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Kolymbas, D.

Bifurcation analysis for sand samples with a non-linear constitutive equation. (English) Zbl 0452.73023

Ing.-Arch. 50, 131-140 (1981).
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Cited in 10 Documents

MSC:

74G60 Bifurcation and buckling
74L05 Geophysical solid mechanics
74A20 Theory of constitutive functions in solid mechanics
74C99 Plastic materials, materials of stress-rate and internal-variable type

Keywords:

bifurcation; sand samples; non-linear constitutive equation; stress- rates; strain-rates; axisymmetric and plane homogeneous deformations; non-homogeneous deformation
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References:

[1] Mróz, Z.: On forms of constitutive laws for elastic-plastic solids. Arch. Mech. Stos. 18 (1966) 3-34
[2] Stören, S., Rice, J. R.: Localized necking in thin sheets. J. Mech. Phys. Solids 23 (1975) 421-441 · Zbl 0328.73029 · doi:10.1016/0022-5096(75)90004-6
[3] Bazant, Z. P.: Endochronic inelasticity and incremental plasticity. Internat. J. Solids Structures 14 (1978) 691-714 · Zbl 0387.73028 · doi:10.1016/0020-7683(78)90029-X
[4] Sewell, M. J.: A yield-surface corner lowers the buckling stress of an elastic-plastic plate under compression. J. Mech. Phys. Solids 21 (1973) 19-45 · Zbl 0264.73049 · doi:10.1016/0022-5096(73)90028-8
[5] Truesdell, C. A.; Noll, W.: The non-linear field theories of mechanics. In: Encyclopedia of Physics, Vol. III/3 Berlin-Heidelberg-New York: Springer 1965 · Zbl 0779.73004
[6] Vardoulakis, I.: Scherfugenbildung in Sandkörpern als Verzweigungsproblem. Dissertation, Universität Karlsruhe, 1977
[7] Vardoulakis, I.; Goldscheider, M.; Gudehus, G.: Formation of shear bands in sand bodies as a bifurcation problem. Int. Journal Num. Analytical Methods in Geomechanics 2 (1968) 99-128 · doi:10.1002/nag.1610020203
[8] Gudehus, G.; Goldscheider, M.; Winter, H.: Mechanical properties of sand and clay and numerical integration methods: Some sources of errors and bounds of accuracy. In: ?Finite Elements for Geomechanics?, New York: J. Wiley 1977
[9] Hill, R.: The essential structure of constitutive laws for metal composites and polycrystals. J. Mech. Phys. Solids 15 (1967) 79-95 · doi:10.1016/0022-5096(67)90018-X
[10] Hutchinson, J. W.: Elastic-plastic behaviour of polycrystalline metals and composites. Proc. Roy. Soc. London A 319 (1970) 247-272 · doi:10.1098/rspa.1970.0177
[11] Kolymbas, D.: A rate-dependent constitutive equation for soils. Mech. Res. Comm. 4 (1977) 367-372 · doi:10.1016/0093-6413(77)90056-8
[12] Gudehus, G.; Kolymbas, D.: A constitutive law of the rate type for soils. Proc. 3rd Int. Conf. Num. Methods Geomechanics in Aachen. Edited by A. A. Balkema, Rotterdam, 1979
[13] Goldscheider, M.: Grenzbedingung und Fließregel von Sand. Mech. Res. Comm. 3 (1976) 463-468 · doi:10.1016/0093-6413(76)90037-9
[14] Kolymbas, D.: Ein nichtlineares viskoplastisches Stoffgesetz für Böden. Dissertation, Universität Karlsruhe, 1978
[15] Vardoulakis, I.: Shear band inclination and shear modulus of sand in biaxial tests. To appear in Int. J. Num. Anal. Meth. in Geomechanics, 1980 · Zbl 0443.73092
[16] Vardoulakis, I.: Bifurcation analysis of the triaxial test on sand samples. Acta Mech., 32 (1979) 35-54 · Zbl 0402.73086 · doi:10.1007/BF01176132
[17] Truesdell, C. A.; Toupin, R. A.: The classical field theories. In: Encyclopedia of Physics. Vol. III/1 Berlin-Heidelberg-New York: Springer 1960
[18] Vardoulakis, I.: Equilibrium bifurcation of granular earth bodies. In ?Advances in Analysis of Geotechnical Instabilities?, University of Waterloo Press, 1978
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