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Register a new userNumerical analysis of impact processes of granular jets
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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.
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We perform three-dimensional simulations of a granular jet impact for both frictional and frictionless grains. Small shear stress observed in the experiment[X. Cheng et al., Phys. Rev. Lett. 99, 188001 (2007) ] is reproduced through our simulation. However, the fluid state after the impact is far from a perfect fluid, and thus, similarity between granular jets and quark gluon plasma is superficial, because the observed viscosity is finite and its value is consistent with the prediction of the kinetic theory.
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.
Using high-speed photography, we investigate two distinct regimes of the impact dynamics of granular jets with non-circular cross-sections. In the steady-state regime, we observe the formation of thin granular sheets with anisotropic shapes and show that the degree of anisotropy increases with the aspect ratio of the jets cross-section. Our results illustrate the liquid-like behavior of granular materials during impact and demonstrate that a collective hydrodynamic flow emerges from strongly interacting discrete particles. We discuss the analogy between our experiments and those from the Relativistic Heavy Ion Collider (RHIC), where similar anisotropic ejecta from a quark-gluon plasma have been observed in heavy-ion impact.
Conditions for the stability under linear perturbations around the homogeneous cooling state are studied for dilute granular gases of inelastic and rough hard disks or spheres with constant coefficients of normal ($alpha$) and tangential ($beta$) restitution. After a formally exact linear stability analysis of the Navier--Stokes--Fourier hydrodynamic equations in terms of the translational ($d_t$) and rotational ($d_r$) degrees of freedom, the transport coefficients derived in the companion paper [A. Megias and A. Santos, Hydrodynamics of granular gases of inelastic and rough hard disks or spheres. I. Transport coefficients, Phys. Rev. E 104, 034901 (2021)] are employed. Known results for hard spheres [V. Garzo, A. Santos, and G. M. Kremer, Phys. Rev. E 97, 052901 (2018)] are recovered by setting $d_t=d_r=3$, while novel results for hard disks ($d_t=2$, $d_r=1$) are obtained. In the latter case, a high-inelasticity peculiar region in the $(alpha,beta)$ parameter space is found, inside which the critical wave number associated with the longitudinal modes diverges. Comparison with event-driven molecular dynamics simulations for dilute systems of hard disks at $alpha=0.2$ shows that this theoretical region of absolute instability may be an artifact of the extrapolation to high inelasticity of the approximations made in the derivation of the transport coefficients, although it signals a shrinking of the conditions for stability. In the case of moderate inelasticity ($alpha=0.7$), however, a good agreement between the theoretical predictions and the simulation results is found.
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.
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