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Torsion of viscoelastic spheres in contact

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The theory of elastic contact between two spherical bodies is used as a basis for an extension to include the contribution of the viscous effects to the total stress for viscoelastic spheres subjected to twisting moments. Expressions relating twisting moment to penetration of slip and penetration of slip to twist angle are derived. Two term power series truncations of the relations are then used to derive approximate expressions for torsional compliance of the bodies. Validation experiments for the extended model were performed by use of a rheometer device. Applications for the model in post-harvest agriculture include extraction of material properties for use in Discrete Element Modelling of mechanical interactions of fruits and other regular shaped produce during machine handling. A specific application is performed involving the use of a rheometer to measure the coefficient of friction for fruit-fruit contact.

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  1. Hertz, H.: J. reine und angewandte Mathematik 94, 156 (1882) (English translation in Miscellaneous Papers by H. Hertz, Eds. Jones and Schott, London, Macmillan, 1896)

  2. Mindlin, R.D.: ASME J. Appl. Mech. 16, 259 (1949)

    Google Scholar 

  3. Timoshenko, S., Goodier, J.N.: Theory of Elasticity. 2nd edn. (McGraw-Hill, New York, 1951)

  4. Love, A.E.H.: A Treatise on the Mathematical Theory of Elasticity. 4th edn. (Cambridge University Press, New York, 1952)

  5. Johnson, K.L.: Contact Mechanics, 2nd edn. (Cambridge University Press, New York, 1985)

  6. Mindlin, R.D., Deresiewicz, H.: ASME J. Appl. Mech. 20, 327 (1953)

    Google Scholar 

  7. Lubkin, J.L.: ASME J.Appl. Mech. 18, 183 (1951)

    Google Scholar 

  8. Hetenyi, M., McDonald, J.R.: ASME J. Appl. Mech. 25, 396 (1958)

    Google Scholar 

  9. Lee, E.H., Radock, J.R.M.: ASME J. Appl. Mech. 27, 438 (1960)

    Google Scholar 

  10. Kuwabara, G., Kono, K.: Jap. J. Appl. Phys. 26, 1230 (1987)

  11. Hertzsh, J.M., Spahn, F., Brilliantov, N.V.: J. Phys. II 5, 1725 (1995)

    Google Scholar 

  12. Ramírez, R., Pöschel, T., Brilliantov, N.V., Schwager, T.: Phys. Rev. E 60, 4465 (1999)

    Google Scholar 

  13. Bardet, J.P., Huang, Q.: In Proceedings of the Second International Conference on Micromechanics of Granular Media, 1993, edited by C. Thornton (A.A. Balkema, Rotterdam, The Netherlands, 1993) 39

  14. Iwashita, K., Oda, M.: ASCE J. Engrg. Mech. 124, 285 (1998)

    Google Scholar 

  15. Brilliantov, N.V., Pöschel, T.: Europhys. Lett. 42, 511 (1998)

    Google Scholar 

  16. Brilliantov, N.V., Pöschel, T.: Eur. Phys. J. B 12, 299 (1999)

    Google Scholar 

  17. Pöschel, T., Schwager, T., Brilliantov, N.V.: Eur. Phys. J. B 10, 169 (1999)

    Google Scholar 

  18. Tijskens, E., Ramon, H., De Baerdemaeker, J.: J. Sound Vib. 266, 493 (2003)

    Google Scholar 

  19. Hamann, D.D.: Trans. ASAE 13, 893 (1970)

    Google Scholar 

  20. Chen, P., Fridley, R.B.: Trans. ASAE 15, 1103 (1972)

    Google Scholar 

  21. De Baerdemaeker, J.G., Segerlind, L.J.: Trans. ASAE 19, 346 (1976)

    Google Scholar 

  22. Akyurt, M., Zachariah, G.L., Haugh, C.G.: Trans. ASAE 15, 766 (1972)

    Google Scholar 

  23. Pitt, R.E., Chen, H.L.: Trans. ASAE 26, 1275 (1983)

    Google Scholar 

  24. Mohsenin, N.: Physical Properties of Plant and Animal Materials, 2nd edn. (Gordon and Breach Science Publishers, New York, 1986)

  25. Lu, R., Puri, V.M.: J. Rheol. 35, 1209 (1991)

    Google Scholar 

  26. Deresiewicz, H.: ASME J. Appl. Mech. 21, 327 (1954)

    Google Scholar 

  27. Boussinesq, J.: Application des potentials à l’etitude de l’équilibre et du mouvement des solides èlastiques. (Gauthier-Villars, Paris, 1885)

  28. Cerruti, V.: Roma, Acc. Lincei., Mem. Fis. Mat. (1882)

  29. Fung, Y.C.: A First Course in Continuum Mechanics, 3rd edn. (Prentice-Hall Inc., Englewood Cliffs, New Jersey, 1994)

  30. Van Zeebroeck, M., Dintwa, E., Tijskens, E., Ramon, H.: Postharvest Biol. Technol. 33, 111 (2004)

    Google Scholar 

  31. Brilliantov, N.V., Spahn, F., Hertzsch, J.M.: Phys. Rev. E 53, 5382 (1996)

    Google Scholar 

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Correspondence to Edward Dintwa.

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Dintwa, E., Zeebroeck, M., Tijskens, E. et al. Torsion of viscoelastic spheres in contact. Granular Matter 7, 169–179 (2005).

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