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  • Letter
  • Open Access

Canceling the elastic Poynting effect with geometry

M. Destrade1, Y. Du2,*, J. Blackwell1, N. Colgan1, and V. Balbi1

  • 1School of Mathematical and Statistical Sciences, University of Galway, Galway H91 TK33, Ireland
  • 2Department of Mathematics and Statistics, University of Glasgow, Glasgow G12 8QQ, Scotland

  • *Corresponding author: duyangkunzju@gmail.com
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Phys. Rev. E 107, L053001 – Published 24 May, 2023

DOI: https://doi.org/10.1103/PhysRevE.107.L053001

Abstract

The Poynting effect is a paragon of nonlinear soft matter mechanics. It is the tendency (found in all incompressible, isotropic, hyperelastic solids) exhibited by a soft block to expand vertically when sheared horizontally. It can be observed whenever the length of the cuboid is at least four times its thickness. Here we show that the Poynting effect can be easily reversed and the cuboid can shrink vertically, simply by reducing this aspect ratio. In principle, this discovery means that for a given solid, say one used as a seismic wave absorber under a building, an optimal ratio exists where vertical displacements and vibrations can be completely eliminated. Here we first recall the classical theoretical treatment of the positive Poynting effect, and then show experimentally how it can be reversed. Using finite-element simulations, we then investigate how the effect can be suppressed. We find that cubes always provide a reverse Poynting effect, irrespective of their material properties (in the third-order theory of weakly nonlinear elasticity).

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References (19)

  1. J. H. Poynting, On pressure perpendicular to the shear planes in finite pure shears, and on the lengthening of loaded wires when twisted, Proc. R. Soc. Lond. A 82, 546 (1909).
  2. R. S. Rivlin, Torsion of a rubber cylinder, J. Appl. Phys. 18, 444 (1947).
  3. R. S. Rivlin, Large elastic deformation of isotropic materials IV. Further developments of the general theory, Philos. Trans. R. Soc. London A 241, 379 (1948).
  4. V. Balbi, A. Trotta, M. Destrade, and A. N. Annaidh, Poynting effect of brain matter in torsion, Soft Matter. 15, 5147 (2019).
  5. R. S. Rivlin and D. W. Saunders, Large elastic deformation of isotropic materials VII. Experiments on the deformation of rubber, Philos. Trans. R. Soc. London A 243, 251 (1951).
  6. M. Destrade, M. D. Gilchrist, and J. G. Murphy, Onset of nonlinearity in the elastic bending of blocks, J. Appl. Mech. 77, 061015 (2010).
  7. ISO 1827:2022, Rubber, vulcanized or thermoplastic – Determination of shear modulus and adhesion to rigid plates – Quadruple-shear methods, Standard, 6th ed. (International Organization for Standardization, Geneva, CH, 2022).
  8. D. Wang and M. Wu, Generalized shear of a soft rectangular block, J. Mech. Phys. Solids 70, 297 (2014).
  9. S. Yan, D. Jia, Y. Yu, L. Wang, Y. Qiu, and Q. Wan, Novel strategies for parameter fitting procedure of the Ogden hyperfoam model under shear condition, Eur. J. Mech. A Solids 86, 104154 (2021).
  10. M. Smith, ABAQUS/Standard User's Manual, Version 2017 (Dassault Systèmes Simulia Corp, USA, 2017).
  11. P. A. Janmey, M. E. McCormick, S. Rammensee, J. L. Leight, P. C. Georges, and F. C. MacKintosh, Negative normal stress in semiflexible biopolymer gels, Nat. Mater. 6, 48 (2007).
  12. M. Destrade, C. Horgan, and J. Murphy, Dominant negative Poynting effect in simple shearing of soft tissues, J. Eng. Math. 95, 87 (2015).
  13. C. Horgan and J. Murphy, The effect of fiber-matrix interaction on the Poynting effect for torsion of fibrous soft biomaterials, J. Mech. Behav. Biomed. Mater. 118, 104410 (2021).
  14. L. M. Kanner and C. O. Horgan, On extension and torsion of strain-stiffening rubber-like elastic circular cylinders, J. Elast. 93, 39 (2008).
  15. M. Destrade, M. D. Gilchrist, J. Motherway, and J. G. Murphy, Slight compressibility and sensitivity to changes in Poisson's ratio, Int. J. Numer. Methods Eng. 90, 403 (2012).
  16. H. C. G. de Cagny, B. E. Vos, M. Vahabi, N. A. Kurniawan, M. Doi, G. H. Koenderink, F. C. MacKintosh, and D. Bonn, Porosity Governs Normal Stresses in Polymer Gels, Phys. Rev. Lett. 117, 217802 (2016).
  17. A. Fall, B. P. Tighe, and D. Bonn, Tuneable normal stresses in hyperelastic emulsions, Phys. Rev. Res. 4, 013167 (2022).
  18. K. Baumgarten and B. P. Tighe, Normal Stresses, Contraction, and Stiffening in Sheared Elastic Networks, Phys. Rev. Lett. 120, 148004 (2018).
  19. S. Budday, T. C. Ovaert, G. A. Holzapfel, P. Steinmann, and E. Kuhl, Fifty shades of brain: A review on the mechanical testing and modeling of brain tissue, Arch. Comput. Methods Eng. 27, 1187 (2020).

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Phys. Rev. E 107, L053001– Published 24 May, 2023
  • Received 15 February 2023
  • Accepted 4 May 2023
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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