A Size and Boundary Effects Model for Quasi-Brittle Fracture.

The fracture behaviors of quasi-brittle materials are commonly specimen size (size effect) and crack size (boundary effect) dependent. In this study, a new failure model is developed for characterizing the size and boundary effects. The derivative of the energy release rate is firstly introduced to predict the nominal strength dominated by the strength mechanism.

Nonlocal constitutive relation for steady granular flow.

Extending recent modeling efforts for emulsions, we propose a nonlocal fluidity relation for flowing granular materials, capturing several known finite-size effects observed in steady flow. We express the local Bagnold-type granular flow law in terms of a fluidity ratio and then extend it with a particular Laplacian term that is scaled by the grain size. The resulting model is calibrated against a sequence of existing discrete element method data sets for two-dimensional annular shear, where it is shown that the model correctly describes the divergence from a local rheology due to the grain size as well as the rate-independence phenomenon commonly observed in slowly flowing zones.

MRI investigation of granular interface rheology using a new cylinder shear apparatus.

The rheology of granular materials near an interface is investigated through proton magnetic resonance imaging. A new cylinder shear apparatus has been inserted in the magnetic resonance imaging device, which allows the control of the radial confining pressure exerted by the outer wall on the grains and the measurement of the torque on the inner shearing cylinder. A multi-layer velocimetry sequence has been developed for the simultaneous measurement of velocity profiles in different sample zones, while the measurement of the solid fraction profile is based on static imaging of the sample.

Annular shear of cohesionless granular materials: from the inertial to quasistatic regime.

Using discrete simulations, we investigate the behavior of a model granular material within an annular shear cell. Specifically, two-dimensional assemblies of disks are placed between two circular walls, the inner one rotating with prescribed angular velocity, while the outer one may expand or shrink and maintains a constant radial pressure. Focusing on steady state flows, we delineate in parameter space the range of applicability of the recently introduced constitutive laws for sheared granular materials (based on the inertial number).