메뉴 건너뛰기




Volumn 470, Issue 2165, 2014, Pages

Micropolar continuum modelling of bi-dimensional tetrachiral lattices

Author keywords

Bi dimensional; Chiral micropolar elasticity; Orthotropic; Tetrachiral lattice

Indexed keywords

CONTINUUM MECHANICS; HOMOGENIZATION METHOD; TENSORS;

EID: 84896978279     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2013.0734     Document Type: Article
Times cited : (88)

References (35)
  • 1
    • 0001083402 scopus 로고
    • A structural model of a micropolar continuum
    • doi:10.1016/0020-7225(68)90060-8
    • Askar A, Cakmak AS. 1968 A structural model of a micropolar continuum. Int. J. Eng. Sci. 6, 583-589. (doi:10.1016/0020-7225(68)90060-8)
    • (1968) Int. J. Eng. Sci. , vol.6 , pp. 583-589
    • Askar, A.1    Cakmak, A.S.2
  • 2
    • 0000500465 scopus 로고
    • Analogy between micropolar continuum and grid frameworks under initial stress
    • doi:10.1016/0020-7683(72)90093-5
    • Bazant ZP, Christensen M. 1972 Analogy between micropolar continuum and grid frameworks under initial stress. Int. J. Solids Struct. 8, 327-346. (doi:10.1016/0020-7683(72)90093-5)
    • (1972) Int. J. Solids Struct. , vol.8 , pp. 327-346
    • Bazant, Z.P.1    Christensen, M.2
  • 3
    • 0032064510 scopus 로고    scopus 로고
    • Fracture analysis of cellular materials: A strain gradient model
    • doi:10.1016/S0022-5096(98)00006-4
    • Chen JY, Huang Y, Ortiz M. 1998 Fracture analysis of cellular materials: a strain gradient model. J. Mech. Phys. Solids 46, 789-828. (doi:10.1016/S0022- 5096(98)00006-4)
    • (1998) J. Mech. Phys. Solids , vol.46 , pp. 789-828
    • Chen, J.Y.1    Huang, Y.2    Ortiz, M.3
  • 4
    • 33746428437 scopus 로고    scopus 로고
    • Micropolar theory for two-dimensional stresses in elastic honeycomb
    • doi101098/rspa1999.0394
    • Wang XL, Stronge WJ. 1999 Micropolar theory for two-dimensional stresses in elastic honeycomb. Proc. R. Soc. Lond. A 455, 2091-2116. (doi:10.1098/rspa. 1999.0394)
    • (1999) Proc. R. Soc. Lond. A , vol.455 , pp. 2091-2116
    • Wang, X.L.1    Stronge, W.J.2
  • 5
    • 0142176759 scopus 로고    scopus 로고
    • Three-fold symmetry restrictions on two-dimensional micropolar materials
    • doi:10.1016/S0997-7538(02)01236-6
    • Warren WE, Byskov E. 2002 Three-fold symmetry restrictions on two-dimensional micropolar materials. Eur. J. Mech. A/Solids 21, 779-792. (doi:10.1016/S0997-7538(02)01236-6)
    • (2002) Eur. J. Mech. A/Solids , vol.21 , pp. 779-792
    • Warren, W.E.1    Byskov, E.2
  • 6
    • 0142185988 scopus 로고    scopus 로고
    • Stress and couple stress in foams
    • doi101016/jcommatsci2003.08.025
    • Diebels S, Steeb H. 2003 Stress and couple stress in foams. Comput. Mater. Sci. 28, 714-722. (doi:10.1016/j.commatsci.2003.08.025)
    • (2003) Comput. Mater. Sci. , vol.28 , pp. 714-722
    • Diebels, S.1    Steeb, H.2
  • 7
    • 4644285304 scopus 로고    scopus 로고
    • Generalized continuum modeling of 2-d periodic cellular solids
    • doi101016/jijsolstr2004.06038
    • Kumar RS, McDowell DL. 2004 Generalized continuum modeling of 2-D periodic cellular solids. Int. J. Solids Struct. 41, 7399-7422. (doi:10.1016/j.ijsolstr.2004.06.038)
    • (2004) Int. J. Solids Struct. , vol.41 , pp. 7399-7422
    • Kumar, R.S.1    McDowell, D.L.2
  • 8
    • 27644439547 scopus 로고    scopus 로고
    • Size effects in the mechanical behavior of cellularmaterials
    • doi:10.1007/s10853-005-5042-5
    • Tekoglu C, Onck PR. 2005 Size effects in the mechanical behavior of cellularmaterials. J. Mater. Sci. 40, 5911-5917. (doi:10.1007/s10853-005-5042-5)
    • (2005) J. Mater. Sci. , vol.40 , pp. 5911-5917
    • Tekoglu, C.1    Onck, P.R.2
  • 9
    • 57249111755 scopus 로고    scopus 로고
    • Micromechanical modeling of honeycomb structures based on a modified couple stress theory
    • doi:10.1080/ 15376490802470499
    • Park SK, Gao XL. 2008 Micromechanical modeling of honeycomb structures based on a modified couple stress theory. Mech. Adv. Mater. Struct. 15, 574-593. (doi:10.1080/ 15376490802470499)
    • (2008) Mech. Adv. Mater. Struct. , vol.15 , pp. 574-593
    • Park, S.K.1    Gao, X.L.2
  • 10
    • 77950208107 scopus 로고    scopus 로고
    • Size-dependent elastic properties of micro-and nano-honeycombs
    • doi:10.1016/j.jmps.2010.02.009
    • Zhu HX. 2010 Size-dependent elastic properties of micro-and nano-honeycombs. J. Mech. Phys. Solids 58, 696-709. (doi:10.1016/j.jmps.2010.02. 009)
    • (2010) J. Mech. Phys. Solids , vol.58 , pp. 696-709
    • Zhu, H.X.1
  • 11
    • 0031103039 scopus 로고    scopus 로고
    • Properties of a chiral honeycomb with a poisson's ratio of 1
    • doi:10.1016/S0020-7403(96)00025-2
    • Prall D, Lakes RS. 1996 Properties of a chiral honeycomb with a Poisson's ratio of 1. Int. J. Mech. Sci. 39, 305-314. (doi:10.1016/S0020-7403(96)00025-2)
    • (1996) Int. J. Mech. Sci. , vol.39 , pp. 305-314
    • Prall, D.1    Lakes, R.S.2
  • 12
    • 79959602755 scopus 로고    scopus 로고
    • An elastic metamaterial with simultaneously negative mass density and bulk modulus
    • doi:10.1063/1.3597651
    • Liu XN, Hu GK, Huang GL, Sun CT. 2011 An elastic metamaterial with simultaneously negative mass density and bulk modulus. Appl. Phys. Lett. 98, 251907. (doi:10.1063/1.3597651)
    • (2011) Appl. Phys. Lett. , vol.98 , pp. 251907
    • Liu, X.N.1    Hu, G.K.2    Huang, G.L.3    Sun, C.T.4
  • 13
    • 77952880436 scopus 로고    scopus 로고
    • Elastic constants of 3-, 4-and 6-connected chiral and anti-chiral honeycombs subject to uniaxial in-plane loading
    • doi101016/jcompscitech.2009.07.009
    • Alderson A et al. 2010 Elastic constants of 3-, 4-and 6-connected chiral and anti-chiral honeycombs subject to uniaxial in-plane loading. Compos. Sci. Technol. 70, 1042-1048. (doi:10.1016/j.compscitech.2009.07.009)
    • (2010) Compos. Sci. Technol. , vol.70 , pp. 1042-1048
    • Alderson, A.1
  • 14
    • 80052931225 scopus 로고    scopus 로고
    • Homogenization of periodic auxeticmaterials
    • doi:10.1016/j.proeng.2011.04.307
    • Dirrenberger J, Forest S, Jeulin D, Colin C. 2011 Homogenization of periodic auxeticmaterials. Procedia Eng. 10, 1847-1852. (doi:10.1016/j.proeng. 2011.04.307)
    • (2011) Procedia Eng. , vol.10 , pp. 1847-1852
    • Dirrenberger, J.1    Forest, S.2    Jeulin, D.3    Colin, C.4
  • 15
    • 70350001815 scopus 로고    scopus 로고
    • Phononic properties of hexagonal chiral lattices
    • doi:10.1016/j.wavemoti.2009.04002
    • Spadoni A, Ruzzene M, Gonella S, Scarpa F. 2009 Phononic properties of hexagonal chiral lattices. Wave Motion 46, 435-450. (doi:10.1016/j.wavemoti. 2009.04.002)
    • (2009) Wave Motion , vol.46 , pp. 435-450
    • Spadoni, A.1    Ruzzene, M.2    Gonella, S.3    Scarpa, F.4
  • 16
    • 80755143407 scopus 로고    scopus 로고
    • Elasto-static micropolar behavior of a chiral auxetic lattice
    • doi:10.1016/j.jmps.2011.09.012
    • Spadoni A, Ruzzene M. 2012 Elasto-static micropolar behavior of a chiral auxetic lattice. J. Mech. Phys. Solids 60, 156-171. (doi:10.1016/j.jmps.2011.09. 012)
    • (2012) J. Mech. Phys. Solids , vol.60 , pp. 156-171
    • Spadoni, A.1    Ruzzene, M.2
  • 17
    • 0020244906 scopus 로고
    • Noncentrosymmetry in micropolar elasticity
    • doi:10.1016/0020-7225(82)90096-9
    • Lakes RS, Benedict RL. 1982 Noncentrosymmetry in micropolar elasticity. Int. J. Eng. Sci. 20, 1161-1167. (doi:10.1016/0020-7225(82)90096-9)
    • (1982) Int. J. Eng. Sci. , vol.20 , pp. 1161-1167
    • Lakes, R.S.1    Benedict, R.L.2
  • 18
    • 84865266021 scopus 로고    scopus 로고
    • Chiral effect in plane isotropic micropolar elasticity and its application to chiral lattices
    • doi:10.1016/j.jmps. 2012.06.008
    • Liu XN, Huang GL, Hu GK. 2012 Chiral effect in plane isotropic micropolar elasticity and its application to chiral lattices. J. Mech. Phys. Solids. 60, 1907-1921. (doi:10.1016/j.jmps. 2012.06.008)
    • (2012) J. Mech. Phys. Solids. , vol.60 , pp. 1907-1921
    • Liu, X.N.1    Huang, G.L.2    Hu, G.K.3
  • 20
    • 0000089781 scopus 로고
    • Linear theory of micropolar elasticity
    • Eringen AC. 1966 Linear theory of micropolar elasticity. J. Math. Mech. 15, 909-923.
    • (1966) J. Math. Mech. , vol.15 , pp. 909-923
    • Eringen, A.C.1
  • 21
    • 33645676548 scopus 로고    scopus 로고
    • Coupling of extension and twist in single-walled carbon nanotubes
    • doi:10.1115/1.2125987
    • Chandraseker K, Mukherjee S. 2006 Coupling of extension and twist in single-walled carbon nanotubes. J. Appl. Mech. 73, 315-326. (doi:10.1115/1. 2125987)
    • (2006) J. Appl. Mech. , vol.73 , pp. 315-326
    • Chandraseker, K.1    Mukherjee, S.2
  • 22
    • 78049315301 scopus 로고    scopus 로고
    • Chiral effects in uniformly loaded rods
    • doi:10.1016/j.jmps.2010.06.004
    • Iȩsan D. 2010 Chiral effects in uniformly loaded rods. J. Mech. Phys. Solids. 58, 1272-1285. (doi:10.1016/j.jmps.2010.06.004)
    • (2010) J. Mech. Phys. Solids. , vol.58 , pp. 1272-1285
    • Iȩsan, D.1
  • 23
    • 0005064324 scopus 로고
    • Elastic wave propagation in non-centrosymmetric, isotropic media: Dispersion and field equations
    • doi:10.1063/1.340387
    • Lakhtakia A, Varadan VV, Varadan VK. 1988 Elastic wave propagation in non-centrosymmetric, isotropic media: dispersion and field equations. J. Appl. Phys. 63, 5246-5250. (doi:10.1063/1.340387)
    • (1988) J. Appl. Phys. , vol.63 , pp. 5246-5250
    • Lakhtakia, A.1    Varadan, V.V.2    Varadan, V.K.3
  • 24
    • 55149101089 scopus 로고    scopus 로고
    • Longitudinal wave response of a chiral slab interposed between micropolar solid half-spaces
    • doi101016/ jijsolstr2008.08.018
    • Khurana A, Tomar SK. 2009 Longitudinal wave response of a chiral slab interposed between micropolar solid half-spaces. Int. J. Solids Struct. 46, 135-150. (doi:10.1016/ j.ijsolstr.2008.08.018)
    • (2009) Int. J. Solids Struct. , vol.46 , pp. 135-150
    • Khurana, A.1    Tomar, S.K.2
  • 25
    • 0030141773 scopus 로고    scopus 로고
    • Symmetry classes for elasticity tensors
    • doi:10.1007/BF00042505
    • Forte S, Vianello M. 1996 Symmetry classes for elasticity tensors. J. Elasticity 43, 81-108. (doi:10.1007/BF00042505)
    • (1996) J. Elasticity , vol.43 , pp. 81-108
    • Forte, S.1    Vianello, M.2
  • 26
    • 0001357580 scopus 로고
    • On first strain-gradient theories in linear elasticity
    • doi:10.1016/0020-7683(68)90036-X
    • Mindlin RD, Eshel NN. 1968 On first strain-gradient theories in linear elasticity. Int. J. Solids Struct. 4, 109-124. (doi:10.1016/0020-7683(68)90036- X)
    • (1968) Int. J. Solids Struct. , vol.4 , pp. 109-124
    • Mindlin, R.D.1    Eshel, N.N.2
  • 27
    • 78651407515 scopus 로고    scopus 로고
    • Chirality in isotropic linear gradient elasticity
    • doi:10.1016/j.ijsolstr.2010.11.007
    • Papanicolopulos SA. 2011 Chirality in isotropic linear gradient elasticity. Int. J. Solids Struct. 48, 745-752. (doi:10.1016/j.ijsolstr.2010.11. 007)
    • (2011) Int. J. Solids Struct. , vol.48 , pp. 745-752
    • Papanicolopulos, S.A.1
  • 28
    • 55649110666 scopus 로고    scopus 로고
    • Derivation of anisotropic matrix for bidimensional strain-gradient elasticity behavior
    • doi101016/j ijsolstr2008.09.009
    • Auffray N, Bouchet R, Brechet Y. 2009 Derivation of anisotropic matrix for bidimensional strain-gradient elasticity behavior. Int. J. Solids Struct. 46, 440-454. (doi:10.1016/j. ijsolstr.2008.09.009)
    • (2009) Int. J. Solids Struct. , vol.46 , pp. 440-454
    • Auffray, N.1    Bouchet, R.2    Brechet, Y.3
  • 29
    • 84875250204 scopus 로고    scopus 로고
    • Matrix representations for 3d strain-gradient elasticity
    • doi:10.1016/j.jmps.2013.01.003
    • Auffray N, Le Quang H, He QC. 2013 Matrix representations for 3D strain-gradient elasticity. J. Mech. Phys. Solids 61, 1202-1223. (doi:10.1016/j.jmps.2013.01.003)
    • (2013) J. Mech. Phys. Solids , vol.61 , pp. 1202-1223
    • Auffray, N.1    Le Quang, H.2    He, Q.C.3
  • 30
    • 84995007716 scopus 로고
    • A geometrical picture of anisotropic elastic tensors
    • doi:10.1029/RG008i003p00633
    • Backus G. 1970 A geometrical picture of anisotropic elastic tensors. Rev. Geophys. 8, 633-671. (doi:10.1029/RG008i003p00633)
    • (1970) Rev. Geophys. , vol.8 , pp. 633-671
    • Backus, G.1
  • 31
    • 0000764178 scopus 로고
    • The description of the physical properties of condensed matter using irreducible tensors
    • doi:10.1080/ 00018737800101454
    • Jerphagnon J, Chemla D, Bonneville R. 1978 The description of the physical properties of condensed matter using irreducible tensors. Adv. Phys. 27, 609-650. (doi:10.1080/ 00018737800101454)
    • (1978) Adv. Phys. , vol.27 , pp. 609-650
    • Jerphagnon, J.1    Chemla, D.2    Bonneville, R.3
  • 32
    • 34249918305 scopus 로고
    • On the completeness of the crystallographic symmetries in the description of the symmetries of the elastic tensor
    • doi:10.1007/ BF00040927
    • Huo YZ, Del Piero G. 1991 On the completeness of the crystallographic symmetries in the description of the symmetries of the elastic tensor. J. Elasticity 25, 203-246. (doi:10.1007/ BF00040927)
    • (1991) J. Elasticity , vol.25 , pp. 203-246
    • Huo, Y.Z.1    Del Piero, G.2
  • 33
    • 0002493697 scopus 로고
    • The description, classification, and reality of material and physical symmetries
    • doi:10.1007/BF01178519
    • Zheng QS, Boehler JP. 1994 The description, classification, and reality of material and physical symmetries. Acta Mech. 102, 73-89. (doi:10.1007/ BF01178519)
    • (1994) Acta Mech. , vol.102 , pp. 73-89
    • Zheng, Q.S.1    Boehler, J.P.2
  • 34
    • 0039847212 scopus 로고
    • A note on the decomposition of tensors into traceless symmetric tensors
    • doi:10.1016/0020-7225(70)90024-8
    • Spencer AJM. 1970 A note on the decomposition of tensors into traceless symmetric tensors. Int. J. Eng. Sci. 8, 475-481. (doi:10.1016/0020-7225(70) 90024-8)
    • (1970) Int. J. Eng. Sci. , vol.8 , pp. 475-481
    • Spencer, A.J.M.1
  • 35
    • 0035365676 scopus 로고    scopus 로고
    • Orthogonal irreducible decompositions of tensors of high orders
    • doi:10.1177/108128650100600303
    • Zou WN, Zheng QS, Du DX, Rychlewski J. 2001 Orthogonal irreducible decompositions of tensors of high orders. Math. Mech. Solids 6, 249-267. (doi:10.1177/108128650100600303)
    • (2001) Math. Mech. Solids , vol.6 , pp. 249-267
    • Zou, W.N.1    Zheng, Q.S.2    Du, D.X.3    Rychlewski, J.4


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.