Continuum theory of dislocations revisited

Continuum Mechanics and Thermodynamics

Volumn 18, Issue 3-4, 2006, Pages 195-222

  Berdichevsky, Victor L ^a  

^a Wayne State University   (United States)

Author keywords

Continuum theory of dislocations; Plastic spin; Strain gradient plasticity

Indexed keywords

CONTINUUM MECHANICS; DISLOCATIONS (CRYSTALS); NUMERICAL ANALYSIS; PLASTICITY;

CONTINUUM THEORY OF DISLOCATIONS; PLASTIC SPIN; STRAIN GRADIENT PLASTICITY;

CRYSTAL STRUCTURE;

EID: 33746768822     PISSN: 09351175     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00161-006-0024-7     Document Type: Article

References (43)

1. Berdichevsky, V.L, Sedov, L.I.: Dynamic theory of continuously distributed dislocations. Its relation to plasticity theory. PMM, 31(6), 981-1000, (1967)
2. (English translation: J. Appl. Math. Mech. (PMM), 989-1006 (1967))
3. Nye, J.F.: Some geometrical relations in dislocated crystals. Acta Metall, 1, 153-162 (1953)
4. Kunin, I.A.: Methods of tensor analysis in the theory of dislocations. A supplement to the Russian edition of J.A. Schouten's Tensor analysis for physicists, English translation (1967) is available from the US Department of Commerce, Clearinghouse for Federal Scientific and Technical Information, TT 67/514 26, Springfield, VA 22151 (1965)
5. Kunin, I.A.: Elastic Media with Microstructure, vol. 2. Springer, Berlin Heidelberg New York (1983)
6. Kröner, E.: Kontinuumtheorie der Versetzungen und Eigenspannungen. Springer, Berlin Heidelberg New York (1958)
7. Kondo, K.: On the geometrical and physical foundations of the theory of yielding. In: Proceedings of the 2nd Japan Congress on Applied Mechanics, (1952), Tokyo, (1953)
8. Kondo, K.: Memoirs of the Unified Study of the Basic Problems in Engineering by Means of Geometry, vol. 1-3. pp 1955-1962. Gakujutsubunken- fukyukai, Tokyo (1955)
9. Bilby, B.A, Bullough, R., Smith, E.: Continuous distributions of dislocations: a new application of the methods of non-Riemannian geometry. Proc R Soc A231 (1955)
10. Bilby, B.A, Smith, E.: Continuous distribution of dislocations. Proc R Soc A236, (1956)
11. Bilby, B.A: Continuous distributions of dislocations. In: Sneddon I. (ed.) Progress. Solid Mechanics, vol. 1, Amsterdam (1960)
12. Le, K.C., Stumpf, H.: On the determination of the crystal reference in nonlinear continuum theory of dislocations. Proc. R. Soc. A452, 359-371 (1996)
13. Sedov, L.I., Berdichevsky, V.L: A dynamic theory of continual dislocations. In: Kröner, E. (ed.) Mechanics of Generalized Continua, pp 214-238. Springer, Berlin Heidelberg New York (1968)
14. Sedov, L.I.: Mathematical methods of constructing models of continuum media. Usp. Matem. Nauk 20(5), 123-182 (1965)
15. Aifantis, E.G.: On the microstructural origin of certain inelastic models. Trans. ASME J. Eng. Mater. Technol. 106, 326-330 (1984)
16. Aifantis, E.G.: Physics of plastic deformation. Int. J. Plasticity, 3, 211-247 (1987)
17. Fleck, N.A., Hutchinson, J.W.: A phenomenological theory for strain gradient effects in plasticity. J. Mech. Phys. Solids 41, 1825-1857 (1993)
18. Fleck, N.A., Muller, G.M., Ashby, M.F., Hutchinson, J.W.: Strain gradient plasticity: theory and experiment. Acta Metall. Material. 42, 475-487 (1994)
19. Acharia, A., Bassani, J.L.: Incompatible lattice deformations and crystal plasticity. In: Ghoneim, N., (ed.) Plastic and Fracture Instabilities in Materials, AMD-Vol. 200/MD-Vol 57, pp 75-80. ASME, New York, (1995)
20. Gao, H., Huang, Y., Nix, W.D., Hutchinson, J.W.: Mechanism-based strain gradient plasticity-I. Theory. J. Mech. Phys. Solids 47, 1239-1263 (1999)
21. Aifantis, E.C.: Strain gradient interpretation of size effects. Int. J. Fracture 95, 299-314 (1999)
22. Shu, J.Y., Fleck, N.A.: Strain gradient crystal plasticity: size-dependent deformation of bicrystals. J. Mech. Phys. Solids 47, 297-324, (1999)
23. Bassani, J.L.: Incompatibility and a simple gradient theory of plasticity. J. Mech. Phys. Solids 49, 1983-1996 (2001)
24. Fleck, N.A., Hutchinson, J.W.: A reformulation of strain- gradient plasticity. J. Mech. Phys Solids 49, 2245-2271 (2001)
25. Gudmundson, P.: A unified treatment of strain gradient plasticity. J. Mech. Phys. Solids 52, 1379-1406 (2004)
26. Gurtin, M.: A gradient theory of small-deformation isotropic plasticity that accounts for the Burgers vector and for dissipation due to plastic spin. J. Mech. Phys. Solids 52, 2545-2568 (2004)
27. Huang, Y., Qu, S., Hwang, K.C., Li, M., Gao, H.: A conventional theory of mechanism-based strain gradient plasticity. Int. J. Plasticity 20, 753-782 (2004)
28. Aifantis, K.E., Willis, J.R.: The role of interfaces in enhancing the yield strength of composites and polycrystals. J. Mech. Phys. Solids 53, 1047-1070 (2005)
29. Han, C.S., Gao, H., Huang, Y., Nix, W.D.: Mechanism-based strain gradient crystal plasticity-I. Theory. J. Mech. Phys. Solids 53, 1188-1203 (2005)
30. Berdichevsky, V., Dimiduk, D.: On failure of continuum plasticity theories on small scales. Scripta Material. 52, 1017-1019 (2005)
31. Berdichevsky, V.: Homogenization in micro-plasticity. J. Mech. Phys. Solids 53, 2457-2469 (2005)
32. Popov, V.L., Kröner, E.: Theory of elastoplastic media with mesostructure. Theor Appl Fracture Mech. 37, 299-310 (2001)
33. Berdichevsky, V.: On thermodynamics of crystal plasticity. Scripta Material. 54, 711-716 (2006)
34. Ortiz, M., Repetto, E.A.: Nonconvex energy minimization and dislocation structures in ductile single crystals. J. Mech. Phys. Solids 47, 397-462 (1999)
35. Berdichevsky, V.L.: Structure of equations of macrophysics. Phys. Rev. E 68:066126 (2003)
36. Berdichevsky, V.L.: Variational principles of continuum mechanics. Nauka, Mascow, (1983)
37. Puglisi, G., Truskinovsky, L.: Thermodynamics of rate independent plasticity. J. Mech. Phys. Solids 53, 655-679 (2005)
38. Berdichevsky, V.L.: Variational-asymptotic method of constructing shell theory. J. Appl. Math. Mech. (PMM) 44(4), 664-687 (1979)
39. Dafalias, Y.F.: The plastic spin. J. Appl. Mech. 52, 865-871 (1985)
40. Bilby, B. A., Gardner, L.R.T., Stroh, A.N. : Extrait des Actes du IX Congrès International de Mechanique Appliquèe, Bruxelles, 35-43 (1957)
41. Kröner, E.: Arch. Ration. Mech. Anal. 4, 273 (1960)
42. Lee, E.H.: ASME J. Appl. Mech. 36, 1 (1969)
43. Mandel, J.: Thermodynamics and plasticity. In: Delgado Domingos, J.J., Nina, M.N.R., Whitelaw, J.H. (eds.) Foundations of Thermodynamics, pp 283-315. Wiley, New York (1973)