On Volterra dislocations of finitely deforming continua

Mathematics and Mechanics of Solids

Volumn 9, Issue 5, 2004, Pages 473-492

  Casey, James ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Discontinuous displacements; Multiply connected continua; Surfaces of discontinuity; Volterra dislocations

Indexed keywords

CONTINUUM MECHANICS; DEFORMATION; DISLOCATIONS (CRYSTALS); KINEMATICS; TENSORS;

DISCONTINUOUS DISPLACEMENTS; FINITE DEFORMATIONS; MULTIPLY CONNECTED CONTINUA; VOLTERRA DISLOCATIONS;

ELASTICITY;

EID: 7444246264     PISSN: 10812865     EISSN: None     Source Type: Journal    
DOI: 10.1177/1081286504038671     Document Type: Article

References (21)

1. Weingarten, G. Sulle superficie di discontinuità nella teoria della elasticità dei corpi solidi. Atti della Reale Accademia dei Lincei, Rendiconti, Ser. 5, Vol. X, 57-60 (1901).
2. Volterra, V. Sur l'équilibre des corps élastiques multiplement connexes. Annales École Normale, Ser. 3, Vol. XXIV, 401-518 (1907)
3. Opere Matematiche, Vol. 3 153-242, Accademia Nazionale dei Lincei, Rome, 1957.
4. Volterra, V. and Volterra, E. Sur les Distorsions des Corps É lastiques (Théorie et Applications), Mémorial des Sciences Mathématiques, Fascicule CXLVI, Gauthier-Villars, Paris, 1960.
5. Love, A. E. H. A Treatise on the Mathematical Theory of Elasticity, 4th edn., Cambridge University Press, Cambridge, 1927.
6. Nabarro, F. R. N. (ed.) Dislocations in Solids, Vols. 1-6, North-Holland, Amsterdam, 1979-83.
7. Cottrell, A. H. Dislocations and Plastic Flow in Crystals, Oxford University Press, Oxford, 1953.
8. Nabarro, F. R. N. Theory of Crystal Dislocations, Oxford University Press, Oxford, 1967 (also Dover, 1987).
9. Gurtin, M. E. The linear theory of elasticity. Handbuch der Physik, V1a/2, ed. S. Flügge, pp. 1-295, Springer, Berlin, 1972.
10. Teodosiu, C. Elastic Models of Crystal Defects, Springer, Berlin, 1982.
11. Goodier, J. N. On the theory of dislocations and an application to the plane stress problem of a system of forces acting on a hole. Proceedings of the 5th International Congress of Applied Mechanics, ed. J. P. den Hartog & H. Peters, pp. 129-133, Wiley, New York (and Chapman and Hall, London), 1939.
12. Zubov, L. M. Nonlinear Theory of Dislocations and Disclinations in Elastic Bodies, Springer, Berlin, 1997.
13. Shield, R. T. The rotation associated with large strains. SIAM Journal of Applied Mathematics, 25, 483-491 (1973).
14. Naghdi, P. M. and Vongsarnpigoon, L. Small strain accompanied by moderate rotation. Archive for Rational Mechanics and Analysis, 80, 263-294 (1982).
15. Truesdell, C. and Toupin, R. A. The classical field theories. Handbuch der Physik, III/1, ed. S. Flügge, pp. 226-793, Springer, Berlin, 1960.
16. Fosdick, R. L. Remarks on compatibility. Modern Developments in the Mechanics of Continua, ed. S. Eskinazi, 109-127, Academic Press, New York, 1966.
17. Blume, J. A. Compatibility conditions for a left Cauchy-Green strain field. Journal of Elasticity, 21, 271-308 (1989).
18. Cosserat, E. and F. Sur la théorie de l'élasticité. Annales de la Faculté des Sciences de l'Université de Toulouse, 10, 1-116(1896).
19. Kosinski, W. Field Singularities and Wave Analysis in Continuum Mechanics, Ellis Horwood, New York (also Wiley, and PWN-Polish Scientific Publishers), 1986.
20. Forsyth, A. R. Theory of Functions of a Complex Variable, Vol. 1, 3rd edn., Cambridge University Press, Cambridge, 1918 (also Dover, New York, 1965).
21. Lamb, H. : Hydrodynamics, 6th edn., Cambridge University Press, Cambridge, 1932 (also Dover, New York, 1945).