No Arabic abstract
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.
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.
Granular intrusion is commonly observed in natural and human-made settings. Unlike typical solids and fluids, granular media can simultaneously display fluid-like and solid-like characteristics in a variety of intrusion scenarios. This multi-phase behavior increases the difficulty of accurately modeling these and other yielding (or flowable) materials. Micro-scale modeling methods, such as DEM (Discrete Element Method), capture this behavior by modeling the media at the grain scale, but there is often interest in the macro-scale characterizations of such systems. We examine the efficacy of a macro-scale continuum approach in modeling and understanding the physics of various macroscopic phenomena in a variety of granular intrusion cases using two basic frictional yielding constitutive models. We compare predicted granular force response and material flow to experimental data in four quasi-2D intrusion cases: (1) depth-dependent force response in horizontal submerged-intruder motion; (2) separation dependent drag variation in parallel-plate vertical-intrusion; (3) initial-density-dependent drag fluctuations in free surface plowing, and (4) flow zone development during vertical plate intrusions in under-compacted granular media. Our continuum modeling approach captures the flow process and drag forces while providing key meso- and macro-scopic insights. The modeling results are then compared to experimental data. Our study highlights how continuum modeling approaches provide an alternative for efficient modeling as well as a conceptual understanding of various granular intrusion phenomena.
Heterogeneous multiscale methods (HMM) combine molecular accuracy of particle-based simulations with the computational efficiency of continuum descriptions to model flow in soft matter liquids. In these schemes, molecular simulations typically pose a computational bottleneck, which we investigate in detail in this study. We find that it is preferable to simulate many small systems as opposed to a few large systems, and that a choice of a simple isokinetic thermostat is typically sufficient while thermostats such as Lowe-Andersen allow for simulations at elevated viscosity. We discuss suitable choices for time steps and finite-size effects which arise in the limit of very small simulation boxes. We also argue that if colloidal systems are considered as opposed to atomistic systems, the gap between microscopic and macroscopic simulations regarding time and length scales is significantly smaller. We also propose a novel reduced-order technique for the coupling to the macroscopic solver, which allows us to approximate a non-linear stress-strain relation efficiently and thus further reduce computational effort of microscopic simulations.
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.