Beyond Failure in Granular Materials

Abstract

SUMMARYRecent investigations on the hypoplastic constitutive model for granular materials show that the failure surface can be surpassed by some stress paths. This is contradictory to the conventional definition of failure surface in plasticity, according to which the stress is allowed to move on the failure surface but never across it. In the present paper, the interrelations among the different constitutive models are discussed with special reference to failure and stability. For the hypoplastic constitutive equation, the accessible stress states and the stable stress states are found to be enclosed by a bound surface and a stability surface in the stress space, respectively. Theoretical findings about the bound surface and the stability surface are verified qualitatively by presenting results of triaxial tests on dry sand.

A basic hypoplastic constitutive model for sand

“…The stress increments Dr are obtained from the probes of strain rates of all possible directions with the same magnitude jj _ jj. The response envelopes can be depicted in the three-dimensional stress space [27]. For visual inspection, however, the Rendulic plane with r 2 ¼ r 3 is often the better choice.…”

“…Figure 10 shows that for initial stresses on the failure surface, some strain rates may lead to stresses outside the failure surface. We proceed to derive the bound surface, which enclose all accessible stresses following the procedure proposed by Wu and Niemunis [27]. Assume that there exists a bound surface bðrÞ ¼ 0 with bðrÞ being an isotropic function of stress.…”

Numerical integration and FE implementation of a hypoplastic constitutive model

“…The hypoplastic model is also characterised by a bound surface that bounds the accessible stress states and which can be derived based on the procedure by Wu [36] and Wu and Niemunis [40]. The explicit formulation of the bound surface is expressed as follows:…”

“…A too large step size may impair the convergence and stability of the numerical calculation. Second, hypoplastic model allows some stress state outside the failure surface [40]. For some well-defined hypoplastic models, Wu and Niemunis [39] showed that all accessible stress states are within a bound surface.…”

“…For some well-defined hypoplastic models, Wu and Niemunis [39] showed that all accessible stress states are within a bound surface. However, the bound surface is often too far from the failure surface, which gives rise to too high strength [40]. Consequently, the error resulted from stress drift away from the failure surface can accumulate in numerical computations and eventually lead to unphysical behaviour [3,22] and the loss of stability for a boundary value problem.…”