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Register a new userScaling and dynamics of sphere and disk impact into granular media
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Direct measurements of the acceleration of spheres and disks impacting granular media reveal simple power law scalings along with complex dynamics which bear the signatures of both fluid and solid behavior. The penetration depth scales linearly with impact velocity while the collision duration is constant for sufficiently large impact velocity. Both quantities exhibit power law dependence on sphere diameter and density, and gravitational acceleration. The acceleration during impact is characterized by two jumps: a rapid, velocity dependent increase upon initial contact and a similarly sharp, depth dependent decrease as the impacting object comes to rest. Examining the measured forces on the sphere in the vicinity of these features leads to a new experimentally based granular force model for collision. We discuss our findings in the context of recently proposed phenomenological models that capture qualitative dynamical features of impact but fail both quantitatively and in their inability to capture significant acceleration fluctuations that occur during penetration and which depend on the impacted material.
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The drag force exerted on an object intruding into granular media can depend on the objects velocity as well as the depth penetrated. We report on intrusion experiments at constant speed over four orders in magnitude together with systematic molecular dynamics simulations well beyond the quasi-static regime. We find that velocity dependence crosses over to depth dependence at a characteristic time after initial impact. This crossover time scale, which depends on penetration speed, depth, gravity and intruder geometry, challenges current models that assume additive contributions to the drag.
Granular impact -- the dynamic intrusion of solid objects into granular media -- is widespread across scientific and engineering applications including geotechnics. Existing approaches for simulating granular impact dynamics have relied on either a pure discrete method or a pure continuum method. Neither of these methods, however, is deemed optimal from the computational perspective. Here, we introduce a hybrid continuum-discrete approach, built on the coupled material-point and discrete-element method (MP-DEM), for simulating granular impact dynamics with unparalleled efficiency. To accommodate highly complex solid-granular interactions, we enhance the existing MP-DEM formulation with three new ingredients: (i) a robust contact algorithm that couples the continuum and discrete parts without any interpenetration under extreme impact loads, (ii) large deformation kinematics employing multiplicative elastoplasticity, and (iii) a trans-phase constitutive relation capturing gasification of granular media. For validation, we also generate experimental data through laboratory measurement of the impact dynamics of solid spheres dropped onto dry sand. Simulation of the experiments shows that the proposed approach can well reproduce granular impact dynamics in terms of impact forces, intrusion depths, and splash patterns. Further, through parameter studies on material properties, model formulations, and numerical schemes, we identify key factors for successful continuum-discrete simulation of granular impact dynamics.
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.
Recent experimental results on the static or quasistatic response of granular materials have been interpreted to suggest the inapplicability of the traditional engineering approaches, which are based on elasto-plastic models (which are elliptic in nature). Propagating (hyperbolic) or diffusive (parabolic) models have been proposed to replace the `old models. Since several recent experiments were performed on small systems, one should not really be surprised that (continuum) elasticity, a macroscopic theory, is not directly applicable, and should be replaced by a grain-scale (``microscopic) description. Such a description concerns the interparticle forces, while a macroscopic description is given in terms of the stress field. These descriptions are related, but not equivalent, and the distinction is important in interpreting the experimental results. There are indications that at least some large scale properties of granular assemblies can be described by elasticity, although not necessarily its isotropic version. The purely repulsive interparticle forces (in non-cohesive materials) may lead to modifications of the contact network upon the application of external forces, which may strongly affect the anisotropy of the system. This effect is expected to be small (in non-isostatic systems) for small applied forces and for pre-stressed systems (in particular for disordered systems). Otherwise, it may be accounted for using a nonlinear, incrementally elastic model, with stress-history dependent elastic moduli. Although many features of the experiments may be reproduced using models of frictionless particles, results demonstrating the importance of accounting for friction are presented.
The way granular materials response to an applied shear stress is of the utmost relevance to both human activities and natural environment. One of the their most intriguing and less understood behavior, is the stick-instability, whose most dramatic manifestation are earthquakes, ultimately governed by the dynamics of rocks and debris jammed within the fault gauge. Many of the features of earthquakes, i.e. intermittency, broad times and energy scale involved, are mimicked by a very simple experimental set-up, where small beads of glass under load are slowly sheared by an elastic medium. Analyzing data from long lasting experiments, we identify a critical dynamical regime, that can be related to known theoretical models used for crackling-noise phenomena. In particular, we focus on the average shape of the slip velocity, observing a breakdown of scaling: while small slips show a self-similar shape, large does not, in a way that suggests the presence of subtle inertial effects within the granular system. In order to characterise the crossover between the two regimes, we investigate the frictional response of the system, which we trat as a stochastic quantity. Computing different averages, we evidence a weakening effect, whose Stribeck threshold velocity can be related to the aforementioned breaking of scaling.
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