Comptes Rendus
Micropolar modeling of planar orthotropic rectangular chiral lattices
Comptes Rendus. Mécanique, Volume 342 (2014) no. 5, pp. 273-283.

Rectangular chiral lattices possess a two-fold symmetry; in order to characterize the overall behavior of such lattices, a two-dimensional orthotropic chiral micropolar theory is proposed. Eight additional material constants are necessary to represent the anisotropy in comparison with triangular ones, four of which are devoted to chirality. Homogenization procedures are also developed for the chiral lattice with rigid or deformable circles, all material constants in the developed micropolar theory are derived analytically for the case of the rigid circles and numerically for the case of the deformable circles. The dependences of these material constants and of wave propagation on the microstructural parameters are also examined.

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Accepted:
Published online:
DOI: 10.1016/j.crme.2014.01.010
Keywords: Chiral micropolar elasticity, Orthotropic, Rectangular chiral lattice, Two-dimensional

Yi Chen 1; Xiaoning Liu 1; Gengkai Hu 1

1 Key Laboratory of Dynamics and Control of Flight Vehicle, Ministry of Education, School of Aerospace Engineering, Beijing Institute of Technology, Beijing 100081, China
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Yi Chen; Xiaoning Liu; Gengkai Hu. Micropolar modeling of planar orthotropic rectangular chiral lattices. Comptes Rendus. Mécanique, Volume 342 (2014) no. 5, pp. 273-283. doi : 10.1016/j.crme.2014.01.010. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2014.01.010/

[1] L.J. Gibson; M.F. Ashby Cellular Solids: Structure and Properties, Cambridge University Press, Cambridge, 1997

[2] R. Lakes Foam structures with a negative Poisson's ratio, Science, Volume 235 (1987), pp. 1038-1040

[3] K.E. Evans; A. Alderson Auxetic materials: functional materials and structures from lateral thinking, Adv. Mater., Volume 12 (2000), pp. 617-624

[4] D. Prall; R.S. Lakes Properties of a chiral honeycomb with a Poisson's ratio ≈−1, Int. J. Mech. Sci., Volume 39 (1996), pp. 305-314

[5] A. Alderson; K.L. Alderson; D. Attard; K.E. Evans; R. Gatt; J.N. Grima; W. Miller; N. Ravirala; C.W. Smith; K. Zied Elastic constants of 3-, 4- and 6-connected chiral and anti-chiral honeycombs subject to uniaxial in-plane loading, Compos. Sci. Technol., Volume 70 (2010), pp. 1042-1048

[6] J. Dirrenberger; S. Forest; D. Jeulin; C. Colin Homogenization of periodic auxetic materials, Proc. Eng., Volume 10 (2011), pp. 1847-1852

[7] A. Spadoni; M. Ruzzene; S. Gonella; F. Scarpa Phononic properties of hexagonal chiral lattices, Wave Motion, Volume 46 (2009), pp. 435-450

[8] J.Y. Chen; Y. Huang; M. Ortiz Fracture analysis of cellular materials: a strain gradient model, J. Mech. Phys. Solids, Volume 46 (1998), pp. 789-828

[9] R.S. Kumar; D.L. McDowell Generalized continuum modeling of 2-D periodic cellular solids, Int. J. Solids Struct., Volume 41 (2004), pp. 7399-7422

[10] A. Spadoni; M. Ruzzene Elasto-static micropolar behavior of a chiral auxetic lattice, J. Mech. Phys. Solids, Volume 60 (2012), pp. 156-171

[11] R.S. Lakes; R.L. Benedict Noncentrosymmetry in micropolar elasticity, Int. J. Eng. Sci., Volume 20 (1982), pp. 1161-1167

[12] N. Auffray; R. Bouchet; Y. Bréchet Strain gradient elastic homogenization of bi-dimensional cellular media, Int. J. Solids Struct., Volume 47 (2010), pp. 1698-1710

[13] N. Auffray; H. Le Quang; Q.C. He Matrix representations for 3D strain-gradient elasticity, J. Mech. Phys. Solids, Volume 61 (2013), pp. 1202-1223

[14] E. Cosserat; F. Cosserat Théorie des corps Déformables, Hermann, Paris, 1909

[15] A.C. Eringen Microcontinuum Field Theories I: Foundations and Solids, Springer, New York, 1999

[16] R. Lakes Elastic and viscoelastic behavior of chiral materials, Int. J. Mech. Sci., Volume 43 (2001), pp. 1579-1589

[17] D. Natroshvili; I.G. Stratis Mathematical problems of the theory of elasticity of chiral materials for Lipschitz domains, Math. Methods Appl. Sci., Volume 29 (2006), pp. 445-478

[18] K. Chandraseker; S. Mukherjee Coupling of extension and twist in single-walled carbon nanotubes, J. Appl. Mech., Volume 73 (2006), pp. 315-326

[19] D. Ieşan Chiral effects in uniformly loaded rods, J. Mech. Phys. Solids, Volume 58 (2010), pp. 1272-1285

[20] R. Lakes; H.S. Yoon; J.L. Katz Slow compressional wave propagation in wet human and bovine cortical bone, Science, Volume 220 (1983), pp. 513-515

[21] A. Lakhtakia; V.V. Varadan; V.K. Varadan Elastic wave propagation in non-centrosymmetric isotropic media: dispersion and field equations, J. Appl. Phys., Volume 63 (1988), pp. 5246-5250

[22] X.N. Liu; G.L. Huang; G.K. Hu Chiral effect in plane isotropic micropolar elasticity and its application to chiral lattices, J. Mech. Phys. Solids, Volume 60 (2012), pp. 1907-1921

[23] Y. Chen; X.N. Liu; G.K. Hu; Q.P. Sun; Q.S. Zheng Micropolar continuum modeling of bi-dimensional tetrachiral lattices, Proc. R. Soc. A, Volume 470 (2014), p. 20130734

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