ABSTRACT
For granular media and more particularly for sands, several authors have shown that, for specific loading paths and loading control variables, bifurcation state or failure of the medium can be met inside the plastic limit condition. This peculiar feature of non-associated materials has been observed equally in theoretical, numerical and experimental studies. Thus, Imposimato & Nova (1998), using the notion of “non controllability” and an elastoplastic strain hardening constitutive model, exhibit in the deviatoric plane loss-of-uniqueness loci for homogeneous stress-strain states inside the plastic limit condition. For the constitutive law used, the loss of uniqueness corresponds to the vanishing of the second order work d2W . For a volume V in which dσ and dε are homogeneous field linked by the constitutive relation d2W is given by:
In the same way, Bigoni & Hueckel (1991) have shown this correspondence between loss of uniqueness of the incremental response and loss of positiveness of d2W for non associative elastoplasticity. Darve & Laouafa (2002) using an octo-linear and a non-linear models give in principal stress space a domain of potential failure/bifurcation for dense and loose Hostun sands. The definition of this domain is based on Hill’s Sufficient Condition of Stability expressed locally in the following way:
More recently, Lancelot et al. (2004) have shown experimentally, for a loose Hostun sand under low stress, a correlation between the vanishing of the second order work and the instability of the sample.
