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Mechanics of Advanced Materials and Structures Volume 30, 2023 - Issue 19
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Original Articles

Cosserat shape effects in the bending of foams

R. S. LakesDepartment of Engineering Physics and Department of Materials Science, University of Wisconsin, Madison, Wisconsin, USACorrespondence[email protected]
Pages 3997-4001 | Received 30 May 2022, Accepted 01 Jun 2022, Published online: 14 Jun 2022

References

  • E. Cosserat, and F. Cosserat, Theorie des Corps Deformables, Hermann et Fils, Paris, 1909.
  • R. D. Mindlin, Stress functions for a Cosserat continuum, Int. J. Solids Struct., vol. 1, no. 3, pp. 265–271, 1965. DOI: 10.1016/0020-7683(65)90033-8.
  • A. C. Eringen, Theory of Micropolar Elasticity, In: H. Liebowitz (ed.), Fracture, Vol. 1, 621–729, Academic Press, New York, 1968.
  • R. D. Gauthier, and W. E. Jahsman, A quest for micropolar elastic constants, J. Appl. Mech., vol. 42, no. 2, pp. 369–374, 1975. DOI: 10.1115/1.3423583.
  • R. S. Lakes, Experimental microelasticity of two porous solids, Int. J. Solids Struct., vol. 22, no. 1, pp. 55–63, 1986. DOI: 10.1016/0020-7683(86)90103-4.
  • Z. Rueger, and R. S. Lakes, Experimental Cosserat elasticity in open cell polymer foam, Philos. Mag., vol. 96, no. 2, pp. 93–111, 2016. DOI: 10.1080/14786435.2015.1125541.
  • Z. Rueger, and R. S. Lakes, Experimental study of elastic constants of a dense foam with weak Cosserat coupling, J. Elast., vol. 137, no. 1, pp. 101–115, 2019. DOI: 10.1007/s10659-018-09714-8.
  • A. J. Beveridge, M. A. Wheel, and D. H. Nash, The micropolar elastic behaviour of model macroscopically heterogeneous materials, Int. J. Solids Struct., vol. 50, no. 1, pp. 246–255, 2013. DOI: 10.1016/j.ijsolstr.2012.09.023.
  • Z. Rueger, and R. S. Lakes, Strong Cosserat elasticity in a transversely isotropic polymer lattice, Phys. Rev. Lett., vol. 120, no. 6, pp. 065501, 2018. Feb DOI: 10.1103/PhysRevLett.120.065501.
  • H. C. Park, and R. S. Lakes, Torsion of a micropolar elastic prism of square cross section, Int. J. Solids, Struct., vol. 23, no. 4, pp. 485–503, 1987. DOI: 10.1016/0020-7683(87)90013-8.
  • W. J. Drugan, and R. S. Lakes, Torsion of a Cosserat Elastic Bar with Square Cross-Section: Theory and Experiment, Zeit. Angew. Math. Phys. (ZAMP), vol. 69, no. 2, pp. 24, 2018.
  • R. S. Lakes, D. Gorman, and W. Bonfield, Holographic screening method for microelastic solids, J. Mater. Sci., vol. 20, no. 8, pp. 2882–2888, 1985. DOI: 10.1007/BF00553052.
  • W. B. Anderson, R. S. Lakes, and M. C. Smith, Holographic evaluation of warp in the torsion of a bar of cellular solid, Cellular Polym., vol. 14, pp. 1–13, 1995.
  • R. S. Lakes, Reduced warp in torsion of reticulated foam due to Cosserat elasticity: experiment, Zeit. Angew. Math. Phys. (ZAMP), vol. 67, no. 3, pp. 1–6, 2016.
  • R. S. Lakes, and W. J. Drugan, Bending of a Cosserat elastic bar of square cross section - theory and experiment, J. Appl. Mech., vol. 82, no. 9, pp. 091002, 2015. DOI: 10.1115/1.4030626.
  • Z. Rueger, C. S. Ha, and R. S. Lakes, Cosserat elastic lattices, Meccanica, vol. 54, no. 13, pp. 1983–1999, 2019. DOI: 10.1007/s11012-019-00968-7.
  • R. D. Mindlin, Micro-structure in linear elasticity, Arch. Rational Mech. Anal., vol. 16, no. 1, pp. 51–78, 1964. DOI: 10.1007/BF00248490.
  • S. C. Cowin, and J. W. Nunziato, Linear elastic materials with voids, J. Elasticity., vol. 13, no. 2, pp. 125–147, 1983. DOI: 10.1007/BF00041230.

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