No Arabic abstract
The mechanics of cohesive or cemented granular materials is complex, combining the heterogeneous responses of granular media, like force chains, with clearly defined material properties. Here, we use a discrete element model (DEM) simulation, consisting of an assemblage of elastic particles connected by softer but breakable elastic bonds, to explore how this class of material deforms and fails under uniaxial compression. We are particularly interested in the connection between the microscopic interactions among the grains or particles and the macroscopic material response. To this end, the properties of the particles and the stiffness of the bonds are matched to experimental measurements of a cohesive granular media with tunable elasticity. The criterion for breaking a bond is also based on an explicit Griffith energy balance, with realistic surface energies. By varying the initial volume fraction of the particle assembles we show that this simple model reproduces a wide range of experimental behaviors, both in the elastic limit and beyond it. These include quantitative details of the distinct failure modes of shear-banding, ductile failure and compaction banding or anti-cracks, as well as the transitions between these modes. The present work, therefore, provides a unified framework for understanding the failure of porous materials such as sandstone, marble, powder aggregates, snow and foam.
The rheology of a three-dimensional granular jet during an impact is investigated numerically. The cone-like scattering pattern and the sheet-like pattern observed in an experiment [X. Cheng, et al. Phys. Rev. Lett. 99, 188001 (2007)] can be reproduced through our calculation. We discuss the constitutive equation for granular jet impact in terms of our simulation. From the analysis of an effective friction constant, which is the ratio between the shear stress and the pressure the assumption of the zero yield stress would be natural in our setup and the shear visocity is not small in contrast to the suggestion by the experiment.
Recent experiments with rotational diffusion of a probe in a vibrated granular media revealed a rich scenario, ranging from the dilute gas to the dense liquid with cage effects and an unexpected superdiffusive behavior at large times. Here we setup a simulation that reproduces quantitatively the experimental observations and allows us to investigate the properties of the host granular medium, a task not feasible in the experiment. We discover a persistent collective rotational mode which emerges at high density and low granular temperature: a macroscopic fraction of the medium slowly rotates, randomly switching direction after very long times. Such a rotational mode of the host medium is the origin of probes superdiffusion. Collective motion is accompanied by a kind of dynamical heterogeneity at intermediate times (in the cage stage) followed by a strong reduction of fluctuations at late times, when superdiffusion sets in.
Recent experiments exhibit a rate-dependence for granular shear such that the stress grows linearly in the logarithm of the shear rate, dot{gamma}. Assuming a generalized activated process mechanism, we show that these observations are consistent with a recent proposal for a stress-based statistical ensemble. By contrast, predictions for rate-dependence using conventional energy-based statistical mechanics to describe activated processes, predicts a rate dependence that of (ln (dot{gamma}))^{1/2}.
We investigate the approach to catastrophic failure in a model porous granular material undergoing uniaxial compression. A discrete element computational model is used to simulate both the micro-structure of the material and the complex dynamics and feedbacks involved in local fracturing and the production of crackling noise. Under strain-controlled loading micro-cracks initially nucleate in an uncorrelated way all over the sample. As loading proceeds the damage localizes into a narrow damage band inclined at 30-45 degrees to the load direction. Inside the damage band the material is crushed into a poorly-sorted mixture of mainly fine powder hosting some larger fragments. The mass probability density distribution of particles in the damage zone is a power law of exponent 2.1, similar to a value of 1.87 inferred from observations of the length distribution of wear products (gouge) in natural and laboratory faults. Dynamic bursts of radiated energy, analogous to acoustic emissions observed in laboratory experiments on porous sedimentary rocks, are identified as correlated trails or cascades of local ruptures that emerge from the stress redistribution process. As the system approaches macroscopic failure consecutive bursts become progressively more correlated. Their size distribution is also a power law, with an equivalent Gutenberg-Richter b-value of 1.22 averaged over the whole test, ranging from 3 down to 0.5 at the time of failure, all similar to those observed in laboratory tests on granular sandstone samples. The formation of the damage band itself is marked by a decrease in the average distance between consecutive bursts and an emergent power law correlation integral of event locations with a correlation dimension of 2.55, also similar to those observed in the laboratory (between 2.75 and 2.25).
We study a general model of granular Brownian ratchet consisting of an asymmetric object moving on a line and surrounded by a two-dimensional granular gas, which in turn is coupled to an external random driving force. We discuss the two resulting Boltzmann equations describing the gas and the object in the dilute limit and obtain a closed system for the first few moments of the system velocity distributions. Predictions for the net ratchet drift, the variance of its velocity fluctuations and the transition rates in the Markovian limit, are compared to numerical simulations and a fair agreement is observed.