear programming approaches for an inverse problem in quasibrittle fracture. International Journal of Mechanical Sciences 2002; 44:843-858.
33. Kanninen MF, Popelar CH. Advanced Fracture Mechanics. The Oxford Engineering Science Series. Oxford University Press: Oxford, 1985.
34. Walmag JMB, Delhez EJM. A note on trust-region radius update. SIAM Journal on Optimization 2005; 16(2): 548-562.
35. Chen B, Harker PT. A non-interior-point continuation method for linear complementarity problems. SIAM Journal on Matrix Analysis and Applications 1993; 14:1168-1190.
36. Sutton MA, Deng X, Ma F, Newman Jr JC, James M. Development and application of a crack tip opening displacement-based mixed mode fracture criterion. International Journal of Solids and Structures 2000; 37: 3591-3618.
37. Gálvez JC, Elices M, Guinea GV, Planas J. Mixed mode fracture of concrete under proportional and nonproportional loading. International Journal of Fracture 1998; 94:267-284.
38. 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.
39. Gálvez J, Elices M, Guinea GV, Planas J, Crack trajectories under mixed mode and non-proportional loading. International Journal of Fracture 1996; 81:171-193.
40. Shen M, Shen M-HH. Direction of crack extension under general loading. International Journal of Fracture 1995; 70:51-58.