Research Papers

Impact Response of Elasto-Plastic Granular Chains Containing an Intruder Particle

[+] Author and Article Information
Raj Kumar Pal

Department of Mechanical
Science and Engineering,
University of Illinois at Urbana-Champaign,
Urbana, IL 61801
e-mail: pal3@illinois.edu

Jeremy Morton

Department of Aerospace Engineering,
University of Illinois at Urbana-Champaign,
Urbana, IL 61801

Erheng Wang

Postdoctoral Associate
Department of Aerospace Engineering,
University of Illinois at Urbana-Champaign,
Urbana, IL 61801
e-mail: erhengwang@gmail.com

John Lambros

Department of Aerospace Engineering,
University of Illinois at Urbana-Champaign,
Urbana, IL 61801
e-mail: lambros@illinois.edu

Philippe H. Geubelle

Department of Aerospace Engineering,
University of Illinois at Urbana-Champaign,
Urbana, IL 61801
e-mail: geubelle@illinois.edu

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received September 12, 2014; final manuscript received October 27, 2014; accepted manuscript posted October 31, 2014; published online November 14, 2014. Editor: Yonggang Huang.

J. Appl. Mech 82(1), 011002 (Jan 01, 2015) (8 pages) Paper No: JAM-14-1421; doi: 10.1115/1.4028959 History: Received September 12, 2014; Revised October 27, 2014; Accepted October 31, 2014; Online November 14, 2014

Wave propagation in homogeneous granular chains subjected to impact loads causing plastic deformations is substantially different from that in elastic chains. To design wave tailoring materials, it is essential to gain a fundamental understanding of the dynamics of heterogeneous granular chains under loads where the effects of plasticity are significant. In the first part of this work, contact laws for dissimilar elasticperfectly plastic spherical granules are developed using finite element simulations. They are systematically normalized, with the normalizing variables determined from first principles, and a unified contact law for heterogeneous spheres is constructed and validated. In the second part, dynamic simulations are performed on granular chains placed in a split Hopkinson pressure bar (SHPB) setup. An intruder particle having different material properties is placed in an otherwise homogeneous granular chain. The position and relative material property of the intruder is shown to have a significant effect on the energy and peak transmitted force down the chain. Finally, the key nondimensional material parameter that dictates the fraction of energy transmitted in a heterogeneous granular chain is identified.

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Fig. 1

von Mises stress contours between steel (top) and brass (bottom) spheres. Though both spheres have a large plastic yield volume, the plastic deformations are entirely in the softer brass sphere, similar to the experimental observations by Wang et al. [29].

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Fig. 2

(Top) Force–displacement data for two contacting spheres with distinct material properties varying over a wide range. (Bottom) When normalized appropriately, the distinct curves collapse to a single curve, showing that a unified model is able to describe the contact force–displacement behavior for a wide range of material combinations.

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Fig. 3

Comparison of quasi-static experimental data with numerical model (9)(10) for three distinct material combinations

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Fig. 4

Schematic of a SHPB experiment used to study force transmission through a heterogeneous granular chain [31]

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Fig. 5

(Top) Comparison of experimental data with numerical simulation for transmitted and reflected force signals, extracted from a SHPB setup. (Bottom) A close-up view of the transmitted signal in the bar.

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Fig. 6

(Top) Schematic illustrating the problem setup for numerical investigation of effect of intruder. A force P (with duration T) is applied on the left end, and the peak transmitted force along with energy transmitted to the bar are computed for various intruders. (Bottom) xt diagram of contact forces and net section forces along the bar and a homogeneous granular chain. The colliding wavefronts give rise to additional wavefronts resulting in a complex pattern.

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Fig. 7

Variation of peak transmitted force (dashed) and total energy (solid) with the position of a single intruder in a brass chain, along with the values for monodisperse chains (indicated by the markers along the vertical axes). These quantities are sensitive to the location in the case of a soft (Al) intruder, while they remain almost constant for a hard (steel) intruder.

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Fig. 8

(a) Ratio of energy eT transmitted to the bar in a chain with intruder to that in a homogeneous chain eT0 as a function of the intruder's material properties. The energy ratio shows little variation with the stiffness of the intruder, while it increases with decreasing density, radius, and increasing yield strength. (b) When normalized appropriately, the distinct curves almost collapse to a single curve, indicating the existence of a single nondimensional parameter governing the fraction of energy transmitted.



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