Complementary energy release rates and dual conservation integrals in micropolar elasticity

Journal of the Mechanics and Physics of Solids

Volumn 55, Issue 10, 2007, Pages 2055-2072

  Lubarda, V A ^a   Markenscoff, X ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Complementary energy; Configurational force; Conservation integrals; Dual integrals; Micropolar elasticity

Indexed keywords

DEFECT DENSITY; ELASTICITY; ENERGY RELEASE RATE; INTEGRAL EQUATIONS; POTENTIAL ENERGY; SHEARING;

COMPLEMENTARY ENERGY; CONFIGURATIONAL FORCES; CONSERVATION INTEGRALS; DUAL INTEGRALS; MICROPOLAR ELASTICITY;

TENSORS;

EID: 34548624306     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jmps.2007.03.005     Document Type: Article

References (38)

1. Asaro R.J., and Lubarda V.A. Mechanics of Solids and Materials (2006), Cambridge University Press, Cambridge
2. Atkinson C., and Leppington F.G. Some calculations of the energy-release rate G for cracks in micropolar and couple-stress elastic media. Int. J. Fract. 10 (1974) 599-602
3. In: Brulin O., and Hsieh R.K.T. (Eds). Mechanics of Micropolar Media (1982), World Scientific, Singapore
4. Budiansky B., and Rice J.R. Conservation laws and energy-release rates. J. Appl. Mech. 40 (1973) 201-203
5. Bui H.D. Dualité entre les intégrals indépendentes du contour dans la théorie des solides fissurés. C. R. Acad. Sci. Paris 276 (1973) 1425-1428
6. Bui H.D. Dual path independent integrals in the boundary-value problems of cracks. Eng. Fract. Mech. 6 (1974) 287-296
7. Bui H.D. Inverse Problems in the Mechanics of Materials: An Introduction (1994), CRC Press, Boca Raton, FL
8. Carlsson A.J. Path independent integrals in fracture mechanics and their relation to variational principles. In: Sih G.C., van Elst H.C., and Broek D. (Eds). Prospects of Fracture Mechanics (1974), Noordhoff, Leyden, The Netherlands 139-158
9. Cosserat E., and Cosserat F. Theorie des Corps Deformables (1909), Hermann, Paris
10. Dai T.A. Some path-independent integrals for micropolar media. Int. J. Solids Struct. 22 (1986) 729-735
11. Eringen A.C. Microcontinuum Field Theories (1999), Springer, New York
12. Eshelby J.D. The force on an elastic singularity. Philos. Trans. R. Soc. A 244 (1951) 87-112
13. Eshelby J.D. The continuum theory of lattice defects. Solid State Phys. 3 (1956) 79-144
14. Eshelby J.D. The elastic energy-momentum tensor. J. Elasticity 5 (1975) 321-335
15. Günther W. Über einige Randintegrale der Elastomechanik. Abh. Braunschw. Wiss. Ges. 14 (1962) 53-72
16. Gurtin M.E. Configurational Forces as Basic Concepts of Continuum Mechanics (2000), Springer, New York
17. Jaric J.P. The energy-release rate in quasi-static crack propagation and J-integral. Int. J. Solids Struct. 22 (1986) 767-778
18. Kienzler R., and Herrmann G. Mechanics in Material Space (2001), Springer, Berlin
19. Knowles J.K., and Sternberg E. On a class of conservation laws in linearized and finite elastostatics. Arch. Ration. Mech. Anal. 44 (1972) 187-211
20. Lazar M., and Kirchner H.O.K. The Eshelby stress tensor, angular momentum tensor and scaling flux in micropolar elasticity. Int. J. Solids Struct. 44 (2007) 4613-4620
21. Li S., and Gupta A. On dual configurational forces. J. Elasticity 84 (2006) 13-31
22. Li X. Dual conservation laws in elastostatics. Eng. Fract. Mech. 29 (1988) 233-241
23. Lubarda V.A. Circular inclusions in anti-plane strain couple stress elasticity. Int. J. Solids Struct. 40 (2003) 3827-3851
24. Lubarda V.A., and Markenscoff X. Conservation integrals in couple stress elasticity. J. Mech. Phys. Solids 48 (2000) 553-564
25. Lubarda V.A., and Markenscoff X. On conservation integrals in micropolar elasticity. Philos. Mag. A 83 (2003) 1365-1377
26. Lubarda V.A., and Markenscoff X. Dual conservation integrals and energy release rates. Int. J. Solids Struct. 44 (2007) 4079-4091
27. Maugin G.A. Material forces: concepts and applications. Appl. Mech. Rev. 48 (1995) 247-285
28. Maugin G.A. On the structure of the theory of polar elasticity. Philos. Trans. R. Soc. London A 356 (1998) 1367-1395
29. Mindlin R.D. Micro-structure in linear elasticity. Arch. Ration. Mech. Anal. 16 (1964) 51-78
30. Moran B., and Shih C.F. A general treatment of crack tip contour integrals. Int. J. Fract. 35 (1987) 295-310
31. Nowacki W. Theory of Asymmetric Elasticity (1986), Pergamon, Oxford, UK
32. Pucci E., and Saccomandi G. Symmetries and conservation laws in micropolar elasticity. Int. J. Eng. Sci. 28 (1990) 557-562
33. Rice J.R. A path independent integral and approximate analysis of strain concentration by notches and cracks. J. Appl. Mech. 38 (1968) 379-386
34. Rice J.R. Conserved integrals and energetic forces. In: Bilby B.A., Miller K.J., and Willis J.R. (Eds). Fundamentals of Deformation and Fracture (1985), Cambridge University Press, Cambridge 33-56
35. Sun S.-X. Dual conservation laws in elastostatics. Int. J. Eng. Sci. 23 (1985) 1179-1186
36. Trimarco C., and Maugin G.A. Bui's path-independent integral in finite elasticity. Meccanica 30 (1995) 139-145
37. Voigt W. Theoritiscke Studienuber die Elastizitatsverhaltnisse der Krystalle. Abhandl. Ges. Wiss. Gottingen 34 (1887) 3-51
38. Vukobrat M.D. Conservations laws in micropolar elastodynamics and path-independent integrals. Int. J. Eng. Sci. 27 (1989) 1093-1106