On variational symmetry of defect potentials and multiscale configurational force

Philosophical Magazine

Volumn 88, Issue 7, 2008, Pages 1059-1084

  Li, Shaofan ^a  

^a 109 McLaughlin Hall   (United States)

Author keywords

Compatibility; Configurational force; Conservation laws; Dislocation; Fracture; Multiscale analysis; Path independent integral

Indexed keywords

BRITTLE FRACTURE; DIFFERENCE EQUATIONS; DIFFERENTIAL EQUATIONS; EQUATIONS OF MOTION; EULER EQUATIONS; FRACTURE FIXATION; INTEGRAL EQUATIONS;

(E ,2E) THEORY; (SPM) CLASSES; APPLIED (CO); COMPATIBILITY CONDITIONS; CONSERVATION LAWS; CONSERVED QUANTITIES; CONSTITUTIVE RELATIONS; CONTOUR INTEGRALS; DEFECT FREE; DEFECT MOTIONS; EULER LAGRANGE (EL) EQUATIONS; FUNCTIONALS; GRIFFITH CRITERION; INVARIANT INTEGRALS; INVARIANT PROPERTIES; MACROSCOPICALLY; MULTI SCALING; SYMMETRY PROPERTIES;

DEFECTS;

EID: 46249085249     PISSN: 14786435     EISSN: 14786443     Source Type: Journal    
DOI: 10.1080/14786430802050427     Document Type: Article

References (50)

1. E. Noether, Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen 2 (1918) p.235.
2. J.K. Knowles and E. Sternberg, Arch. Rational Mech. Anal. 44 (1972) p.187.
3. M.E. Gurtin, Arch. Rational Mech. Anal. 131 (1995) p.67.
4. J.D. Eshelby, Phil. Trans. R. Soc. A 244 (1951) p.87.
5. J.D. Eshelby, The continuum theory of lattice defects, in Solid State Physics, Vol. 3, F. Seitz and D. Turnbull eds., Academic Press, New York, 1956, pp.79-144.
6. G.A. Maugin, Material Inhomogeneities in Elasticity, Chapman & Hall, London, 1993.
7. M.E. Gurtin, Configurational Forces as Basic Concepts of Continuum Mechanics, Springer-Verlag, New York, 1999.
8. R. Kienzler and G. Herrmann, Mechanics in Material Space, Springer-Verlag, New York, 1956.
9. P. Steinmann and G.A. Maugin, Mechanics of Material Forces, Springer-Verlag, New York, 2005.
10. M.C. Valsakumar and D. Sahoo, Bull. Mater. Sci. 10 (1988) p.3.
11. M. Lazar, J. Phys. A: Math. Gen. 35 (2002) p.1983.
12. M. Lazar, J. Phys. A: Math. Gen. 36 (2003) p.1415.
13. P. Sharma and S. Ganti, Proc. R. Soc. London, A 461 (2005) p.1081.
14. V.A. Lubarda and X. Markenscoff, J. Mech. Phys. Solids 48 (2000) p.553.
15. V.A. Lubarda and X. Markenscoff, Phil. Mag. 83 (2003) p.1365.
16. M. Lazar and H.O.K Kirchner, Int. J. Mater. Struct. 1 (2006) p.325.
17. M. Lazar and G.A. Maugin, Phil. Mag. 87 (2007) p.3853.
18. R. Maranganti and P. Sharma, Phys. Rev. Lett. 98 (2007) p.195504.
19. S. Li, C. Linder and J.W. Foulk III, J. Mech. Phys. Solids 55 (2007) p.980.
20. S. Li, A. Gupta and X. Markenscoff, Proc. R. Soc. London A 461 (2005) p.99.
21. E. Kröner, Ergebnisse der angewandten Mathematik, Bd. 5, Springer-Verlag, Berlin, 1958.
22. E. Kröner, Continuum theory of defects, in Physics of Defects, R. Balian ed., North-Holland Pub. Co, New York, 1981, pp.215-312.
23. J.F. Nye, Acta Metall. 1 (1953) p.153.
24. K.-H. Anthony, Arch. Rational Mech. Anal. 39 (1970) p.43.
25. R. deWit, Linear theory of static disclinations, in Fundamental Aspects of Dislocation Theory, Vol. 1, J.A. Simmons, R. deWit and R. Bullough eds., US Government Printing Office, Washington, 1970, pp.651-673.
26. N.A. Fleck and J.W. Hutchinson, Strain gradient plasticity, in Advances in Applied Mechanics, Vol. 33, J.W. Hutchinson and T.Y. Wu eds., Academic Press, New York, 1997, pp.295-361.
27. P. Cermelli and M.E. Gurtin, J. Mech. Phys. Solids 49 (2001) p.1539.
28. A. Kadic and D.G.B Edelen, Int. J. Engng. Sci. 20 (1982) p.433.
29. A. Kadic and D.G.B Edelen, A Gauge Theory of Dislocations and Disclinations, Springer-Verlag, Berlin, 1983.
30. D.G.B Edelen and D.C. Lagoudas, Gauge Theory and Defects in Solids, North-Holland, Amsterdam, 1983.
31. P. Steinmann, Int. J. Engng. Sci. 34 (1996) p.1717.
32. M.E. Gurtin, J. Mech. Phys. Solids 50 (2002) p.5.
33. E. Kröner, Int. J. Sol. Struct. 38 (2001) p.1115.
34. E. Tonti, Meccanica 2 (1967) p.201.
35. N.H. Ibragimov, CRC Handbook of Lie Group Analysis of Differential Equations, Vols. 1-3, CRC Press, Boca Raton, 1994.
36. H. Kleinert, Gauge Fields in Condensed Matter, Vol. II, World Scientific, Singapore, 1989.
37. C. Malyshev, Ann. Phys. 286 (2000) p.249.
38. M. Baus and R. Lovett, Phys. Rev. Lett. 65 (1990) p.1781.
39. M. Baus and R. Lovett, Phys. Rev. A 44 (1991) p.1211.
40. K. Washizu, Variational Methods in Elasticity and Plasticity, 2nd ed., Oxford University Press, Oxford, 1975.
41. H.D. Bui, Engng. Frac. Mech. 6 (1974) p.287.
42. S. Li and A. Gupta, J. Elast. 84 (2006) p.12.
43. S. Li, Nonlin. Dynam. 36 (2004) p.77.
44. A.A. Griffith, Phil. Trans. R. Soc. London A 221 (1921) p.163.
45. G.R. Irwin, Fracture dynamics, in Fracturing of Metals, American Society for Metals, Cleveland, Ohio, 1948, pp.147-166.
46. R.A. Toupin, Arch. Rational Mech. Anal. 11 (1962) p.385.
47. R.D. Mindlin, Int. J. Sol. Struct. 1 (1965) p.417.
48. J.R. Rice, J. Appl. Mech. 35 (1968) p.379.
49. J.A.H Hult and F.A. McClintock, Elastic-plastic stress and strain distributions around sharp notches under repeated shear, in Proc. 9th Int. Cong. Appl. Mech., Vol. 8, University of Brussels, Brussels, 1957, pp.51-58.
50. S. Li, Phil. Magaz. Lett. 87 (2007) p.945.