Tailorable elasticity of cantilever using spatio-angular functionally graded biomimetic scales

Abstract

Cantilevered beams are of immense importance as structural and sensorial members for a number of applications. Endowing tailorable elasticity can have wide ranging engineering ramification. Such tailorability could be possible using some type of spatial gradation in the beam’s material or cross section. However, these often require extensive additive and subtractive material processing or specialized casts. Herein, we demonstrate an alternative bio-inspired mechanical pathway, which is based on exploiting the nonlinearity that would arise from a functionally graded (FG) distribution of biomimetic scales on the surface using an analytical approach. This functional gradation is geometrically sourced and could arise from either spatial or angular gradation of scales. We analyze such FG cantilever beams under different loading conditions including point loading at the free end, uniform traction, linearly distributed traction, and concentrated moment loading at the free end. In comparison with uniformly distributed scales for all cases of the loading addressed, we find significant differences in bending stiffness for both spatial and angular gradations. Spatial and angular functional gradations share some universality but also sharp contrasts in their effect on the underlying beam. We also quantify the landscape of spatio-angular tailorability on stiffness gains. We compare our models with select experiments for validation. This highlights that a combination of both types of gradation in the structure can be used to alter stiffness and therefore offer a pathway to tailor the elasticity of a cantilever beam relatively easily. These results demonstrate an architected framework for designing and optimizing scale-covered FG beams.

This is a preview of subscription content, access via your institution.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8

References

  1. 1.

    Bassiri-Gharb, N.: In: Piezoelectric and Acoustic Materials for Transducer Applications, pp 413–430. Springer (2008)

  2. 2.

    Carpinteri, A.: Structural mechanics: a unified approach. CRC Press, Boca Raton (2014)

    MATH  Google Scholar 

  3. 3.

    Banica, F.G.: Chemical sensors and biosensors: fundamentals and applications. Wiley, New Jersey (2012)

    Book  Google Scholar 

  4. 4.

    El Daou, H., Salumäe, T., Chambers, L.D., Megill, W.M., Kruusmaa, M.: Bioinspiration & Biomimetics 9(1), 016010 (2014)

    Article  Google Scholar 

  5. 5.

    Chen, J., Nie, X., Zhou, X.: In: Journal of Physics: Conference Series, vol. 916 (IOP Publishing), p 012004 (2017)

  6. 6.

    Ak, C., Yildiz, A.: J. Microelectromech. Syst. 27(3), 392 (2018)

    Article  Google Scholar 

  7. 7.

    Rabenorosoa, K., Rakotondrabe, M.: In: Next-Generation Robotics II; and Machine Intelligence and Bio-inspired Computation: Theory and Applications IX, vol. 9494 (International Society for Optics and Photonics), p 94940E (2015)

  8. 8.

    Zhu, J.H., Zhang, W.H., Xia, L.: Arch. Comput. Meth. Eng. 23(4), 595 (2016)

    Article  Google Scholar 

  9. 9.

    Yang, A., Li, P., Wen, Y., Lu, C., Peng, X., He, W., Zhang, J., Wang, D., Yang, F.: Rev. Sci. Instrum. 85(6), 066103 (2014)

    Article  Google Scholar 

  10. 10.

    Khushalani, D.G., Dubey, V.R., Bheley, P.P., Kalambe, J.P., Pande, R.S., Patrikar, R.M.: Sensors Actuators A Phys. 225, 1 (2015)

    Article  Google Scholar 

  11. 11.

    Sola, A., Bellucci, D., Cannillo, V.: Biotechnol. Adv. 34(5), 504 (2016)

    Article  Google Scholar 

  12. 12.

    Pompe, W., Worch, H., Epple, M., Friess, W., Gelinsky, M., Greil, P., Hempel, U., Scharnweber, D., Schulte, K.: Mater. Sci. Eng. A 362(1-2), 40 (2003)

    Article  Google Scholar 

  13. 13.

    Zhang, X.C., An, L.Q., Ding, H.M.: J. Sandw. Struct. Mater. 16(2), 125 (2014)

    Article  Google Scholar 

  14. 14.

    Mousanezhad, D., Ghosh, R., Ajdari, A., Hamouda, A., Nayeb-Hashemi, H., Vaziri, A.: Int. J. Mech. Sci. 89, 413 (2014)

    Article  Google Scholar 

  15. 15.

    Brothers, A.H., Dunand, D.C.: Mater. Sci. Eng. A 489(1-2), 439 (2008)

    Article  Google Scholar 

  16. 16.

    Tissandier, C., González-Núñez, R., Rodrigue, D.: J. Cell. Plast. 50(5), 449 (2014)

    Article  Google Scholar 

  17. 17.

    Maskery, I., Hussey, A., Panesar, A., Aremu, A., Tuck, C., Ashcroft, I., Hague, R.: J. Cell. Plast. 53(2), 151 (2017)

    Article  Google Scholar 

  18. 18.

    Duan, S., Tao, Y., Lei, H., Wen, W., Liang, J., Fang, D.: Extreme Mech. Lett. 18, 9 (2018)

    Article  Google Scholar 

  19. 19.

    Kumar, K., Liu, J., Christianson, C., Ali, M., Tolley, M.T., Aizenberg, J., Ingber, D.E., Weaver, J.C., Bertoldi, K.: Soft Rob. 4(4), 317 (2017)

    Article  Google Scholar 

  20. 20.

    Bartlett, N.W., Tolley, M.T., Overvelde, J.T., Weaver, J.C., Mosadegh, B., Bertoldi, K., Whitesides, G.M., Wood, R.J.: Science 349(6244), 161 (2015)

    Article  Google Scholar 

  21. 21.

    Birman, V.: In: Encyclopedia of Thermal Stresses, pp 3104–3112. Springer (2014)

  22. 22.

    Bohidar, S.K., Sharma, R., Mishra, P.R.: Int. J. Res. 1(4), 289 (2014)

    Google Scholar 

  23. 23.

    Kieback, B., Neubrand, A., Riedel, H.: Mater. Sci. Eng. A 362(1-2), 81 (2003)

    Article  Google Scholar 

  24. 24.

    Mahamood, R.M., Akinlabi E.T.: Functionally graded materials. Springer, Berlin (2017)

    Book  Google Scholar 

  25. 25.

    Arciszewski, T., Cornell, J.: In: Intelligent Computing in Engineering and Architecture, pp 32–53. Springer (2006)

  26. 26.

    Huang, J., Wang, X., Wang, Z.L.: Nano letters 6(10), 2325 (2006)

    Article  Google Scholar 

  27. 27.

    Colbert, E.H., et al.: Evolution of the vertebrates a history of the backboned animals through time (1955)

  28. 28.

    Naleway, S.E., Taylor, J.R., Porter, M.M., Meyers, M.A., McKittrick, J.: Mater. Sci. Eng. C 59, 1143 (2016)

    Article  Google Scholar 

  29. 29.

    Prum, R.O., Quinn, T., Torres, R.H.: J. Exp. Biol. 209(4), 748 (2006)

    Article  Google Scholar 

  30. 30.

    Motta, P.J.: Copeia, pp. 454–464 (1977)

  31. 31.

    Wainwright, S., Vosburgh, F., Hebrank, J.: Science 202(4369), 747 (1978)

    Article  Google Scholar 

  32. 32.

    Brown, G., Wellings, S.: Zeitschrift für Zellforschung und Mikroskopische Anatomie 103(2), 149 (1970)

    Article  Google Scholar 

  33. 33.

    Hebrank, M.R.: Biol. Bull. 158(1), 58 (1980)

    Article  Google Scholar 

  34. 34.

    Nadol, J.B. Jr, Gibbins, J.R., Porter, K.R.: Dev. Biol. 20(4), 304 (1969)

    Article  Google Scholar 

  35. 35.

    Videler, J.J.: Netherlands Journal of Zoology 25(2), 143 (1974)

    Article  Google Scholar 

  36. 36.

    Lee, J.L., Thompson, A., Mulcahy, D.G.: J. Herpetol. 50(4), 616 (2016)

    Article  Google Scholar 

  37. 37.

    Wainwright, D.K., Ingersoll, S., Lauder, G.V.: J. Morphol. 279(6), 828 (2018)

    Article  Google Scholar 

  38. 38.

    Wainwright, D.K., Lauder, G.V.: In: Functional Surfaces in Biology III, pp 223–246. Springer (2017)

  39. 39.

    Sanderson, J.G., Pimm, S.L.: Patterns in nature: the analysis of species co-occurrences. University of Chicago Press, Chicago (2015)

    Book  Google Scholar 

  40. 40.

    Currie, D.J.: Am. Nat. 137(1), 27 (1991)

    Article  Google Scholar 

  41. 41.

    Olalla-Tárraga, M.A.́, Rodríguez, M.Á., Hawkins, B.A.: Journal of Biogeography 33(5), 781 (2006)

    Article  Google Scholar 

  42. 42.

    Gaston, K.J.: Nature 405(6783), 220 (2000)

    Article  Google Scholar 

  43. 43.

    Greene, H.W.: Snakes: the evolution of mystery in nature. University of California Press, Berkeley (2000)

    Google Scholar 

  44. 44.

    Bellwood, D., Wainwright, P., Fulton, C., Hoey, A.: Funct. Ecol. 16(5), 557 (2002)

    Article  Google Scholar 

  45. 45.

    Chang, C., Wu, P., Baker, R.E., Maini, P.K., Alibardi, L., Chuong, C.M.: Int. J. Dev. Biol. 53(5-6), 813 (2009)

    Article  Google Scholar 

  46. 46.

    Yu, Y., Yang, W., Wang, B., Meyers, M.A.: Mater. Sci. Eng. C 73, 152 (2017)

    Article  Google Scholar 

  47. 47.

    Martini, R., Barthelat, F.: Bioinspiration & Biomimetics 11(6), 066001 (2016)

    Article  Google Scholar 

  48. 48.

    Ghosh, R., Ebrahimi, H., Vaziri, A.: Appl. Phys. Lett. 105(23), 233701 (2014)

    Article  Google Scholar 

  49. 49.

    Funk, N., Vera, M., Szewciw, L.J., Barthelat, F., Stoykovich, M.P., Vernerey, F.J.: ACS Appl. Mater. Interfaces 7(10), 5972 (2015)

    Article  Google Scholar 

  50. 50.

    White, Z.W., Vernerey, F.J.: Bioinspiration & Biomimetics 13(4), 041004 (2018)

    Article  Google Scholar 

  51. 51.

    Vernerey, F.J., Barthelat, F.: Int. J. Solids Struct. 47(17), 2268 (2010)

    Article  Google Scholar 

  52. 52.

    Vernerey, F.J., Barthelat, F.: J. Mech. Phys. Solids 68, 66 (2014)

    MathSciNet  Article  Google Scholar 

  53. 53.

    Vernerey, F.J., Musiket, K., Barthelat, F.: Int. J. Solids Struct. 51(1), 274 (2014)

    Article  Google Scholar 

  54. 54.

    Browning, A., Ortiz, C., Boyce, M. C.: J. Mech. Behav. Biomed. Mater. 19, 75 (2013)

    Article  Google Scholar 

  55. 55.

    Ghosh, R., Ebrahimi, H., Vaziri, A.: EPL (Europhysics Letters) 113(3), 34003 (2016)

    Article  Google Scholar 

  56. 56.

    Ebrahimi, H., Ali, H., Horton, R.A., Galvez, J., Gordon, A.P., Ghosh, R.: EPL (Europhysics Letters) 127(2), 24002 (2019)

    Article  Google Scholar 

  57. 57.

    Ali, H., Ebrahimi, H., Ghosh, R.: International Journal of Solids and Structures (2019)

  58. 58.

    Shigley, J.E., Mischke, C., Budynas, R.: Mechanical Engineering Design (McGraw-Hill Series in Mechanical Engineering). McGraw-Hill (1988)

  59. 59.

    Fenner, R.T., Reddy, J.N.: Mechanics of solids and structures. CRC Press, Boca Raton (2012)

    MATH  Book  Google Scholar 

  60. 60.

    ABAQUS, C.: Analysis user’s manual, version 6.12 (2012)

Download references

Author information

Affiliations

Authors

Corresponding author

Correspondence to Ranajay Ghosh.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Ali, H., Ebrahimi, H. & Ghosh, R. Tailorable elasticity of cantilever using spatio-angular functionally graded biomimetic scales. Mech Soft Mater 1, 10 (2019). https://doi.org/10.1007/s42558-019-0012-2

Download citation

Keywords

  • Biomimetic scales
  • Functionally graded material
  • Nonlinear elasticity
  • Stiffness tailorability