Spatial convergence of crack nucleation using a cohesive finite-element model on a pinwheel-based mesh

International Journal for Numerical Methods in Engineering

Volumn 67, Issue 1, 2006, Pages 1-16

  Papoulia, Katerina D ^a   Vavasis, Stephen A ^b   Ganguly, Pritam ^c  

^a Cornell University   (United States)

^b Department of Computer Science and School of Operations Research and Information Engineering   (United States)

^c Department of Obstetrics Gynecology   (United States)

Author keywords

Cohesive zone modelling; Convergence; Crack nucleation; Finite element; Mesh dependence

Indexed keywords

APPROXIMATION THEORY; CRACK PROPAGATION; FINITE ELEMENT METHOD; FRACTURE; MATHEMATICAL MODELS;

COHESIVE ZONE MODELLING; CRACK NUCLEATION; MESH DEPENDENCE;

NUCLEATION;

APPROXIMATION THEORY; CRACK PROPAGATION; FINITE ELEMENT METHOD; FRACTURE; MATHEMATICAL MODELS; NUCLEATION;

EID: 33745610863     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.1598     Document Type: Article

References (42)

1. Dugdale DS. Yielding of steel sheets containing slits. Journal of the Mechanics and Physics of Solids 1960; 8:100-104.
2. Barenblatt GI. The mathematical theory of equilibrium of cracks in brittle fracture. Advances in Applied Mechanics 1962; 7:55-129.
3. Rice JR. A path independent integral and the approximate analysis of strain concentration by notches and cracks. ASME Journal of Applied Mechanics 1968; 35:379-386.
4. Rahul-Kumar P, Jagota A, Bennison SJ, Saigal S, Muralidhar S. Polymer interfacial fracture simulations using cohesive elements. Acta Materialia 1999; 47(15-16):4161-4169.
5. Shabrov MN, Needleman A. An analysis of inclusion morphology effects on void nucleation. Modelling and Simulation in Materials Science and Engineering 2002; 10:163-183.
6. Tvergaard V. Effect of fibre debonding in a whisker-reinforced material. Material Science and Engineering 1990; A125:203-213.
7. Rosakis AJ, Samudrala O, Singh RP, Shukla A. Intersonic crack propagation in bimaterials. Journal of the Mechanics and Physics of Solids 1998; 46:1789-1813.
8. Siegmund T. Needleman A. A numerical study of dynamic crack growth in elastic-viscoplastic solids. International Journal of Solids and Structures 1997; 34(7):769-787.
9. 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.
10. Han TS, Ural A, Chen CS, Zehnder AT, Ingraffea AR, Billington SL. Delamination buckling and propagation analysis of honeycomb panels using a cohesive element approach. International Journal of Fracture 2002; 115(2):101-123.
11. Dwivedi SK, Espinosa HD. Modeling dynamic crack propagation in fiber-reinforced composites including frictional effects. Mechanics of Materials 2003; 35:481-509.
12. Espinosa HD, Zavattieri PD. A grain level model for the study of failure initiation and evolution in polycrystalline brittle materials. Part I: theory and numerical implementation. Mechanics of Materials 2003; 35:333-364.
13. Espinosa HD, Zavattieri PD. A grain level model for the study of failure initiation and evolution in polycrystalline brittle materials. Part II numerical examples. Mechanics of Materials 2003; 35:365-394.
14. Zavattieri PD, Espinosa HD. Grain level analysis of crack initiation and propagation in brittle materials. Acta Materialia 2001; 49:4291-4311.
15. Needleman A. A continuum model for void nucleation by inclusion debonding. Journal of Applied Mechanics 1987; 38:289-324.
16. Xu XP Needleman A. Numerical simulations of fast crack growth in brittle solids. Journal of the Mechanics and Physics of Solids 1994; 42(9):1397-1434.
17. Camacho GT, Ortiz M. Computational modeling of impact damage in brittle materials. International Journal of Solids and Structures 1996; 33(22-29):2899-2938.
18. Miller O, Freund LB, Needleman A. Modeling and simulation of dynamic fragmentation in brittle materials. International Journal of Fracture 1999; 96:101-125.
19. Repetto EA, Radovitzky R, Ortiz M. Finite element simulation of dynamic fracture and fragmentation of glass rods. Computer Methods in Applied Mechanics and Engineering 2000; 183(1-2):3-14.
20. Zhai J, Zhou M. Finite element analysis of micromechanical failure mode in heterogeneous brittle solids. International Journal of Fracture (special issue on Failure Mode Transition) 1999; 161-180.
21. Bittencourt T, Ingraffea AR, Llorca J. Simulation of arbitrary, cohesive crack propagation. In Fracture Mechanics of Concrete Structures, Bazant Z (ed.). Elsevier Applied Science: New York, 1992; 339-350.
22. 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.
23. Pandolfi A, Krysl P, Ortiz M. Finite element simulation of ring expansion and fragmentation. International Journal of Fracture 1999; 95:279-297.
24. Klein P, Foulk J, Chen E, Wimmer S, Gao H. Physics-based modeling of brittle fracture: cohesive formulations and the application of meshfree methods. Technical Report SAND2001-8099, Sandia National Laboratories, December 2000.
25. Papoulia KD, Sam C-H, Vavasis SA. Time continuity in cohesive finite element modeling. International Journal for Numerical Methods in Engineering 2003; 58(5):679-701.
26. Kubair DV, Geubelle PH. Comparative analysis of extrinsic and intrinsic cohesive models of dynamic fracture. International Journal of Solids and Structures 2003; 40(15):3853-3868.
27. Remmers JJC, de Borst R, Needleman A. A cohesive segments method for the simulation of crack growth. Computational Mechanics 2003; 31:69-77.
28. Rabczuk T, Belytschko T. Cracking particles: a simplified meshfree method for arbitrary evolving cracks. International Journal for Numerical Methods in Engineering 2004; 61:2316-2343.
29. Belytschko T, Chen H, Xu J, Zi G. Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment. International Journal for Numerical Methods in Engineering 2003; 58:1873-1905.
30. C-H Sam. A robust formulation and solution of initially rigid cohesive interface models. Ph.D. Thesis, Cornell University, 2005.
31. Kalthoff JF, Winkler S. Failure mode transition at high rates of shear loading. International Conference on Impact Loading and Dynamic Behavior of Materials, vol. 1, 1987; 185-195.
32. Zhang Z, Paulino GH. Cohesive zone modeling of dynamic failure in homogeneous and functionally graded materials. International Journal of Plasticity 2005; 21:1195-1254.
33. Radin C. The pinwheel tilings of the plane. The Annals of Mathematics 1994; 139(3):661-702.
34. Radin C, Sadun L. The isoperimetric problem for pinwheel tilings. Communications in Mathematical Physics 1996; 177:255-263.
35. Ganguly P, Vavasis SA, Papoulia KD. An algorithm for two-dimensional mesh generation based on the pinwheel tiling. SIAM Journal on Scientific Computing 2004, submitted.
36. Sam C-H, Papoulia KD. Obtaining initially rigid cohesive finite element models that are temporally convergent. Engineering Fracture Mechanics 2005, in press.
37. LeVeque RJ. Numerical Methods for Conservation Laws. Birkhauser: Basel, 1990.
38. Süli E. Private communication, 2005.
39. Rittel D, Maigre H. A study of mixed-mode dynamic crack initiation in PMMA, Mechanics Research Communications 1996; 23(5):475-481.
40. Maigre H, Rittel D. Mixed-mode quantification for dynamic fracture initiation: application to the compact compression specimen. International Journal of Solids and Structures 1993; 30(23):3233-3244.
41. Shewchuk JR. A two-dimensional quality mesh generator and Delaunay triangulator. Technical Report, Computer Science Division, University of California, Berkeley, 2002.
42. Ahlfors LV. Complex Analysis: An Introduction to the Theory of Analytic Functions of One Complex Variable. McGraw-Hill: New York, 1979.