On the nonlinear mechanics of Bravais crystals with continuous distributions of defects

Mathematics and Mechanics of Solids

Volumn 3, Issue 3, 1998, Pages 331-358

  Cermelli, Paolo ^a   Sellers, Shaun ^b  

^a UNIVERSITY OF TURIN   (Italy)

^b UNIVERSITY OF EAST ANGLIA   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

DISLOCATIONS (CRYSTALS); MATHEMATICAL MODELS; MECHANICS; POINT DEFECTS;

BRAVAIS CRYSTALS; NONLINEAR MECHANICS;

CRYSTALS;

EID: 0032162984     PISSN: 10812865     EISSN: None     Source Type: Journal    
DOI: 10.1177/108128659800300306     Document Type: Article

References (56)

1. Larché, F. C. and Cahn, J. W.: The interaction of composition and stress in crystalline solids. Acta Metall., 33, 331-357 (1985).
2. Mullins, W. W. and Sekerka, R. F.: On the thermodynamics of crystalline solids. J. Chem. Phys., 82, 5192-5202 (1985).
3. Gurtin, M. E. and Voorhees, P. W.: The continuum mechanics of coherent two-phase elastic solids with mass transport. Proc. R. Soc. Lond., A 440, 323-343 (1993).
4. Kondo, K.: On the geometrical and physical foundations of the theory of yielding, in Proc. 2. Japan Nat. Congr. Appl. Mech., 41-47 (1952).
5. Kondo, K.: Non-Riemannian geometry of imperfect crystals from a macroscopic viewpoint, in RAAG Memoirs of the Unifying Study of Basic Problems in Engineering and Physical Science by Means of Geometry, Vol. 1, ed., K. Kondo, Gakuyusty Bunken Fukin-Kay, Tokyo, 1955.
6. Bilby, B. A., Bullough, R., and Smith, E.: Continuous distributions of dislocations: A new application of the methods of non-Riemannian geometry. Proc. R. Soc. Lond., A 231, 263-273 (1955).
7. Bilby, B. A. and Smith, E.: Continuous distribution of dislocations III. Proc. R. Soc. Lond., A 236, 481-505 (1956).
8. e congrès international de mécanique appliquée, 35-44 (1957).
9. Bilby, B. A.: Continuous distributions of dislocations, in Progress in Solid Mechanics, Vol. 1, ed., I. Sneddon, North Holland, Amsterdam, 1960.
10. Eshelby, J. D.: The continuum theory of lattice defects, in Solid State Physics, ed., F. Seitz and D. Turnbull, Vol. 3, pp. 79-144, Academic Press, New York, 1956.
11. Kröner, E.: Kontinuumstheorie der Versetzungen und Eigenspannungen, Ergebnisse der angewandten Mathematik, Vol. 5, Springer, Berlin, 1958.
12. Kröner, E.: Allgemeine Kontinuumstheorie der Versetzungen und Eigenspannungen. Arch. Rational Mech. Anal., 4, 273-334 (1960).
13. Maugin, G.: Material Inhomogeneities in Elasticity, Chapman Hall, London, 1993.
14. Kröner, E.: Dislocations in crystals and in continua: A confrontation. Int. J. Engng. Sci., 33, 2127-2135 (1995).
15. Le, K. C. and Stumpf, H.: Finite elastoplasticity with microstructure, in Mitteilungen aus dem Institut für Mechanik, No. 92, Ruhr-Universität Bochum, 1994.
16. Le, K. C. and Stumpf, H.: Nonlinear continuum theory of dislocations. Int. J. Engng. Sci., 34, 339-358 (1996).
17. Le, K. C. and Stumpf, H.: A model of elastoplastic bodies with continuously distributed dislocations. Int. J. Plasticity, 12, 611-627 (1996).
18. Anthony, K.-H. and Azirhi, A.: Dislocation dynamics by means of Lagrange formalism or irreversible processes: Complex fields and deformation processes. Int. J. Engng. Sci., 33, 2137-2148 (1995).
19. Steinmann, P.: Views on multiplicative elastoplasticity and the continuum theory of dislocations. Int. J. Engng. Sci., 34, 1717-1736 (1996).
20. Lee, E. H.: Elastic-plastic deformation at finite strains. J. App. Mechanics, 36, 1-6 (1996).
21. Teodosiu, C.:, Bull. Acad. Polon. Sci., 15, 95, 103 (1967).
22. Teodosiu, C.:, Rev. Raum. Sci. Techn., 12, 961, 1061, 1291 (1967).
23. Turski, L.:, Bull. Pol. Acad. Sci. Techn. Sci., 14, 289 (1966).
24. Kadić, A. and Edelen, D. G. B.: A Gauge Theory of Dislocations and Disclinations, Springer, Berlin, 1983.
25. Edelen, D. G. B. and Lagoudas, D.: Gauge Theory and Defects in Solids, Elsevier, Amsterdam, 1988.
26. Thomas, J. P.: The application of gauge theory to the modeling of material defects, in Defects and Anelasticity in the Characterization of Crystalline Solids, p. 133, ed., C. M. Brock, ASME, New York, 1992.
27. Popov, V. L.: Gauge theory of plastically incompressible medium: I. Dispersion relations and propagation of perturbations without dissipation. Int. J. Engng. Sci., 30, 329 (1992).
28. Popov, V. L. and Tshertova, N. V: Gauge theory of plastically incompressible medium: II. Dispersion relations with dissipation. Int. J. Engng. Sci., 30, 335 (1992).
29. Edelen, D. G. B.: A correct, globally defined solution of the screw dislocation problem in the gauge theory of defects. Int. J. Engng. Sci., 34, 81-86 (1996).
30. Toupin, R. A.: Dislocated and oriented media, in Mechanics of Generalized Continua, pp. 126-140, ed., E. Kröner, Springer, Berlin, 1967.
31. Davini, C.: A continuum approach to crystals with defects, Istituto di Meccanica Teorica ed Applicata (Udine, Italy) report IMTA/014, 1983.
32. Davini, C.: A proposal for a continuum theory of defective crystals. Arch. Rational Mech. Anal., 96, 295-317 (1986).
33. Davini, C. and Parry, G. P.: On defect-preserving deformations in crystals. Int. J. Plasticity, 5, 337-369 (1989).
34. Davini, C. and Parry, G. P.: A complete list of invariants for defective crystals. Proc. R. Soc. Lond., A 432, 341-365 (1991).
35. Naghdi, P. M. and Srinivasa, A. R.: A dynamical theory of structured solids: I. Basic development. Phil. Trans. R. Soc. Lond., A 345, 425-458 (1993).
36. Naghdi, P. M. and Srinivasa, A. R.: A dynamical theory of structured solids: II. Special constitutive equations and special cases of the theory. Phil. Trans. R. Soc. Lond., A 345, 459 (1993).
37. Naghdi, P. M. and Srinivasa, A. R.: Characterization of dislocations and their influence on plastic deformation in single crystals. Int. J. Engng. Sci., 32, 1157-1182 (1994).
38. Besseling, J. F. and van der Giessen, E.: Mathematical Modeling of Inelastic Deformations, Chapman & Hall, London, 1993.
39. Pitteri, M.: On v + 1 lattices. J. Elasticity, 15, 3-25 (1985).
40. Gurtin, M. E.: The nature of configurational forces. Arch. Rational Mech. Anal., 131, 67-100 (1995).
41. Gurtin, M. E.: Configurational forces as basic concepts of continuum mechanics, preprint (1997).
42. Eshelby, J. D.: The force on an elastic singularity. Phil. Trans. R. Soc. Lond., A 244, 87 (1951).
43. Kosevich, A. M.: Crystal dislocations and the theory of elasticity, in Dislocations in Solids, Vol. 1, pp. 33-141, ed., F.R.N. Nabarro, North-Holland, Amsterdam, 1979.
44. Peach, M. O. and Koehler, J. S.: The forces exerted on dislocations and the stress fields produced by them. Phys. Rev., 80, 436 (1950).
45. Dlużewski, P.: On the geometry and continuum thermodynamics of movement of structural defects. Mechanics of Materials, 22, 23-41 (1996).
46. Ericksen, J. L.: The Cauchy and Bom hypothesis for crystals, in Phase Transformations and Material Instabilities in Solids, pp. 61-77, ed., M. E. Gurtin, Academic Press, New York, 1984.
47. Zanzotto, G.: On the material symmetry group of elastic crystals and the Born rule. Arch. Rational Mech. Anal., 121, 1-36 (1992).
48. Ericksen, J. L.: Equilibrium theory for X-ray observations of crystals, preprint (1996).
49. Born, M. and Huang, K.: Dynamical Theory of Crystal Lattices, Oxford University Press, Oxford, 1954.
50. Ericksen, J. L.: On the symmetry of deformable crystals. Arch. Rational Mech. Anal., 72, 1-13 (1979).
51. Kosevich, A. M.: The deformation field in an isotropic elastic medium containing moving dislocations. Soviet Phys. JEPT (English transl.), 15, 108 (1962).
52. Mura, T.: Continuous distribution of moving dislocations. Phil. Mag., 8, 843 (1963).
53. Naghdi, P. M. and Srinivasa, A. R.: Some general results in the theory of crystallographic slip. Z. angew. Math. Phys., 45, 687-732 (1994).
54. Nye, J. F.: Some geometrical relations in dislocated solids. Acta Metall., 1, 153-162 (1953).
55. Parry, G. P.: Defects and rearrangements in crystals, in Defects and Anelasticity in the Characterization of Crystalline Solids, pp. 117-132, ed., C. M. Brock, ASME, New York, 1992.
56. Cermelli, P. and Gurtin, M. E.: The dynamics of solid-solid phase transitions: 2. Incoherent interfaces. Arch. Rational Mech. Anal., 127, 41-99 (1994).