Bifurcation and generalized mixed loading conditions in geomaterials

François Nicot (1) , Noël Challamel (2) , Jean Lerbet (3) , Florent Prunier (4) , Félix Darve (5)

1 CEMAGREF - Centre national du machinisme agricole, du génie rural, des eaux et forêts
2 INSA Rennes - Institut National des Sciences Appliquées - Rennes
3 IBISC - Informatique, Biologie Intégrative et Systèmes Complexes
4 INSA Lyon - Institut National des Sciences Appliquées de Lyon
5 3SR - Laboratoire sols, solides, structures - risques [Grenoble]

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.

Keywords: second-order work; controllability; constitutive uniqueness; bifurcation; sustainability; loading parameters

Domains: Mechanics [physics.med-ph]

François Nicot, Noël Challamel, Jean Lerbet, Florent Prunier, Félix Darve. Bifurcation and generalized mixed loading conditions in geomaterials. International Journal for Numerical and Analytical Methods in Geomechanics, 2011, 35 (13), pp.1409-1431. ⟨10.1002/nag.959⟩. ⟨hal-00767565⟩