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Bifurcation and generalized mixed loading conditions in geomaterials
Author(s) -
Nicot François,
Challamel Noel,
Lerbet Jean,
Prunier Florent,
Darve Félix
Publication year - 2011
Publication title -
international journal for numerical and analytical methods in geomechanics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.419
H-Index - 91
eISSN - 1096-9853
pISSN - 0363-9061
DOI - 10.1002/nag.959
Subject(s) - bifurcation , context (archaeology) , quasistatic process , mathematics , geomechanics , bifurcation theory , solid mechanics , stiffness , matrix (chemical analysis) , stiffness matrix , extension (predicate logic) , mathematical analysis , nonlinear system , structural engineering , physics , geotechnical engineering , computer science , engineering , materials science , geology , thermodynamics , paleontology , quantum mechanics , composite material , programming language
SUMMARY The concept of bifurcation has been widely discussed, based, for example, on homogeneous tests in soil mechanics. Essentially two‐dimensional (axisymmetric) conditions have been considered. This paper aims at deriving a bifurcation criterion in geomechanics, independently of the problem's dimension. This criterion is related to the vanishing of the determinant of the symmetric part of the material's (or the discrete system's) constitutive (or stiffness) matrix. The derivation is essentially based on the notion of loading parameters (controlling the loading). Basically, a bifurcation occurs when the existence of a unique solution to the quasistatic problem, involving a given set of loading parameters, is lost. Interestingly, the criterion is shown to be independent of the choice of loading parameters. As a possible extension, the context of structure mechanics is considered, and the close connection between both soil and structure analysis is discussed. Copyright © 2010 John Wiley & Sons, Ltd.