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Register a new userGranular Response to Impact: Topology of the Force Networks
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Impact of an intruder on granular matter leads to formation of mesoscopic force networks seen particularly clearly in the recent experiments carried out with photoelastic particles, e.g., Clark et al., Phys. Rev. Lett., 114 144502 (2015). These force networks are characterized by complex structure and evolve on fast time scales. While it is known that total photoelastic activity in the granular system is correlated with the acceleration of the intruder, it is not known how the structure of the force network evolves during impact, and if there is a dominant features in the networks that can be used to describe intruders dynamics. Here, we use topological tools, in particular persistent homology, to describe these features. Persistent homology allows quantification of both structure and time evolution of the resulting force networks. We find that there is a clear correlation of the intruders dynamics and some of the topological measures implemented. This finding allows us to discuss which properties of the force networks are most important when attempting to describe intruders dynamics. Regarding temporal evolution of the networks, we are able to define the upper bound on the relevant time scale on which the networks evolve.
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A remarkable feature of static granular matter is the distribution of force along intricate networks. Even regular inter-particle contact networks produce wildly inhomogeneous force networks where certain chains of particles carry forces far larger than the mean. In this paper, we briefly review past theoretical approaches to understanding the geometry of force networks. We then investigate the structure of experimentally-obtained granular force networks using a simple algorithm to obtain corresponding graphs. We compare our observations with the results of geometric models, including random bond percolation, which show similar spatial distributions without enforcing vector force balance. Our findings suggest that some aspects of the mean geometry of granular force networks may be captured by these simple descriptions.
When dense granular systems are exposed to external forcing, they evolve on the time scale that is typically related to the externally imposed one (shear or compression rate, for example). This evolution could be characterized by observing temporal evolution of contact networks. However, it is not immediately clear whether the force networks, defined on contact networks by considering force interactions between the particles, evolve on a similar time scale. To analyze the evolution of these networks, we carry out discrete element simulations of a system of soft frictional disks exposed to compression that leads to jamming. By using the tools of computational topology, we show that close to jamming transition, the force networks evolve on the time scale which is much faster than the externally imposed one. The presentation will discuss the factors that determine this fast time scale.
We have made experimental observations of the force networks within a two-dimensional granular silo similar to the classical system of Janssen. Models like that of Janssen predict that pressure within a silo saturates with depth as the result of vertical forces being redirected to the walls of the silo where they can then be carried by friction. By averaging ensembles of experimentally-obtained force networks in different ways, we compare the observed behavior with various predictions for granular silos. We identify several differences between the mean behavior in our system and that predicted by Janssen-like models: We find that the redirection parameter describing how the force network transfers vertical forces to the walls varies with depth. We find that changes in the preparation of the material can cause the pressure within the silo to either saturate or to continue building with depth. Most strikingly, we observe a non-linear response to overloads applied to the top of the material in the silo. For larger overloads we observe the previously reported giant overshoot effect where overload pressure decays only after an initial increase [G. Ovarlez et al., Phys. Rev. E 67, 060302(R) (2003)]. For smaller overloads we find that additional pressure propagates to great depth. This effect depends on the particle stiffness, as given for instance by the Youngs modulus, E, of the material from which the particles are made. Important measures include E, the unscreened hydrostatic pressure, and the applied load. These experiments suggest that when the load and the particle weight are comparable, particle elasticity acts to stabilize the force network, allowing non-linear network effects to be seen in the mean behavior.
The response to a localized force provides a sensitive test for different models of stress transmission in granular solids. The elasto-plastic models traditionally used by engineers have been challenged by theoretical and experimental results which suggest a wave-like (hyperbolic) propagation of the stress, as opposed to the elliptic equations of static elasticity. Numerical simulations of two-dimensional granular systems subject to a localized external force are employed to examine the nature of stress transmission in these systems as a function of the magnitude of the applied force, the frictional parameters and the disorder (polydispersity). The results indicate that in large systems (typically considered by engineers), the response is close to that predicted by isotropic elasticity whereas the response of small systems (or when sufficiently large forces are applied) is strongly anisotropic. In the latter case the applied force induces changes in the contact network accompanied by frictional sliding. The larger the coefficient of static friction, the more extended is the range of forces for which the response is elastic and the smaller the anisotropy. Increasing the degree of polydispersity (for the range studied, up to 25%) decreases the range of elastic response. This article is an extension of a previously published letter [1].
We examine the impact of a solid sphere into a fine-grained granular bed. Using high-speed X-ray radiography we track both the motion of the sphere and local changes in the bed packing fraction. Varying the initial packing density as well as the ambient gas pressure, we find a complete reversal in the effect of interstitial gas on the impact response of the bed: The dynamic coupling between gas and grains allows for easier penetration in initially loose beds but impedes penetration in more densely packed beds. High-speed imaging of the local packing density shows that these seemingly incongruous effects have a common origin in the resistance to bed packing changes caused by interstitial air.
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