The 1 / r singularity in weakly nonlinear fracture mechanics

Journal of the Mechanics and Physics of Solids

Volumn 57, Issue 9, 2009, Pages 1568-1577

  Bouchbinder, Eran ^a   Livne, Ariel ^a   Fineberg, Jay ^a  

^a HEBREW UNIVERSITY OF JERUSALEM   (Israel)

Author keywords

Asymptotic analysis; Crack mechanics; Dynamic fracture; Nonlinear elasticity

Indexed keywords

CONCENTRATION OF; CONSTITUTIVE LAW; CRACK MECHANICS; DYNAMIC FRACTURE; FIRST ORDER; FRACTURE DYNAMICS; IRREVERSIBLE DEFORMATION; J INTEGRAL; LARGE DISPLACEMENTS; LENGTH SCALE; LINEAR ELASTIC; LINEAR-ELASTIC FRACTURE MECHANICS; MATERIAL FAILURES; NONLINEAR ELASTICITY; NONLINEAR FRACTURE MECHANICS; NONLINEAR REGIONS; QUANTITATIVE AGREEMENT; SECOND ORDERS; UNBALANCED FORCE; WEAKLY NON-LINEAR THEORY;

BRITTLE FRACTURE; CRACK TIPS; DYNAMICS; ELASTICITY; ENERGY DISSIPATION; FRACTURE MECHANICS; PLATES (STRUCTURAL COMPONENTS); STRENGTH OF MATERIALS;

ASYMPTOTIC ANALYSIS;

EID: 68049083555     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmps.2009.05.006     Document Type: Article

References (23)

1. Bouchbinder E., and Procaccia I. Oscillatory instability in two-dimensional dynamic fracture. Physical Review Letters 98 (2007) 124302
2. Bouchbinder E., Livne A., and Fineberg J. Weakly nonlinear theory of dynamic fracture. Physical Review Letters 101 (2008) 264302
3. Bouchbinder E., and Lo T.S. Elastic nonlinearities in a one-dimensional model of fracture. Physical Review E 78 (2008) 056105
4. Broberg K.B. Cracks and Fracture (1999), Academic Press, San Diego
5. Buehler M.J., Abraham F.F., and Gao H. Hyperelasticity governs dynamic fracture at a critical length scale. Nature 426 (2003) 141-146
6. Buehler M.J., and Gao H. Dynamical fracture instabilities due to local hyperelasticity at crack tips. Nature 439 (2006) 307-310
7. Fineberg J., and Marder M. Instability in dynamic fracture. Physics Reports 313 (1999) 1-108
8. Freund L.B. Dynamic Fracture Mechanics (1998), Cambridge University Press, Cambridge
9. Gao H. A theory of local limiting speed in dynamic fracture. Journal of the Mechanics and Physics of Solids 44 9 (1996) 1453-1474
10. Geubelle P.H. Finite deformation effects in homogeneous and interfacial fracture. International Journal of Solids and Structures 32 (1995) 1003-1016
11. Geubelle P.H., and Knauss W.G. Propagation of a crack in homogeneous and bimaterial sheets under general in-plane loading: nonlinear analysis. Journal of Applied Mechanics 62 (1995) 601-606
12. Gurtin M.E., and Yatomi C. On the energy release rate in elastodynamic crack propagation. Archive for Rational Mechanics and Analysis 74 (1980) 231-247
13. Holzapfel G.A. Nonlinear Solid Mechanics (2000), Wiley, Chichester
14. Knowles J.K., and Sternberg E. Large deformations near a tip of an interface-crack between two Neo-Hookean sheets. Journal of Elasticity 13 (1983) 257-293
15. Krishnan V.R., Hui C.Y., and Long R. Finite strain crack tip fields in soft incompressible elastic solids. Langmuir 24 (2008) 14245-14253
16. Livne A., Cohen G., and Fineberg J. Universality and hysteretic dynamics in rapid fracture. Physical Review Letters 94 (2005) 224301
17. Livne A., Ben-David O., and Fineberg J. Oscillations in rapid fracture. Physical Review Letters 98 (2007) 124301
18. Livne A., Bouchbinder E., and Fineberg J. Breakdown of linear elastic fracture mechanics near the tip of a rapid crack. Physical Review Letters 101 (2008) 264301
19. Rice J.R. Mathematical analysis in the mechanics of fracture. In: Liebowitz H. (Ed). Fracture: An Advanced Treatise, Mathematical Fundamentals vol. 2 (1968), Academic Press, New York 191-311
20. Rice J.R. A path independent integral and the approximate analysis of strain concentration by notches and cracks. Journal of Applied Mechanics 35 (1968) 379-386
21. Rice J.R. Limitations to the small scale yielding approximation for crack tip plasticity. Journal of the Mechanics and Physics of Solids 22 1 (1974) 17-26
22. Tarantino A.M. Crack propagation in finite elastodynamics. Mathematics and Mechanics of Solids 10 (2005) 577-601
23. Williams M.L. On the stress distribution at the base of a stationary crack. Journal of Applied Mechanics 24 (1957) 109-114