Skip to main content
Top

2015 | OriginalPaper | Chapter

2. Micromechanical Models for Auxetic Materials

Author : Teik-Cheng Lim

Published in: Auxetic Materials and Structures

Publisher: Springer Singapore

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

This chapter provides a survey of micromechanical models that seek to predict and explain auxetic behavior, based on re-entrant microstructures, nodule-fibril microstructure, 3D tethered-nodule model, rotating squares, rectangles, triangles and tetrahedrals models, hard cyclic hexamers model, missing rib models, chiral and anti-chiral models, interlocking hexagon model, and the “egg rack” model. All the micromechanical models exhibit a common trait—auxeticity is highly dependent on the microstructural geometry. In some of the micromechanical geometries, comparisons between analytical results have been made with experimental or computational results.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literature
go back to reference Abramovitch H, Burgard M, Edery-Azulay L, Evans KE, Hoffmeister M, Miller W, Scarpa F, Smith CW, Tee KF (2010) Smart tetrachiral and hexachiral honeycomb: sensing and impact detection. Compos Sci Technol 70(7):1072–1079CrossRef Abramovitch H, Burgard M, Edery-Azulay L, Evans KE, Hoffmeister M, Miller W, Scarpa F, Smith CW, Tee KF (2010) Smart tetrachiral and hexachiral honeycomb: sensing and impact detection. Compos Sci Technol 70(7):1072–1079CrossRef
go back to reference Alderson KL, Neale PJ (1994) Private communication Alderson KL, Neale PJ (1994) Private communication
go back to reference Alderson A, Evans KE (1995) Microstructural modelling of auxetic microporous polymers. J Mater Sci 30(13):3319–3332CrossRef Alderson A, Evans KE (1995) Microstructural modelling of auxetic microporous polymers. J Mater Sci 30(13):3319–3332CrossRef
go back to reference Alderson A, Evans KE (1997) Modelling concurrent deformation mechanisms in auxetic microporous polymers. J Mater Sci 32(11):2797–2809CrossRef Alderson A, Evans KE (1997) Modelling concurrent deformation mechanisms in auxetic microporous polymers. J Mater Sci 32(11):2797–2809CrossRef
go back to reference Alderson KL, Alderson A, Evans KE (1997) The interpretation of the strain-dependent Poisson’s ratio in auxetic polyethylene. J Strain Anal Eng Des 32(3):201–212CrossRef Alderson KL, Alderson A, Evans KE (1997) The interpretation of the strain-dependent Poisson’s ratio in auxetic polyethylene. J Strain Anal Eng Des 32(3):201–212CrossRef
go back to reference Alderson A, Evans KE (2001) Rotation and dilation deformation mechanisms for auxetic behavior in the α-cristobalite tetrahedral framework structure. Phys Chem Miner 28(10):711–718CrossRef Alderson A, Evans KE (2001) Rotation and dilation deformation mechanisms for auxetic behavior in the α-cristobalite tetrahedral framework structure. Phys Chem Miner 28(10):711–718CrossRef
go back to reference Alderson A, Alderson KL, Chirima G, Ravirala N, Zied KM (2010a) The in-plane linear elastic constants and out-of-plane bending of 3-coordinated ligament and cylinder-ligament honeycombs. Compos Sci Technol 70(7):1034–1041CrossRef Alderson A, Alderson KL, Chirima G, Ravirala N, Zied KM (2010a) The in-plane linear elastic constants and out-of-plane bending of 3-coordinated ligament and cylinder-ligament honeycombs. Compos Sci Technol 70(7):1034–1041CrossRef
go back to reference Alderson A, Alderson KL, Attard D, Evans KE, Gatt R, Grima JN, Miller W, Ravirala N, Smith CW, Zied K (2010b) Elastic constants of 3-, 4- and 6-connected chiral and anti-chiral honeycombs subject to uniaxial in-plane loading. Compos Sci Technol 70(7):1042–1048CrossRef Alderson A, Alderson KL, Attard D, Evans KE, Gatt R, Grima JN, Miller W, Ravirala N, Smith CW, Zied K (2010b) Elastic constants of 3-, 4- and 6-connected chiral and anti-chiral honeycombs subject to uniaxial in-plane loading. Compos Sci Technol 70(7):1042–1048CrossRef
go back to reference Branka AC, Pieranski P, Wojciechowski KW (1982) Rotatory phase in a system of hard cyclic hexamers; an experimental modelling study. J Phys Chem Solids 43(9):817–818CrossRef Branka AC, Pieranski P, Wojciechowski KW (1982) Rotatory phase in a system of hard cyclic hexamers; an experimental modelling study. J Phys Chem Solids 43(9):817–818CrossRef
go back to reference Caddock BD, Evans KE (1989) Microporous materials with negative Poisson’s ratios I: microstructure and mechanical properties. J Phys D Appl Phys 22(12):1877–1882CrossRef Caddock BD, Evans KE (1989) Microporous materials with negative Poisson’s ratios I: microstructure and mechanical properties. J Phys D Appl Phys 22(12):1877–1882CrossRef
go back to reference Chen YJ, Scarpa F, Liu YJ, Leng JS (2013) Elasticity of anti-tetrachiral anisotropic lattices. Int J Solids Struct 50(6):996–1004CrossRef Chen YJ, Scarpa F, Liu YJ, Leng JS (2013) Elasticity of anti-tetrachiral anisotropic lattices. Int J Solids Struct 50(6):996–1004CrossRef
go back to reference Chetcuti E, Ellul B, Manicaro E, Brincat JP, Attard D, Gatt R, Grima JN (2014) Modeling auxetic foams through semi-rigid rotating triangles. Phys Status Solidi B 251(2):297–306CrossRef Chetcuti E, Ellul B, Manicaro E, Brincat JP, Attard D, Gatt R, Grima JN (2014) Modeling auxetic foams through semi-rigid rotating triangles. Phys Status Solidi B 251(2):297–306CrossRef
go back to reference Choi JB, Lakes RS (1992) Non-linear properties of polymer cellular materials with a negative Poisson’s ratio. J Mater Sci 27(19):5375–5381CrossRef Choi JB, Lakes RS (1992) Non-linear properties of polymer cellular materials with a negative Poisson’s ratio. J Mater Sci 27(19):5375–5381CrossRef
go back to reference Choi JB, Lakes RS (1995) Nonlinear analysis of the Poisson’s ratio of negative Poisson’s ratio foams. J Compos Mater 29(1):113–128CrossRef Choi JB, Lakes RS (1995) Nonlinear analysis of the Poisson’s ratio of negative Poisson’s ratio foams. J Compos Mater 29(1):113–128CrossRef
go back to reference Evans KE, Nkansah MA, Hutchinson IJ, Rogers SC (1991) Molecular network design. Nature 353(6340):124CrossRef Evans KE, Nkansah MA, Hutchinson IJ, Rogers SC (1991) Molecular network design. Nature 353(6340):124CrossRef
go back to reference Gaspar N, Ren XJ, Smith CW, Grima JN, Evans KE (2005) Novel honeycombs with auxetic behavior. Acta Mater 53(8):2439–2445CrossRef Gaspar N, Ren XJ, Smith CW, Grima JN, Evans KE (2005) Novel honeycombs with auxetic behavior. Acta Mater 53(8):2439–2445CrossRef
go back to reference Gaspar N, Smith CW, Alderson A, Grima JN, Evans KE (2011) A generalised three-dimensional tethered-nodule model for auxetic materials. J Mater Sci 46(2):372–384CrossRef Gaspar N, Smith CW, Alderson A, Grima JN, Evans KE (2011) A generalised three-dimensional tethered-nodule model for auxetic materials. J Mater Sci 46(2):372–384CrossRef
go back to reference Gibson LJ, Ashby MF (1988) Cellular solids: structure and properties. Pergamon Press, OxfordMATH Gibson LJ, Ashby MF (1988) Cellular solids: structure and properties. Pergamon Press, OxfordMATH
go back to reference Grima JN, Evans KE (2000) Auxetic behavior from rotating squares. J Mater Sci Lett 19(17):1563–1565CrossRef Grima JN, Evans KE (2000) Auxetic behavior from rotating squares. J Mater Sci Lett 19(17):1563–1565CrossRef
go back to reference Grima JN, Alderson A, Evans KE (2004) Negative Poisson’s ratios from rotating rectangles. Comput Methods Sci Technol 10(2):137–145CrossRef Grima JN, Alderson A, Evans KE (2004) Negative Poisson’s ratios from rotating rectangles. Comput Methods Sci Technol 10(2):137–145CrossRef
go back to reference Grima JN, Williams JJ, Evans KE (2005) Networked calix[4]arene polymers with unusual mechanical properties. Chem Commun 32:4065–4067CrossRef Grima JN, Williams JJ, Evans KE (2005) Networked calix[4]arene polymers with unusual mechanical properties. Chem Commun 32:4065–4067CrossRef
go back to reference Grima JN, Evans KE (2006) Auxetic behavior from rotating triangles. J Mater Sci 41(10):3193–3196CrossRef Grima JN, Evans KE (2006) Auxetic behavior from rotating triangles. J Mater Sci 41(10):3193–3196CrossRef
go back to reference Grima JN, Zammit V, Gatt R, Alderson A, Evans KE (2007) Auxetic behavior from rotating semi-rigid units. Phys Status Solidi B 244(3):866–882CrossRef Grima JN, Zammit V, Gatt R, Alderson A, Evans KE (2007) Auxetic behavior from rotating semi-rigid units. Phys Status Solidi B 244(3):866–882CrossRef
go back to reference Grima JN, Farrugia PS, Caruana C, Gatt R, Attard D (2008) Auxetic behavior from stretching connected squares. J Mater Sci 43(17):5962–5971CrossRef Grima JN, Farrugia PS, Caruana C, Gatt R, Attard D (2008) Auxetic behavior from stretching connected squares. J Mater Sci 43(17):5962–5971CrossRef
go back to reference Grima JN, Gatt R, Ellul B, Chetcuti E (2010) Auxetic behavior in non-crystalline materials having star or triangular shaped perforations. J Non-Cryst Solids 356(37–40):1980–1987CrossRef Grima JN, Gatt R, Ellul B, Chetcuti E (2010) Auxetic behavior in non-crystalline materials having star or triangular shaped perforations. J Non-Cryst Solids 356(37–40):1980–1987CrossRef
go back to reference Grima JN, Manicaro E, Attard D (2011) Auxetic behavior from connected different-sized squares and rectangles. Proc R Soc A 467(2126):439–458CrossRefMATHMathSciNet Grima JN, Manicaro E, Attard D (2011) Auxetic behavior from connected different-sized squares and rectangles. Proc R Soc A 467(2126):439–458CrossRefMATHMathSciNet
go back to reference Grima JN, Chetcuti E, Manicaro E, Attard D, Camilleri M, Gatt R, Evans KE (2012) On the auxetic properties of generic rotating rigid triangles. Proc R Soc A 468(2139):810–830CrossRefMathSciNet Grima JN, Chetcuti E, Manicaro E, Attard D, Camilleri M, Gatt R, Evans KE (2012) On the auxetic properties of generic rotating rigid triangles. Proc R Soc A 468(2139):810–830CrossRefMathSciNet
go back to reference Kopyt P, Damian R, Celuch M, Ciobanu R (2010) Dielectric properties of chiral honeycombs—modelling and experiment. Compos Sci Technol 70(7):1080–1088CrossRef Kopyt P, Damian R, Celuch M, Ciobanu R (2010) Dielectric properties of chiral honeycombs—modelling and experiment. Compos Sci Technol 70(7):1080–1088CrossRef
go back to reference Lim TC, Acharya UR (2009) An hexagonal array of fourfold interconnected hexagonal nodules for modeling auxetic microporous polymers: a comparison of 2D and 3D. J Mater Sci 44:4491-4494 Lim TC, Acharya UR (2009) An hexagonal array of fourfold interconnected hexagonal nodules for modeling auxetic microporous polymers: a comparison of 2D and 3D. J Mater Sci 44:4491-4494
go back to reference Lim TC, Alderson A, Alderson KL (2014) Experimental studies on the impact properties of auxetic materials. Phys Status Solidi B 251(2):307–313CrossRef Lim TC, Alderson A, Alderson KL (2014) Experimental studies on the impact properties of auxetic materials. Phys Status Solidi B 251(2):307–313CrossRef
go back to reference Lorato A, Innocenti P, Scarpa F, Alderson A, Alderson KL, Zied KM, Ravirala N, Miller W, Smith CW, Evans KE (2010) The transverse elastic properties of chiral honeycombs. Compos Sci Technol 70(7):1057–1063CrossRef Lorato A, Innocenti P, Scarpa F, Alderson A, Alderson KL, Zied KM, Ravirala N, Miller W, Smith CW, Evans KE (2010) The transverse elastic properties of chiral honeycombs. Compos Sci Technol 70(7):1057–1063CrossRef
go back to reference Michelis P, Spitas V (2010) Numerical and experimental analysis of a triangular auxetic core made of CFR-PEEK using the directionally reinforced integrated single-yarn (DIRIS) architecture. Compos Sci Technol 70(7):1064–1071CrossRef Michelis P, Spitas V (2010) Numerical and experimental analysis of a triangular auxetic core made of CFR-PEEK using the directionally reinforced integrated single-yarn (DIRIS) architecture. Compos Sci Technol 70(7):1064–1071CrossRef
go back to reference Masters IG, Evans KE (1996) Models for the elastic deformation of honeycombs. Compos Struct 35(4):403–422CrossRef Masters IG, Evans KE (1996) Models for the elastic deformation of honeycombs. Compos Struct 35(4):403–422CrossRef
go back to reference Miller W, Smith CW, Scarpa F, Evans KE (2010) Flatwise buckling optimization of hexachiral and tetrachiral honeycombs. Compos Science Technol 70(7):1049–1056CrossRef Miller W, Smith CW, Scarpa F, Evans KE (2010) Flatwise buckling optimization of hexachiral and tetrachiral honeycombs. Compos Science Technol 70(7):1049–1056CrossRef
go back to reference Nakamura S, Lakes RS (1995) Finite element analysis of Saint-Venant end effects in micropolar elastic solids. Eng Comput 12(6):571–587CrossRefMATH Nakamura S, Lakes RS (1995) Finite element analysis of Saint-Venant end effects in micropolar elastic solids. Eng Comput 12(6):571–587CrossRefMATH
go back to reference Neale PJ, Alderson KL, Pickles AP, Evans KE (1993) Negative Poisson’s ratio of microporous polyethylene in compression. J Mater Sci Lett 12(19):1529–1532 Neale PJ, Alderson KL, Pickles AP, Evans KE (1993) Negative Poisson’s ratio of microporous polyethylene in compression. J Mater Sci Lett 12(19):1529–1532
go back to reference Pozniak AA, Smardzewski J, Wojciechowski KW (2013) Computer simulations of auxetic foams in two dimensions. Smart Mater Struct 22(8):084009CrossRef Pozniak AA, Smardzewski J, Wojciechowski KW (2013) Computer simulations of auxetic foams in two dimensions. Smart Mater Struct 22(8):084009CrossRef
go back to reference Pozniak AA, Wojciechowski KW (2014) Poisson’s ratio of rectangular anti 0-chiral structures with size dispersion of circular nodes. Phys Status Solidi B 251(2):367–374CrossRef Pozniak AA, Wojciechowski KW (2014) Poisson’s ratio of rectangular anti 0-chiral structures with size dispersion of circular nodes. Phys Status Solidi B 251(2):367–374CrossRef
go back to reference Prall D, Lakes RS (1997) Properties of a chiral honeycomb with a Poisson’s ratio of -1. Int J Mech Sci 39(3):305–314CrossRefMATH Prall D, Lakes RS (1997) Properties of a chiral honeycomb with a Poisson’s ratio of -1. Int J Mech Sci 39(3):305–314CrossRefMATH
go back to reference Ravirala N, Alderson A, Alderson KL, Davies PJ (2005) Auxetic polypropylene films. Polym Eng Sci 45(4):517–528CrossRef Ravirala N, Alderson A, Alderson KL, Davies PJ (2005) Auxetic polypropylene films. Polym Eng Sci 45(4):517–528CrossRef
go back to reference Ravirala N, Alderson A, Alderson KL (2007) Interlocking hexagon model for auxetic behavior. J Mater Sci 42(17):7433–7445CrossRef Ravirala N, Alderson A, Alderson KL (2007) Interlocking hexagon model for auxetic behavior. J Mater Sci 42(17):7433–7445CrossRef
go back to reference Rothenburg L, Berlin AA, Bathurst RJ (1991) Microstructure of isotropic materials with negative Poisson’s ratio. Nature 354(6353):470–472CrossRef Rothenburg L, Berlin AA, Bathurst RJ (1991) Microstructure of isotropic materials with negative Poisson’s ratio. Nature 354(6353):470–472CrossRef
go back to reference Smith CW, Grima JN, Evans KE (2000) A novel mechanism for generating auxetic behavior in reticulated foams: missing rib foam model. Acta Mater 48(17):4349–4356CrossRef Smith CW, Grima JN, Evans KE (2000) A novel mechanism for generating auxetic behavior in reticulated foams: missing rib foam model. Acta Mater 48(17):4349–4356CrossRef
go back to reference Spadoni A, Ruzzene M (2012) Elasto-static micro polar behavior of a chiral auxetic lattice. J Mech Phys Solids 60(1):156–171CrossRef Spadoni A, Ruzzene M (2012) Elasto-static micro polar behavior of a chiral auxetic lattice. J Mech Phys Solids 60(1):156–171CrossRef
go back to reference Taylor CM, Smith CW, Miller W, Evans KE (2011) The effects of hierarchy on the in-plane elastic properties of honeycombs. Int J Solids Struct 48(9):1330–1339CrossRefMATH Taylor CM, Smith CW, Miller W, Evans KE (2011) The effects of hierarchy on the in-plane elastic properties of honeycombs. Int J Solids Struct 48(9):1330–1339CrossRefMATH
go back to reference Taylor M, Francesconi L, Gerendas M, Shanian A, Carson C, Bertoldi K (2013) Low porosity metallic periodic structures with negative Poisson’s ratio. Adv Mater 26(15):2365–2370CrossRef Taylor M, Francesconi L, Gerendas M, Shanian A, Carson C, Bertoldi K (2013) Low porosity metallic periodic structures with negative Poisson’s ratio. Adv Mater 26(15):2365–2370CrossRef
go back to reference Wojciechowski KW (1987) Constant thermodynamic tension Monte-Carlo studies of elastic properties of a two-dimensional system of hard cyclic hexamers. Mol Phys 61(5):1247–1258CrossRef Wojciechowski KW (1987) Constant thermodynamic tension Monte-Carlo studies of elastic properties of a two-dimensional system of hard cyclic hexamers. Mol Phys 61(5):1247–1258CrossRef
go back to reference Wojciechowski KW (1989) Two-dimensional isotropic system with a negative Poisson ratio. Phys Lett A 137(1,2):60–64CrossRef Wojciechowski KW (1989) Two-dimensional isotropic system with a negative Poisson ratio. Phys Lett A 137(1,2):60–64CrossRef
go back to reference Wojciechowski KW, Branka AC (1989) Negative Poisson ratio in a two-dimensional ‘‘isotropic’’ solid. Phys Rev A 40(12):7222–7225CrossRef Wojciechowski KW, Branka AC (1989) Negative Poisson ratio in a two-dimensional ‘‘isotropic’’ solid. Phys Rev A 40(12):7222–7225CrossRef
go back to reference Wojciechowski KW (2003) Remarks on “Poisson ratio beyond the Limits of the elasticity theory”. J Phys Soc Jpn 72(7):1819–1820CrossRef Wojciechowski KW (2003) Remarks on “Poisson ratio beyond the Limits of the elasticity theory”. J Phys Soc Jpn 72(7):1819–1820CrossRef
go back to reference Yang DU, Huang FY (2001) Analysis of Poisson’s ratio for a micropolar elastic rectangular plate using finite element method. Eng Comput 18(7):1012–1030CrossRefMATH Yang DU, Huang FY (2001) Analysis of Poisson’s ratio for a micropolar elastic rectangular plate using finite element method. Eng Comput 18(7):1012–1030CrossRefMATH
Metadata
Title
Micromechanical Models for Auxetic Materials
Author
Teik-Cheng Lim
Copyright Year
2015
Publisher
Springer Singapore
DOI
https://doi.org/10.1007/978-981-287-275-3_2

Premium Partners