0
Research Papers

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

[+] Author and Article Information
Jinxiu Qiao

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

Chang Qing Chen

AML and CNMM,
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.

FIGURES IN THIS ARTICLE
<>
Copyright © 2015 by ASME
Your Session has timed out. Please sign back in to continue.

References

Gibson, L. J., and Ashby, M. F., 1999, Cellular Solids: Structure and Properties, Cambridge University Press, Cambridge, UK.
Reid, S. R., and Peng, C., 1997, “Dynamic Uniaxial Crushing of Wood,” Int. J. Impact Eng., 19(5–6), pp. 531–570. [CrossRef]
Lopatnikov, S. L., Gama, B. A., Haque, M. J., Krauthauser, C., Gillespie, J. W., Guden, M., and Hall, I. W., 2003, “Dynamics of Metal Foam Deformation During Taylor Cylinder-Hopkinson Bar Impact Experiment,” Compos. Struct., 61(1–2), pp. 61–71. [CrossRef]
Harrigan, J. J., Reid, S. R., Tan, P. J., and Reddy, T. Y., 2005, “High Rate Crushing of Wood Along the Grain,” Int. J. Mech. Sci., 47(4–5), pp. 521–544. [CrossRef]
Tan, P. J., Reid, S. R., Harrigan, J. J., Zou, Z., and Li, S., 2005, “Dynamic Compressive Strength Properties of Aluminium Foams—Part II: ‘Shock’ Theory and Comparison With Experimental Data and Numerical Models,” J. Mech. Phys. Solids, 53(10), pp. 2206–2230. [CrossRef]
Wang, L. L., Yang, L. M., and Ding, Y. Y., 2013, “On the Energy Conservation and Critical Velocities for the Propagation of a “Steady-Shock” Wave in a Bar Made of Cellular Material,” Acta Mech. Sin., 29(3), pp. 420–428. [CrossRef]
Zheng, Z. J., Liu, Y. D., Yu, J. L., and Reid, S. R., 2012, “Dynamic Crushing of Cellular Materials: Continuum-Based Wave Models for the Transitional and Shock Modes,” Int. J. Impact Eng., 42, pp. 66–79. [CrossRef]
Zheng, Z. J., Wang, C. F., Yu, J. L., Reid, S. R., and Harrigan, J. J., 2014, “Dynamic Stress–Strain States for Metal Foams Using a 3D Cellular Model,” J. Mech. Phys. Solids, 72, pp. 93–114. [CrossRef]
Fleck, N. A., and Deshpande, V. S., 2004, “The Resistance of Clamped Sandwich Beams to Shock Loading,” ASME J. Appl. Mech., 71(3), pp. 386–401. [CrossRef]
Yi, T., and Chen, C. Q., 2012, “The Impact Response of Clamped Sandwich Beams With Ordinary and Hierarchical,” Int. J. Impact Eng., 47, pp. 14–23. [CrossRef]
Yu, B., Han, B., Ni, C. Y., Zhang, Q. C., Chen, C. Q., and Lu, T. J., 2015, “Dynamic Crushing of All-Metallic Corrugated Panels Filled With Close-Celled Aluminum Foams,” ASME J. Appl. Mech., 82(1), p. 011006. [CrossRef]
Hönig, A., and Stronge, W. J., 2002, “In-Plane Dynamic Crushing of Honeycomb—Part II: Application to Impact,” Int. J. Mech. Sci., 44(8), pp. 1697–1714. [CrossRef]
Ruan, D., Lu, G., Wang, B., and Yu, T. X., 2003, “In-Plane Dynamic Crushing of Honeycombs-Finite Element Study,” Int. J. Impact Eng., 28(2), pp. 161–182. [CrossRef]
Li, K., Gao, X. L., and Wang, J., 2007, “Dynamic Crushing Behavior of Honeycomb Structures With Irregular Cell Shapes and Non-Uniform Cell Wall Thickness,” Int. J. Solids Struct., 44(14–15), pp. 5003–5026. [CrossRef]
Qiu, X. M., Zhang, J., and Yu, T. X., 2009, “Collapse of Periodic Planar Lattices Under Uniaxial Compression—Part II: Dynamic Crushing Based on Finite Element Simulation,” Int. J. Impact Eng., 36(10–11), pp. 1231–1241. [CrossRef]
Liao, S. F., Zheng, Z. J., and Yu, J. L., 2013, “Dynamic Crushing of 2D Cellular Structures: Local Strain Field and Shock Wave Velocity,” Int. J. Impact Eng., 57, pp. 7–16. [CrossRef]
Liao, S. F., Zheng, Z. J., and Yu, J. L., 2014, “On the Local Nature of the Strain Field Calculation Method for Measuring Heterogeneous Deformation of Cellular Materials,” Int. J. Solids Struct., 51(2), pp. 478–490. [CrossRef]
Hu, L. L., and Yu, T. X., 2010, “Dynamic Crushing Strength of Hexagonal Honeycombs,” Int. J. Impact Eng., 37(5), pp. 467–474. [CrossRef]
Hu, L. L., and Yu, T. X., 2013, “Mechanical Behavior of Hexagonal Honeycombs Under Low-Velocity Impact—Theory and Simulations,” Int. J. Solids Struct., 50(20–21), pp. 3152–3165. [CrossRef]
Barnes, A. T., Ravi-Chandar, K., Kyriakides, S., and Gaitanaros, S., 2013, “Dynamic Crushing of Aluminum Foams—Part I: Experiments,” Int. J. Solids Struct., 51(9), pp. 1631–1645. [CrossRef]
Barnes, A. T., and Kyriakides, S., 2013, “Dynamic Crushing of Aluminum Foams—Part II: Analysis,” Int. J. Solids Struct., 51(9), pp. 1646–1661. [CrossRef]
Scarpa, F., Panayiotou, P., and Tomlinson, G., 2000, “Numerical and Experimental Uniaxial Loading on In-Plane Auxetic Honeycombs,” J. Strain Anal. Eng. Des., 35(5), pp. 383–388. [CrossRef]
Wan, H., Ohtaki, H., Kotosaka, S., and Hu, G., 2004, “A Study of Negative Poisson's Ratios in Auxetic Honeycombs Based on a Large Deflection Model,” Eur. J. Mech. A Solids, 23(1), pp. 95–106. [CrossRef]
Lira, C., and Scarpa, F., 2010, “Transverse Shear Stiffness of Thickness Gradient Honeycombs,” Compos. Sci. Technol., 70(6), pp. 930–936. [CrossRef]
Hou, Y., Neville, R., Scarpa, F., Remillat, C., Gu, B., and Ruzzene, M., 2014, “Graded Conventional-Auxetic Kirigami Sandwich Structures: Flatwise Compression and Edgewise Loading,” Composites, Part B, 59, pp. 33–42. [CrossRef]
Ma, Z. D., Bian, H., Sun, C., Hulbert, G. M., Bishnoi, K., and Rostam-Abadi, F., 2010, “Functionally-Graded NPR (Negative Poisson's Ratio) Material for a Blast-Protective Deflector,” Ground Vehicle Systems Engineering and Technology Symposium, Dearborn, MI, Aug. 17–19.
Zhang, X. C., Liu, Y., and Li, N., 2012, “In-Plane Dynamic Crushing of Honeycombs With Negative Poisson's Ratio Effects,” Explos. Shock Waves, 32(5), pp. 475–482 (in Chinese).
Yang, S., Qi, C., Wang, D., Gao, B. J., Hu, H. T., and Shu, J., 2013, “A Comparative Study of Ballistic Resistance of Sandwich Panels With Aluminum Foam and Auxetic Honeycomb Cores,” Adv. Mech. Eng., 2013, p. 589216. [CrossRef]
Qi, C., Yang, S., Wang, D., and Yang, L. J., 2013, “Ballistic Resistance of Honeycomb Sandwich Panels Under In-Plane High-Velocity Impact,” Adv. Mech. Eng., 2013, p. 892781. [CrossRef]
Larsen, U. D., Sigmund, O., and Bouwstra, S., 1996, “Design and Fabrication of Compliant Micromechanisms and Structures With Negative Poisson's Ratio,” Micro Electro Mech. Syst., 6(2), pp. 365–371. [CrossRef]
Ali, M., Qamhiyah, A., Flugrad, D., and Shakoor, M., 2008, “Theoretical and Finite Element Study of a Compact Energy Absorber,” Adv. Eng. Software, 39(2), pp. 95–106. [CrossRef]
Ajdari, A., Nayeb-Hashemi, H., and Vaziri, A., 2011, “Dynamic Crushing and Energy Absorption of Regular, Irregular and Functionally Graded Cellular Structures,” Int. J. Solids Struct., 48(3–4), pp. 506–516. [CrossRef]

Figures

Grahic Jump Location
Fig. 1

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

Grahic Jump Location
Fig. 2

Proposed collapse modes of DAHs under quasi-static compression

Grahic Jump Location
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%

Grahic Jump Location
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

Grahic Jump Location
Fig. 5

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

Grahic Jump Location
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

Grahic Jump Location
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.

Grahic Jump Location
Fig. 8

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

Grahic Jump Location
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

Grahic Jump Location
Fig. 10

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

Grahic Jump Location
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

Grahic Jump Location
Fig. 12

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

Grahic Jump Location
Fig. 13

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

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In