Skip to main content

Advertisement

SpringerLink
Log in

Deformation mode and energy absorption of polycrystal-inspired square-cell lattice structures

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

Lattice structures are widely used in many engineering fields due to their excellent mechanical properties such as high specific strength and high specific energy absorption (SEA) capacity. In this paper, square-cell lattice structures with different lattice orientations are investigated in terms of the deformation modes and the energy absorption (EA) performance. Finite element (FE) simulations of in-plane compression are carried out, and the theoretical models from the energy balance principle are deve-loped for calculating the EA of these lattice structures. Satisfactory agreement is achieved between the FE simulation results and the theoretical results. It indicates that the 30° oriented lattice has the largest EA capacity. Furthermore, inspired by the polycrystal microstructure of metals, novel structures of bi-crystal lattices and quad-crystal lattices are developed through combining multiple singly oriented lattices together. The results of FE simulations of compression indicate that the EA performances of symmetric lattice bi-crystals and quad-crystals are better than those of the identical lattice polycrystal counterparts. This work confirms the feasibility of designing superior energy absorbers with architected meso-structures from the inspiration of metallurgical concepts and microstructures.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. HOLLISTER, S. J. Porous scaffold design for tissue engineering. Nature Materials, 4(7), 518–524 (2005)

    Article  Google Scholar 

  2. IMBALZANO, G., LINFORTH, S., NGO, T. D., LEE, P. V. S., and TRAN, P. Blast resistance of auxetic and honeycomb sandwich panels: comparisons and parametric designs. Composite Structures, 183, 242–261 (2018)

    Article  Google Scholar 

  3. YANG, X. F., YANG, J. L., ZHANG, Z. Q., MA, J. X., SUN, Y. X., and LIU, H. A review of civil aircraft arresting system for runway overruns. Progress in Aerospace Sciences, 102, 99–121 (2018)

    Article  Google Scholar 

  4. GALEHDARI, S. A. and KHODARAHMI, H. Design and analysis of a graded honeycomb shock absorber for a helicopter seat during a crash condition. International Journal of Crashworthiness, 21(3), 231–241 (2016)

    Article  Google Scholar 

  5. KIM, M., CHOE, J., and LEE, D. G. Development of the fire-retardant sandwich structure using an aramid/glass hybrid composite and a phenolic foam-filled honeycomb. Composite Structures, 158, 227–234 (2016)

    Article  Google Scholar 

  6. THOMAS, T. and TIWARI, G. Crushing behavior of honeycomb structure: a review. International Journal of Crashworthiness, 24(5), 555–579 (2019)

    Article  Google Scholar 

  7. GIBSON, L. J. and ASHBY, M. F. Cellular Solids: Structure and Properties, Cambridge University Press, Cambrigde, 98–148 (1999)

    Google Scholar 

  8. CHUNG, J. and WAAS, A. M. The inplane elastic properties of circular cell and elliptical cell honeycombs. Acta Mechanica, 144(1), 29–42 (2000)

    Article  MATH  Google Scholar 

  9. RUAN, D., LU, G., WANG, B., and YU, T. X. In-plane dynamic crushing of honeycombs — a finite element study. International Journal of Impact Engineering, 28(2), 161–182 (2003)

    Article  Google Scholar 

  10. WANG, A. J. and MCDOWELL, D. L. In-plane stiffness and yield strength of periodic metal honeycombs. Journal of Engineering Materials and Technology, 126(2), 137–156 (2004)

    Article  Google Scholar 

  11. YANG, M. J. and QIAO, P. Z. Quasi-static crushing behavior of aluminum honeycomb materials. Journal of Sandwich Structures and Materials, 10(2), 133–160 (2008)

    Article  Google Scholar 

  12. SUN, D. Q. and ZHANG, W. H. Mean in-plane plateau stresses of hexagonal honeycomb cores under impact loadings. Composite Structures, 91, 168–185 (2009)

    Article  Google Scholar 

  13. LIU, Y. and ZHANG, X. C. The influence of cell micro-topology on the in-plane dynamic crushing of honeycombs. International Journal of Impact Engineering, 36(1), 98–109 (2009)

    Article  Google Scholar 

  14. QIU, X. M., ZHANG, J., and YU, T. X. Collapse of periodic planar lattices under uniaxial compression, part II: dynamic crushing based on finite element simulation. International Journal of Impact Engineering, 36(10/11), 1231–1241 (2009)

    Article  Google Scholar 

  15. QIU, X. M., ZHANG, J., and YU, T. X. Collapse of periodic planar lattices under uniaxial compression, part I: quasi-static strength predicted by limit analysis. International Journal of Impact Engineering, 36(10/11), 1223–1230 (2009)

    Article  Google Scholar 

  16. AJDARI, A., NAYEB-HASHEMI, H., and VAZIRI, A. Dynamic crushing and energy absorption of regular, irregular and functionally graded cellular structures. International Journal of Solids and Structures, 48(3/4), 506–516 (2011)

    Article  MATH  Google Scholar 

  17. HU, L. L., YOU, F. F., and YU, T. X. Effect of cell-wall angle on the in-plane crushing behaviour of hexagonal honeycombs. Materials and Design, 46, 511–523 (2013)

    Article  Google Scholar 

  18. ZHANG, X. C., AN, L. Q., and DING, H. M. Dynamic crushing behavior and energy absorption of honeycombs with density gradient. Journal of Sandwich Structures and Materials, 16(2), 125–147 (2013)

    Article  Google Scholar 

  19. AN, L. Q., ZHANG, X. C., WU, H. X., and JIANG, W. Q. In-plane dynamic crushing and energy absorption capacity of self-similar hierarchical honeycombs. Advances in Mechanical Engineering, 9(6), 1–15 (2017)

    Article  Google Scholar 

  20. MA, F. W., ZHAO, Y., YANG, L. F., and LIANG, H. Y. Theoretical study and simulation analysis on re-entrant square cellular material’s mechanical properties. Advances in Mechanical Engineering, 10(4), 1–19 (2018)

    Google Scholar 

  21. WANG, H., LU, Z. X., YANG, Z. Y., and LI, X. In-plane dynamic crushing behaviors of a novel auxetic honeycomb with two plateau stress regions. International Journal of Mechanical Sciences, 151, 746–759 (2019)

    Article  Google Scholar 

  22. WANG, Z. G. Recent advances in novel metallic honeycomb structure. Composites Part B: Engineering, 166, 731–741 (2019)

    Article  Google Scholar 

  23. ZHANG, S. and XU, F. X. A two-stage hybrid optimization for honeycomb-type cellular structures under out-of-plane dynamic impact. Applied Mathematical Modelling, 80, 755–770 (2020)

    Article  MathSciNet  MATH  Google Scholar 

  24. CALLADINE, C. R. and ENGLISH, R. W. Strain-rate and inertia effects in the collapse of two types of energy-absorbing structure. International Journal of Mechanical Sciences, 26(11/12), 689–701 (1984)

    Article  Google Scholar 

  25. HABIB, F. N., IOVENITTI, P., MASOOD, S. H., and NIKZAD, M. Cell geometry effect on in-plane energy absorption of periodic honeycomb structures. International Journal of Advanced Manufacturing Technology, 94(5), 2369–2380 (2017)

    Google Scholar 

  26. WU, H. X., LIU, Y., and ZHANG, X. C. In-plane crushing behavior and energy absorption design of composite honeycombs. Acta Mechanica Sinica, 34(6), 1108–1123 (2018)

    Article  MathSciNet  Google Scholar 

  27. YANG, X. F., XI, X. L., PAN, Q. F., and LIU, H. In-plane dynamic crushing of a novel circular-celled honeycomb nested with petal-shaped mesostructure. Composite Structures, 226, 111219 (2019)

    Article  Google Scholar 

  28. ZHANG, T. G. and YU, T. X. A note on a ‘velocity sensitive’ energy-absorbing structure. International Journal of Impact Engineering, 8(1), 43–51 (1989)

    Article  Google Scholar 

  29. SU, X. Y., YU, T. X., and REID, S. R. Inertia-sensitive impact energy-absorbing structures part I: effects of inertia and elasticity. International Journal of Impact Engineering, 16(4), 651–672 (1995)

    Article  Google Scholar 

  30. SU, X. Y., YU, T. X., and REID, S. R. Inertia-sensitive impact energy-absorbing structures part II: effect of strain rate. International Journal of Impact Engineering, 16(4), 673–689 (1995)

    Article  Google Scholar 

  31. WEBB, D. C., KORMI, K., and AL-HASSANI, S. T. S. The influence of inertia and strain-rate on large deformation of plate-structures under impact loading. Computers and Structures, 79(19), 1781–1797 (2001)

    Article  Google Scholar 

  32. GAO, Z. Y., YU, T. X., and LU, G. A study on type II structures, part II: dynamic behavior of a chain of pre-bent plates. International Journal of Impact Engineering, 31(7), 911–926 (2005)

    Google Scholar 

  33. PHAM, M. S., LIU, C., TODD, I., and LERTTHANASARN, J. J. N. Damage-tolerant architected materials inspired by crystal microstructure. nature, 565(7739), 305–311 (2019)

    Article  Google Scholar 

  34. SUN, D. Q., CAO, W. T., and CAI, M. In-plane crushing of square honeycomb cores, part I: mechanical behaviors. Applied Mechanics and Materials, 170–173, 3220–3223 (2012)

    Article  Google Scholar 

  35. SUN, D. Q., JIANG, Z. Y., and WEI, Y. B. In-plane crushing of square honeycomb cores, part II: energy absorption and cushioning optimization. Applied Mechanics and Materials, 170–173, 3237–3240 (2012)

    Article  Google Scholar 

  36. LU, G. and YU, T. X. Energy Absorption of Structures and Naterials, Woodhead Publishing, Cambrigde, 269–286 (2003)

    Book  Google Scholar 

  37. YU, T. X. and ZHANG, L. C. Plastic Bending: Theory and Applications, World Scientific, River Edge, 477–487 (1996)

    Book  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, 200092, China

    Yijie Bian, Puhao Li, Fan Yang & Peng Wang

  2. Research Center of Lightweight Structures and Intelligent Manufacturing, State Key Laboratory of Mechanics and Control of Mechanical Structures, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Weiwei Li & Hualin Fan

Authors
  1. Yijie Bian
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Puhao Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Fan Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Peng Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Weiwei Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Hualin Fan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Fan Yang or Hualin Fan.

Additional information

Citation: BIAN, Y. J., LI, P. H., YANG, F.,WANG, P., LI,W.W., and FAN, H. L. Deformation mode and energy absorption of polycrystal-inspired square-cell lattice structures. Applied Mathematics and Mechanics (English Edition) 41(10), 1561—1582 (2020) https://doi.org/10.1007/s10483-020-2648-8

Project supported by the National Natural Science Foundation of China (No. 11772231)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bian, Y., Li, P., Yang, F. et al. Deformation mode and energy absorption of polycrystal-inspired square-cell lattice structures. Appl. Math. Mech.-Engl. Ed. 41, 1561–1582 (2020). https://doi.org/10.1007/s10483-020-2648-8

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-020-2648-8

Key words

Chinese Library Classification

2010 Mathematics Subject Classification

Search

Navigation