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Numerical methods for bifurcation analysis in geomechanics

Numerische Methoden zur Verzweigungsanalyse in der Bodenmechanik

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Summary

A numerical approach to bifurcation problems in soil plasticity is outlined. While previously published results have been obtained using non-associated plasticity models, results are now presented for strain-softening plasticity. Attention is focused on a biaxial test, for which results have been obtained starting from a perfectly homogeneous sample and for a sample that contains imperfections. It is shown that the mere introduction of an imperfection not always transfers a bifurcation problem into a limit problem. This observation illustrates the need for an option in a finite element program that carries out a bifurcation analysis.

übersicht

Skizziert wird eine numerische Behandlung von Verzweigungsproblemen in der PlastizitÄt von Böden. WÄhrend frühere Ergebnisse für nicht-assoziiertes plastisches Verhalten gewonnen wurden, werden hier solche für entfestigendes Verhalten dargestellt. Das Hauptaugenmerk ist auf einen zweiachsigen Versuch gerichtet. Für ihn werden Ergebnisse beschrieben in den FÄllen, da\ von einer vollstÄndig homogenen Probe bzw. einer Probe mit Imperfektionen ausgegangen wird. Es wird gezeigt, da\ die alleinige Einführung von Imperfektionen nicht immer ein Verzweigungsproblem in ein Grenzlastproblem überführt. Diese Beobachtung zeigt die Notwendigkeit, da\ Finite-Element-Programme eine Option zur Durchführung von Verzweigungsanalysen enthalten sollten.

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  1. TNO Institute for Building Materials and Structures, Delft University of Technology, P.O. Box 49, NL-2600, AA Delft, The Netherlands

    R. de Borst

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de Borst, R. Numerical methods for bifurcation analysis in geomechanics. Ing. arch 59, 160–174 (1989). https://doi.org/10.1007/BF00538369

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