Dynamical systems, rate and gradient effects in material instability

International Journal of Mechanical Sciences

Volumn 42, Issue 11, 2000, Pages 2101-2114

  Béda, Péter B ^a  

^a BUDAPEST UNIVERSITY OF TECHNOLOGY AND ECONOMICS   (Hungary)

Author keywords

[No Author keywords available]

Indexed keywords

BIFURCATION (MATHEMATICS); BOUNDARY CONDITIONS; COMPUTATIONAL METHODS; DYNAMICS; EIGENVALUES AND EIGENFUNCTIONS; LYAPUNOV METHODS;

MATERIAL INSTABILITY;

MATERIALS SCIENCE;

EID: 0343353890     PISSN: 00207403     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0020-7403(00)00007-2     Document Type: Article

References (21)

1. Arnold V.I. Geometrical methods in the theory of ordinary differential equations. 1983;Springer, New York.
2. Wiggins S. Introduction to applied nonlinear dynamical systems and chaos. 1990;Springer, New York.
3. Béda P.B. Bifurcation and postbifurcation of rods. Journal of Theoretical and Applied Mechanics. 34:1996;91-100.
4. Troger H, Steindl A, Nonlinear stability and bifurcation theory. An introduction for scientists and engineers. New York: Springer, Wien, 1990.
5. Béda PB, Localization as instability of dynamical systems. In: Batra RC, Zbib H, editors. Material instabilities. New York: ASME Press, 1994. p. 279-84.
6. Béda P.B. Material instability in dynamical systems. European Journal of Mechanics, A/Solids. 16:1997;501-513.
7. Dobovsek I. Adiabatic material instabilities in rate-dependent solids. Archives of Mechanics. 46:1994;893-936.
8. Zbib H.M., Aifantis E.C. On the localization and postlocalization behavior of plastic deformation. I. Res Mechanica. 23:1988;261-277.
9. Rice JR, The localization of plastic deformation. In: Koiter WT, editor. Theoretical and applied mechanics. Amsterdam: North-Holland Publ, 1976. p. 207-20.
10. De Borst R., Sluys L.J., Mühlhaus H.B., Pamin J. Fundamental issues in finite element analyses of localization of deformation. Engineering Computations. 10:1993;99-121.
11. Sluys LJ, Wave propagation, localization and dispersion in softening solids. Dissertation, Delft University of Technology, Delft, 1992.
12. Sluys L.J., De Borst R. Wave propagation and localization in a rate-dependent cracked medium - model formulation and one-dimensional examples. International Journal of Solids Structures. 29:1992;2945-2958.
13. Eringen C. Continuum physics, vol. II. 1975;Academic Press, New York.
14. Vardoulakis I. Potentials and limitations of softening models in geomechanics. European Journal of Mechanics, A/Solids. 13:1994;195-226.
15. Béda Gy. Methode zur Bestimmung der Materialgleichung. Publication of the Technical University for Heavy Industry Miskolc. 12:1962;271-286.
16. Béda Gy. Possible constitutive equations of the moving plastic body. Advances in Mechanics. 10:1987;65-87.
17. Béda PB, Dynamical systems and the rate dependence of cracked medium. In: Karihaloo BL, Mai YW, Ripley MI, Ritchie DO, editors. Advances in fracture research. New York: Pergamon Press, 1997. p. 2949-57.
18. Nguyen Q.S. Bifurcation and stability of dissipative systems. 1992;Springer, New York.
19. Chetayev N.G. The stability of motion. 1961;Pergamon Press, New York.
20. Martins JAC, Simoes FMF, On some sources of instability/ill-posedness in elasticity problems with Coulomb's friction. In: Raous M, editor. Contact mechanics. New York: Plenum Press, 1995. p. 95-106.
21. Zbib HM, Aifantis EC, On the structure and width of shear bands in finite elastoplastic deformations. In: Boehler JP, Khan AS, editors. Anisotropy and localization of plastic deformations. New York: Elsevier, 1991. p. 99-103.