Strain measures, integrability condition and frame indifference in the theory of oriented media

International Journal of Solids and Structures

Volumn 35, Issue 9-10, 1998, Pages 783-798

  Le, K C ^a   Stumpf, H ^a  

^a RUHR UNIVERSITY BOCHUM   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

DEFORMATION; DISLOCATIONS (CRYSTALS); FREE ENERGY; INVERSE PROBLEMS; STRAIN MEASUREMENT;

FRAME INDIFFERENCE; ORIENTED MEDIA THEORY;

MATERIALS SCIENCE;

EID: 0032017681     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-7683(97)00087-5     Document Type: Article

References (23)

1. Bilby, B. A., Bullough, R. and Smith, E. (1955) Continuous distributions of dislocations: a new application of the methods of non-Riemannian geometry. Proceedings of the Royal Society of London, A231, 263-273.
2. e Congrès International de Mécanique Appliquée, pp. 35-44, Brüssel.
3. Capriz, G. and Podio-Guidugli, P. (1976) Discrete and continuous bodies with affine structure. Annali di Matematica, 4(61), 195-211.
4. Capriz, G. (1988) Continua with Microstructure, Springer Tracts in Natural Philosophy, Vol. 35, pp. 57-59. Springer, Berlin.
5. Cosserat, E. and Cosserat, F. (1909) Théorie des Corps Déformables. Hermann, Paris.
6. Eringen, A. C. and Kafadar, Ch. B. (1976) Polar field theories. In Continuum Physics, Vol. IV, pp. 33-63. Academic Press, New York.
7. Gantmacher, F. R. (1960) The Theory of Matrices. Chelsea, New York.
8. Kröner, E. (1958) Kontinuumstheorie der Versetzungen und Eigenspannungen. Ergebnisse der Angewandten Mathematik, Vol. 5. Springer, Berlin.
9. Kröner, E. (1960) Allgemeine Kontinuumstheorie der Versetzungen und Eigenspannungen. Archiv Rational Mechanics and Analysis, 4, 273-334.
10. Kröner, E. (1992) Mikrostrukturmechanik. GAMM-Mitteilungen, 15, 104-119.
11. Le, K. C. and Stumpf, H. (1993) Constitutive equations for elastoplastic bodies at finite strain: thermodynamic implementation. Acta Mechanica, 100, 155-170.
12. Le, K. C. and Stumpf. H. (1994) Finite elastoplasticity with microstructure. In Mitteilungen Institute für Mechanik, Vol. 93. Ruhr-Universität, Bochum.
13. Le, K. C. and Stumpf, H. (1996a) On the determination of the crystal reference in nonlinear continuum theory of dislocations. Proceedings of the Royal Society of London, A452, 1-13.
14. Le, K. C. and Stumpf, H. (1996b) Nonlinear continuum theory of dislocations. Internatioanl Journal ofEngineering Science, 34, 339-358.
15. Le, K. C. and Stumpf, H. (1996c) A model of elastoplastic bodies with continuously distributed dislocations. International Journal of Plasticity, 12, 611-627.
16. Lee, E. H. (1969) Elasto-plastic deformation at finite strains. Journal of Applied Mechanics, 36, 1-6.
17. Naghdi, P. M. and Srinivasa, A. R. (1993) A dynamical theory of structured solids. I - Basic developments. Philosophical Transactions of the Royal Society of London, A345, 425-458.
18. Naghdi, P. M. and Srinivasa, A. R. (1994) Characterization of dislocations and their influence on plastic deformation in single crystals. International Journal of Engineering Science, 32, 1157-1182.
19. Noll, W. (1967) Materially uniform simple bodies with inhomogeneities. Archive Rational and Mechanical Analysis, 27, 1-32.
20. Sternberg, S. (1983) Lectures on Differential Geometry. Chelsea, New York.
21. Stumpf, H. and Le, K. C. (1993) On a general concept for finite elastoplasticity based on a nonlinear continuum theory of dislocations. In Proceedings of the 4th International Symposium on Plasticity and its Current Applications, Baltimore, 1993.
22. Toupin, R. A. (1964) Elastic materials with couple-stresses. Archive Rational Mechanics and Analysis, 11, 385-414.
23. Truesdell, C. and Noll, W. (1965) The non-linear field theories of mechanics. In Handbuch der Physik, Vol. III/3, pp. 389-401. Springer, Berlin.