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Abstrakty
The paper contains a short presentation of some models of material continua with microstructure applying the methods of differential geometry. Two main kinds of microstructure are considered: dislocation, disclination, and unholonomic defects in plasticity, nematic liquid crystal as an example of oriented medium. The aim of this presentation is to illustrate the effectiveness of the methods of differential geometry in construction of the theory of microstructural media.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
277--285
Opis fizyczny
Bibliogr. 15 poz., rys.
Twórcy
autor
- Military University of Technology, Warsaw, Kaliskiego 2, 00-908 Warszawa, Poland
Bibliografia
- 1. K. Kondo, On the geometrical and physical foundations of the theory of yielding, in Proc. 2-nd. Jap. Nat. Cong., 41-47, Tokyo 1953.
- 2. B.A. Bilby, Bullough, E. Smith, Continuous distribution of dislocations; a new application of the methods of non-Riemannian geometry, Proc. Roy. Soc., A231, 1185, 263, 273, 1955.
- 3. R. De Wit, A new form of the relation between the continuous theory of lattice defects and non-Euclidean geometry in the linear approximation, Int. J. Enging. Sci. 19, 12, 1475-1506, 1981.
- 4. Y. A. Povstenko, Connection between non-metric differential geometry and mathematical theory of imperfections, Int. J. Engng. Sci., 29, 37-46, 1991.
- 5. K. M. Deng et al., A new gauge field theory of a continuum with dislocations and disclinations, Int. J. Engng. Sci., 29, 1, 79-86.
- 6. J. Saczuk, The balance laws of the continuum mechanics within the geometry of higher order contact-1, Int. J. Engng Sci., 32, 5, 768-778, 1994.
- 7. Cz. Rymarz, Differential geometry in modeling the microstructural material media, J. Tech. Phys., 42, 1, 24-32, 2001.
- 8. E. Cosserat, F. Cosserat, Theorie de corps deformable, Hermann, Paris, 1909.
- 9. W. Nowacki, Theory of nonsymmetrical elasticity [in Polish], PWN, Warsaw, 1981.
- 10. H. Schaefer, Analysis der Motorfelder im Cosserat-Kontinuum, Z. Angew. Math. Mech., 47, 5, 319-328, 1967.
- 11. J. Badur, Pure gauge theory of Cosserat surface, Int. J. Engng Sci., 31, 1, 41-59, 1993.
- 12. J. Badur, Y. Povstenko, On two reinterpretations of Cosserat contnuum; fiber bundle versus motor calculus, Arch. Mech., 50, 3, 367-376, 1998.
- 13. C. Papenfuss, W. Muschik, Liquid crystal theory as an example of mesoscopic continuum mechanics, [in:] Trends in Continuum Mechanics, 271-291, 1998.
- 14. C. Rymarz, Microstructural media in bundle space, Int. J. Engng Sci., 38, 1999.
- 15. A.C. Eringen, Micropolar theory of liquid crystals, Cryst. Orien. Fluid, 3, Plenum Publ. Corp., London 1974.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BAT5-0001-0102