Summary
A thoroughly non-linear constitutive equation connecting stress-rates and strain-rates is shown to yield realistic predictions for the conditions at which bifurcation may appear in the course of axisymmetric and plane homogeneous deformations of sand samples. The features of the non-homogeneous deformation after the bifurcation are also realistically predicted, a fact which is of importance in understanding and describing rupture phenomena (formation of shear bands) in geomechanics.
Übersicht
In dieser Arbeit wird gezeigt, daß eine nichtlineare Beziehung zwischen der Spannungsrate und der Deformationsgeschwindigkeit realistische Voraussagen für Verzweigungen liefert, die sich im Verlauf von achsensymmetrischer und ebener Verformung von Sandproben einstellen können. Die Geometrie der inhomogenen Verformung, die sich nach der Verzweigung einstellt, kann ebenfalls realistisch vorausgesagt werden. Diese Tatsache ist von Bedeutung für das Verständnis und die Beschreibung von Brucherscheinungen (Bildung von Scherfugen u. ä.) in der Geomechanik.
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References
Mróz, Z.: On forms of constitutive laws for elastic-plastic solids. Arch. Mech. Stos. 18 (1966) 3–34
Stören, S., Rice, J. R.: Localized necking in thin sheets. J. Mech. Phys. Solids 23 (1975) 421–441
Bazant, Z. P.: Endochronic inelasticity and incremental plasticity. Internat. J. Solids Structures 14 (1978) 691–714
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
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
Vardoulakis, I.: Scherfugenbildung in Sandkörpern als Verzweigungsproblem. Dissertation, Universität Karlsruhe, 1977
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
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
Hill, R.: The essential structure of constitutive laws for metal composites and polycrystals. J. Mech. Phys. Solids 15 (1967) 79–95
Hutchinson, J. W.: Elastic-plastic behaviour of polycrystalline metals and composites. Proc. Roy. Soc. London A 319 (1970) 247–272
Kolymbas, D.: A rate-dependent constitutive equation for soils. Mech. Res. Comm. 4 (1977) 367–372
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
Goldscheider, M.: Grenzbedingung und Fließregel von Sand. Mech. Res. Comm. 3 (1976) 463–468
Kolymbas, D.: Ein nichtlineares viskoplastisches Stoffgesetz für Böden. Dissertation, Universität Karlsruhe, 1978
Vardoulakis, I.: Shear band inclination and shear modulus of sand in biaxial tests. To appear in Int. J. Num. Anal. Meth. in Geomechanics, 1980
Vardoulakis, I.: Bifurcation analysis of the triaxial test on sand samples. Acta Mech., 32 (1979) 35–54
Truesdell, C. A.; Toupin, R. A.: The classical field theories. In: Encyclopedia of Physics. Vol. III/1 Berlin-Heidelberg-New York: Springer 1960
Vardoulakis, I.: Equilibrium bifurcation of granular earth bodies. In “Advances in Analysis of Geotechnical Instabilities”, University of Waterloo Press, 1978
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Kolymbas, D. Bifurcation analysis for sand samples with a non-linear constitutive equation. Ing. arch 50, 131–140 (1981). https://doi.org/10.1007/BF00539697
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DOI: https://doi.org/10.1007/BF00539697