Research Papers

Analyses on the In-Plane Impact Resistance of Auxetic Double Arrowhead Honeycombs

[+] Author and Article Information
Jinxiu Qiao

Department of Engineering Mechanics,
Tsinghua University,
Beijing 100084, China
e-mail: qiao-jinxiu@163.com

Chang Qing Chen

Department of Engineering Mechanics,
Tsinghua University,
Beijing 100084, China
e-mail: chencq@tsinghua.edu.cn

1Corresponding author.

Manuscript received January 26, 2015; final manuscript received March 6, 2015; published online March 31, 2015. Editor: Yonggang Huang.

J. Appl. Mech 82(5), 051007 (May 01, 2015) (9 pages) Paper No: JAM-15-1047; doi: 10.1115/1.4030007 History: Received January 26, 2015; Revised March 06, 2015; Online March 31, 2015

Double arrowhead honeycombs (DAHs) are a type of auxetic materials, i.e., showing negative Poisson's ratio (NPR), and are promising for energy absorption applications. Their in-plane impact responses are theoretically and numerically explored. Theoretical models for the collapse stress under quasi-static, low-velocity, and high-velocity impacts are developed, based upon the corresponding microstructural deformation modes. Obtained results show that the collapse stress under quasi-static and low velocity impacts depends upon the two re-entrant angles responsible for NPR, while it is insensitive to them under high-velocity impact. The developed theoretical models are employed to analyze the energy absorption capacity of DAHs, showing the absorbed energy under high-velocity impact approximately proportional to the second power of velocity. Extension of the high-velocity impact model to functionally graded (FG) DAHs is also discussed. Good agreement between the theoretical and finite element (FE) predictions on the impact responses of DAHs is obtained.

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Fig. 1

(a) Schematic of a DAH under impact loading and (b) its unit cell

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Fig. 2

Proposed collapse modes of DAHs under quasi-static compression

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Fig. 3

FE predicted quasi-static (V = 1 m/s) deformations of two DAHs subject to global compressive strain of ɛ = 30%: (a) ρ¯ = 5% and (b) ρ¯ = 1%

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Fig. 4

FE predicted quasi-static (V = 1 m/s) responses for DAHs: (a) ρ¯ = 5%, θ1 = 60 deg, θ2 = 30 deg; (b) ρ¯ = 1%, θ1 = 60 deg, θ2 = 30 deg; (c) ρ¯ = 5%, θ1 = 75 deg, θ2 = 30 deg; and (d) ρ¯ = 5%, θ1 = 45 deg, θ2 = 30 deg

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Fig. 5

The global reaction stresses at the distal ends for various impact velocities

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Fig. 6

The low-velocity impact deformations with V = 10 m/s: (a) representative cells; (b) FE predicted deformation pattern; (c) proposed failure mode at t = t1; (d) FE predicted deformation pattern; and (e) proposed failure mode at t = t2

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Fig. 7

Normalized velocities of the vertices marked in Fig. 6. Here, V¯ = Vη/V with V = 10 m/s, Vη being the velocities of the vertices (η = A, B, C, D, E, F, and G) and t¯ being the impact time normalized by the total time.

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Fig. 8

FE predicted low-velocity impact responses for a DAH with: (a) V = 10 m/s and (b) V = 20 m/s

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Fig. 9

The low-velocity impact deformations with V = 100 m/s: (a) representative cells; (b) FE predicted deformation pattern; (c) proposed failure mode at t = t1; (d) FE predicted deformation pattern; and (e) proposed failure mode at t = t2

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Fig. 10

FE predicted high-velocity impact responses for a DAH with: (a) V = 50 m/s and (b) V = 100 m/s

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Fig. 13

FE predicted high-velocity impact responses for a FG DAH with V = 200 m/s and ρ¯ave = 5%

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Fig. 12

Comparison of the FE and analytical results: (a) collapse stress and (b) absorbed energy

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Fig. 11

Effects of geometrical parameters θ1 and θ2 on the impact responses of DAHs: (a) V = 10 m/s and (b) V = 100 m/s



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