ABSTRACT
In practice, failure appears as induced by instabilities. These instabilities can have a geometric origin as in the well known case of buckling. Slender triaxial samples collapse due to geometrical instabilities. Other instabilities have a material origin and two different modes are possible in this class. The localized failure mode is characterized by shear band formation, due to localization of plastic strains. This failure mode is well described by the localization condition, which corresponds to the vanishing values of the determinant of the acoustic tensor:
(1)
where L is the elasto-plastic tensor:
(2)
and n is the normal to the shear band (Rice 1976; Darve 1984). On the contrary, diffuse modes of failure are characterized by the absence of localization and a chaotic displacement field. This aspect is illustrated for continuous media in section 2 of this paper and for discrete materials (Schneebeli material constituted by piled cylinders) in Darve et al. (2003). The most known examples of diffuse failure are given by liquefaction phenomenon in continuum mechanics and by grain avalanches in discrete mechanics. For all these kinds of failure, the most basic definition of stability as proposed by Lyapunov (1907) is satisfied.
