Elastic–Plastic Wave Propagation in Uniform and Periodic Granular Chains

Abstract

We investigate the properties of high-amplitude stress waves propagating through chains of elastic-plastic particles using experiments and simulations. We model the system after impact using discrete element method (DEM) with strain-rate dependent contact interactions. Experiments are performed on a Hopkinson bar coupled with a laser vibrometer. The bar excites chains of 50 identical particles and dimer chains of two alternating materials. After investigating how the speed of the initial stress wave varies with particle properties and loading amplitude, we provide an upper bound for the leading pulse velocity that can be used to design materials with tailored wave propagation.

Nonlinear coherent structures in granular crystals

“…All cutoff frequencies show a systematic upshift of about 9% compared to the predictions from standard specifications. We have identified four possible explanations: (i) the uncertainty in the standard values of material parameters [20]; (ii) non-Hookean elastic dynamics might lead to a slight shift in the nonlinear exponent p and accordingly a large deviation in the coefficient A [21]; (iii) imperfect surface smoothness might induce fluctuations in p and hence in A [24]; and (iv) dissipative mechanisms, such as viscoelasticity and solid friction, can induce stiffening of the interaction potential between particles [12,25].…”

“…In the presence of precompression, the scaling Y (ε(n − t), ε 3 t) = Y (X, T ) leads to another log-KdV equation, similar to Eq. (25), that is well posed (because the nonlinear term is no longer divergent) [50]. This variant of the log-KdV equation is a useful model for general initial data, as opposed to Eq.…”

“…Our review complements [166,179,188] and highlights a wealth of exciting research on granular crystals has appeared since those papers were published. 2 The explosion of recent results in granular crystals has resulted from the emergence of numerous research groups with the ability to perform detailed quantitative monitoring of granular crystals by using novel techniques (including noninvasive ones, such as photography [203] or laser Doppler vibrometry [25,116]). These exciting advances have ushered the investigation of granular crystals into a new era of theory, computation, and experiments [153] that we will explore in the present paper.…”

Kuwabara-Kono numerical dissipation: a new method to simulate granular matter

“…Classical choices correspond to β = 1 (Hertzian spring with linear dashpot [22]), β = 5/2 (Simon-Hunt-Crossley model [23,24]), and β = 3/2 which leads to the Kuwabara-Kono (KK) model [25] (see also [26] for a ball impacting a plate). This approach applies to small impact velocities and does not account for energy loss due to plastic deformations (see [27,28,8,29,30] for impact laws incorporating plasticity and their application to granular chains). The above compliant dissipative models agree reasonably well with several experiments on binary collisions [21,25,31,32] and impacts on granular chains [33,34], and an optimal choice of model seems to depend actually on the experimental configuration [35].…”

Nonlinear wave in granular systems based on elastoplastic dashpot model

“…Since these elastoplastic contact models depend entirely on the constitutive relation of contact bodies, they can accurately reflect the relationship between the force and displacement in the elastoplastic phase. Whereupon, these quasi‐static elastoplastic models 16 had been used in calculating the solitary wave propagation of elastoplastic granular chain 17 in past decades 16,17,52–54 . The conclusions obtained by the experimental data and numerical analysis illuminated that the elastoplastic deformation between the particles plays an essential role in propagating solitary waves in the granular chain 17,54 .…”