Universal Power-Law Decay of the Impulse Energy in Granular Protectors

Abstract

Protecting a big impulse from outside is one of the important issues of our everyday life. A granular medium is often used as a protecting material. The impulse inside a granular medium is a solitary wave which may be confined temporarily to a particular region of the medium, which we call the granular container that plays the role of the protector. We find a universal power-law behavior in time for the leakage of the impulse energy confined inside various granular containers.

Wave propagation in one-dimensional microscopic granular chains

“…More generally, by modifying the contact geometry and particle arrangements (i.e., changing the stress-strain relation and the direction of contact forces) [8], granular crystals can be designed to behave as highly flexible wave guides [9], focusing lenses [10] and filtering materials [11]. These features of granular crystals have inspired their use in engineering applications, such as shock mitigation [12][13][14][15], acoustic rectification [16], and logic elements [17]. However, the macroscopic size of the particles tested experimentally to date imposes important limitations to their applicability.…”

Impact Dispersion Using 2D and 3D Composite Granular Packing

“…These studies have been instrumental in the design of novel granular materials with widespread applications. It is now well understood that introducing a mass mismatch in these one dimensional granular systems, either by changing the size of the spheres such as in tapered (Doney R. and Sen S., 2005;Nakagawa M. et al, 2003;Melo F. et al, 2006) and decorated chains (see e.g., Doney R. and Sen S., 2006;, Machado L.P. et al, 2014), or by changing of the material properties by introducing spheres of different materials (Hong J. and Xu A., 2002;Hong J., 2005;Nesterenko V.F. et al, 2005;Daraio C. et al, 2006;Wang P.J.…”

Pulse mitigation by a composite discrete medium

“…The passage of a solitary wave through the interface of two SV type systems from a region of particles with a higher elastic modulus (or higher mass) to a region of lower elastic modulus (or lower mass) results in the impulse decomposition into a train of solitary pulses [1][2][3][4][5]11]. The reflection from light and heavy inclusions was earlier proposed as a technique for nondestructive identification of impurities in a granular medium (with implications in the analysis/detection in geological or biological fields) [12].…”

“…Yet another way of protecting materials may be realized exploiting the unique dynamic properties observed at the interface of two strongly nonlinear media. Theoretical analysis [3,4] predicted the possibility of designing a novel shielding medium called a "granular container" acting through the confinement of an impulse. The study of these one-dimensional cases is of general interest for developing the fundamental understanding of the strongly nonlinear behavior of these complex media.…”

“…They exhibit a very unique dynamic behavior, especially at the interface between two different granular systems [1][2][3][4][5] or at the interface between the granular media and solid matter [6]. In the past, the design of shock protectors focused mainly on the enhanced energy dissipation provided by layered systems or by the friction in granular media, i.e.…”