Journal of Elasticity

, Volume 134, Issue 1, pp 103–118 | Cite as

Torsion of Chiral Porous Elastic Beams

  • D. IeşanEmail author


This paper is concerned with the equilibrium theory of chiral porous elastic solids. We study the problem of torsion, bending and extension of chiral cylinders. First, it is shown that the solution can be found as a vector field which has the property that its partial derivative with respect to axial coordinate corresponds to a rigid deformation. Then, we reduce the problem to the study of some two-dimensional problems. With the help of these results we can investigate the bending by terminal couples and the problems of extension and torsion. The solution is used to study the torsion of a chiral circular cylinder.


Chiral materials Porous elastic solids Microstretch continua Plane deformation Torsion problem 

Mathematics Subject Classification (2010)

74A35 74G50 74K10 74L15 



I express my gratitude to the referees for their helpful suggestions.


  1. 1.
    Lakes, R.: Elastic and viscoelastic behaviour of chiral materials. Int. J. Mech. Sci. 43, 1579–1589 (2001) CrossRefzbMATHGoogle Scholar
  2. 2.
    Lakes, R.S.: Dynamical study of couple stress effects in human compact bone. J. Biomech. Eng. 104, 6–11 (1982) CrossRefGoogle Scholar
  3. 3.
    Lakes, R.S., Benedict, R.L.: Noncentrosymmetry in micropolar elasticity. Int. J. Eng. Sci. 29, 1161–1167 (1982) CrossRefzbMATHGoogle Scholar
  4. 4.
    Lakes, R.S., Yoon, H.S., Katz, J.L.: Slow compressional wave propagation in wet human and bovine cortical bone. Science 200, 513–515 (1983) ADSCrossRefGoogle Scholar
  5. 5.
    Park, H.C., Lakes, R.S.: Cosserat micromechanics of human bone: strain redistribution by a hydratation-sensitive constituent. J. Biomech. 19, 1038–1040 (1986) CrossRefGoogle Scholar
  6. 6.
    Lakes, R.S.: Elastic freedom in cellular solids and composite materials. In: Golden, K., Grimmert, G., James, R., Milton, G., Sen, P. (eds.) Mathematics of Multiscale Materials, IMA, vol. 99, pp. 129–153. Springer, Berlin (1988) CrossRefGoogle Scholar
  7. 7.
    Prall, D., Lakes, R.S.: Properties of a chiral honeycomb with a Poisson’s ratio-1. Int. J. Mech. Sci. 39, 305–314 (1997) CrossRefzbMATHGoogle Scholar
  8. 8.
    Ha, C.S., Plesha, M.E., Lakes, R.S.: Chiral three dimensional lattices with tunable Poissons ratio. Smart Mater. Struct. 25, 054005 (2016) ADSCrossRefGoogle Scholar
  9. 9.
    Dyszlewicz, J.: Micropolar Theory of Elasticity. Springer, New York (2004) CrossRefzbMATHGoogle Scholar
  10. 10.
    Natroshvili, D., Stratis, I.G.: Mathematical problems of the theory of elasticity of chiral materials for Lipschitz domains. Math. Methods Appl. Sci. 29, 445–478 (2005) MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Chandraseker, K., Mukherjee, S., Paci, J.T., Schatz, G.C.: An atomistic continuum Cosserat rod model of carbon nanotubes. J. Mech. Phys. Solids 57, 932–958 (2009) ADSCrossRefGoogle Scholar
  12. 12.
    Nunziato, J.W., Cowin, S.C.: A non-linear theory of elastic materials with voids. Arch. Ration. Mech. Anal. 72, 175–201 (1979) CrossRefzbMATHGoogle Scholar
  13. 13.
    Cowin, S.C., Nunziato, J.W.: Linear elastic materials with voids. J. Elast. 13, 125–147 (1983) CrossRefzbMATHGoogle Scholar
  14. 14.
    Eringen, A.C.: Microcontinuum Field Theories I: Foundations and Solids. Springer, Heidelberg (1999) CrossRefzbMATHGoogle Scholar
  15. 15.
    Kohles, S.S., Roberts, J.B.: Linear poroelastic cancellous bone anisotropy: trabecular solid elastic and fluid transport properties. J. Biomech. Eng. 124, 521–526 (2002) CrossRefGoogle Scholar
  16. 16.
    Fatemi, J., van Keulen, F., Onck, P.R.: Generalized continuum theories: applications to stress analysis of bone. Meccanica 37, 385–396 (2002) MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    DeCicco, S., Nappa, L.: Torsion and flexure of microstretch elastic circular cylinders. Int. J. Eng. Sci. 35, 573–583 (1997) CrossRefzbMATHGoogle Scholar
  18. 18.
    Scalia, A.: Extension, bending and torsion of anisotropic microstretch elastic cylinders. Math. Mech. Solids 5, 31–40 (2000) CrossRefzbMATHGoogle Scholar
  19. 19.
    Ieşan, D., Pompei, A.: On the equilibrium theory of microstretch elastic solids. Int. J. Eng. Sci. 33, 399–410 (1995) MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Ieşan, D.: On Saint-Venants problem. Arch. Ration. Mech. Anal. 91, 363–373 (1986) MathSciNetCrossRefzbMATHGoogle Scholar
  21. 21.
    Hlavacek, I., Hlavacek, M.: On the existence and uniqueness of solution and some variational principles in linear theories of elasticity with couple-stresses. Apl. Mat. 14, 411–427 (1969) MathSciNetzbMATHGoogle Scholar
  22. 22.
    Fichera, G.: Existence theorems in elasticity. In: Truesdel, C. (ed.) Handbuch der Physik, vol. VI a/2. Springer, Berlin (1972) Google Scholar
  23. 23.
    Ieşan, D.: Classical and Generalized Models of Elastic Rods. Chapman & Hall/CRC Press, London/New York (2009) zbMATHGoogle Scholar

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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.“Octav Mayer” Institute of MathematicsRomanian AcademyIaşiRomania

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