A model of crystal plasticity based on the theory of continuously distributed dislocations

Journal of the Mechanics and Physics of Solids

Volumn 49, Issue 4, 2001, Pages 761-784

  Acharya, Amit ^a,b  

^a UNIVERSITY OF ILLINOIS AT URBANA CHAMPAIGN   (United States)

^b CARNEGIE MELLON UNIVERSITY   (United States)

Author keywords

B. Crystal plasticity; Continuous distribution of dislocations; Dislocation mechanics

Indexed keywords

EID: 0000364551     PISSN: 00225096     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-5096(00)00060-0     Document Type: Article

References (18)

1. Carlson, D.E., 1967. On Gunther's stress functions for couple stresses. Quart. Appl. Math. XXV, 139-146.
2. Clifton, R.J., 1983. Dynamic plasticity. J. Appl. Mech. 105, 941-952.
3. Edelen, D.G.B., 1985. Applied Exterior Calculus. Wiley-Interscience, Wiley, New York.
4. Edelen, D.G.B., Lagoudas, D.C., 1988. Gauge theory and defects in solids. In: Sih, G.C. (Ed.), Mechanics and Physics of Discrete Systems, Vol. 1. North-Holland, Elsevier Science Publishers, Amsterdam.
5. Eshelby, J.D., 1956. The continuum theory of lattice defects. In: Seitz, Turnbull (Eds.), Progress in Solid State Physics, Vol. 3. Academic Press, New York, pp. 79-144.
6. Fox, N., 1966. A continuum theory of dislocations for single crystals. J. Inst Math. Appl. 2, 285-298.
7. Hutchinson, J., 2000. Plasticity at the micron scale. Int. J. Solids Struct. 37, 225-238.
8. Kosevich, A.M., 1979. Crystal dislocations and the theory of elasticity. In: Nabarro, F.R.N. (Ed.), Dislocations in Solids. North-Holland Publishing Company, Amsterdam, pp. 33-141.
9. Milstein, F., 1982. Crystal elasticity. In: Hopkins, H.G., Sewell, M.J. (Eds.), Mechanics of Solids, The Rodney Hill 60th Anniversary Volume. Pergamon Press, Oxford, pp. 417-452.
10. Mura, T., 1963. Continuous distribution of moving dislocations. Philos. Mag. 89, 843-857.
11. Nye, J.F., 1953. Some geometrical relations in dislocated crystals. Acta Metall, 1, 153-162.
12. Ortiz, M., Phillips, R., 1999. Nanomechanics of defects in solids. Adv. Appl. Mech. 36, 1-79.
13. Rosakis, P., Rosakis, A.J., 1988. The screw dislocation problem in incompressible finite elastostatics: a discussion of nonlinear effects. J. Elasticity 20, 3-40.
14. Teodosiu, C., Soos, E., 1981a. Non-linear elastic models of single dislocations. Rev. Roum. Sci. Tech. Ser. Mec. Appl. 26, 731-745.
15. Teodosiu, C., Soos, E., 1981b. Non-linear effects in the elastic field of single dislocations. I. Iteration scheme for solving non-linear problems. Rev. Roum. Sci. Tech., Ser. Mec. Appl. 26, 785-793.
16. Teodosiu, C., Soos, E., 1982. Non-linear effects in the elastic field of single dislocations. II. Second-order elastic effects of an edge dislocation. Rev. Roum. Sci. Tech. Ser. Mec. Appl. 27, 15-35.
17. Weyl, H., 1940. The method of orthogonal projection in potential theory. Duke Math. J. 7, 411-444.
18. Willis, J.R., 1967. Second-order effects of dislocations in anisotropic crystals. Int. J. Eng. Sci. 5, 171-190.