Journal of Materials Science

, Volume 52, Issue 5, pp 2534–2548 | Cite as

Creating three-dimensional (3D) fiber networks with out-of-plane auxetic behavior over large deformations

  • Amit Rawal
  • Vijay Kumar
  • Harshvardhan Saraswat
  • Dakshitha Weerasinghe
  • Katharina Wild
  • Dietmar Hietel
  • Martin Dauner
Original Paper


Fiber networks with out-of-plane auxetic behavior have been sporadically investigated. One of the major challenges is to design such materials with giant negative Poisson’s ratio over large deformations. Here in, we report a systematic investigation to create three-dimensional (3D) fiber networks in the form of needlepunched nonwoven materials with out-of-plane auxetic behavior over large deformations via theoretical modeling and extensive set of experiments. The experimental matrix has encapsulated the key parameters of the needlepunching nonwoven process. Under uniaxial tensile loading, the anisotropy coupled with local fiber densification in networks has yielded large negative Poisson’s ratio (up to −5.7) specifically in the preferential direction. The in-plane and out-of-plane Poisson’s ratios of fiber networks have been predicted and, subsequently, compared with the experimental results. Fiber orientation was found to be a core parameter that modulated the in-plane Poisson’s ratio of fiber networks. A parametric analysis has revealed the interplay between the anisotropy of the fiber network and the out-of-plane Poisson’s ratio based upon constant volume consideration.


Fiber Orientation Nonwoven Material Fiber Network Fiber Segment Needle Penetration 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

List of symbols

\( \bar{b} \)

Mean distance between the contacts

\( \bar{b}_{j} \)

Projection of \( \bar{b} \) on j direction

\( \bar{b}_{k} \)

Projection of \( \bar{b} \) on k direction


Mean force experienced by the microelement at contact point in direction j

Cjn, Cjp

Normal and tangential components of C j respectively


Fiber modulus


Area moment of inertia of the fiber

Kj, Kk

Directional parameters representing the projection of \( \bar{b} \) in directions j and k, respectively


Proportion of free fiber length

mjj, mjk

Geometric coefficients associated with two component of deformation caused by T j in directions j and k, respectively


Total external load applied in direction j


Initial volume of the nonwoven material


Volume of the nonwoven material under a defined level of applied strain


Nonwoven volume expansion (contraction) coefficient


Transverse strain of nonwoven along k direction for the applied stress in direction j


Transverse strain of nonwoven along l direction for the applied stress in direction j


Longitudinal strain in nonwoven along j direction for the applied stress in direction j

δ, δaxial, δbend

Overall, axial and bending deformations of the fiber segment, respectively

\( \bar{\delta }_{jj} \), \( \bar{\delta }_{jk} \)

Statistical mean projection of the bending deflection of all microelements due to C jn in directions j and k, respectively

νjk, νjl

In-plane and out-of-plane Poisson’s ratios of nonwoven, respectively

ϕ, θ

In-plane and out-of-plane fiber orientation angles, respectively

Ω(θ, ϕ)

Probability density function


In-plane probability density function



Direction of the applied stress


Nonwoven plane or in-plane orientation of fibers


Plane perpendicular to the nonwoven plane and along the direction of applied stress (j)


Plane mutually perpendicular to the nonwoven plane and along the direction of applied stress (j)



One of the authors (AR) wishes to acknowledge the Alexander von Humboldt Foundation for the research fellowship for experienced researchers at the Fraunhofer Institute for Industrial Mathematics (ITWM), Kaiserslautern, Germany and Institut für Textil- und Verfahrenstechnik, Denkendorf, Germany.


  1. 1.
    Evans KE, Nkansah MA, Hutchinson IJ, Rogers SC (1991) Molecular network design. Nature 353:124–124CrossRefGoogle Scholar
  2. 2.
    Lakes R (1987) Foam structures with a negative Poisson’s ratio. Science 235:1038–1040CrossRefGoogle Scholar
  3. 3.
    Alderson KL, Evans KE (1992) The fabrication of microporous polyethylene having a negative Poisson’s ratio. Polymer 33:4435–4438CrossRefGoogle Scholar
  4. 4.
    Baughman RH, Shacklette JM, Zakhidov AA, Stafström S (1998) Negative Poisson’s ratios as a common feature of cubic metals. Nature 392:362–365CrossRefGoogle Scholar
  5. 5.
    Liu Y, Hu H, Jimmy KC, Liu S (2010) Negative Poisson’s ratio weft-knitted fabrics. Text Res J 80:856–863CrossRefGoogle Scholar
  6. 6.
    Wu H, Wei G (2004) Molecular design of new kinds of auxetic polymers and networks. Chin J Polym Sci 22:355–362Google Scholar
  7. 7.
    Huang C, Chen L (2016) Negative Poisson’s ratio in modern functional materials. Adv Mater 28:8079–8096.CrossRefGoogle Scholar
  8. 8.
    Evans KE, Alderson A (2000) Auxetic materials: functional materials and structures from lateral thinking. Adv Mater 12:617–628CrossRefGoogle Scholar
  9. 9.
    Grima JN, Evans KE (2000) Auxetic behavior from rotating squares. J Mater Sci Lett 19:1563–1565CrossRefGoogle Scholar
  10. 10.
    Gibson LJ, Ashby MF, Schajer GS, Robertson CI (1982) The mechanics of two-dimensional cellular materials. Proc R Soc Lond A 382:25–42CrossRefGoogle Scholar
  11. 11.
    Alderson KL, Alderson A, Evans KE (1997) The interpretation of the strain-dependent Poisson’s ratio in auxetic polyethylene. J Strain Anal Eng Des 32:201–212CrossRefGoogle Scholar
  12. 12.
    Clausen A, Wang F, Jensen JS et al (2015) Topology optimized architectures with programmable Poisson’s ratio over large deformations. Adv Mater 27:5523–5527CrossRefGoogle Scholar
  13. 13.
    Jayanty S, Crowe J, Berhan L (2011) Auxetic fibre networks and their composites. Phys Stat Sol B 248:73–81CrossRefGoogle Scholar
  14. 14.
    Delincé M, Delannay F (2004) Elastic anisotropy of a transversely isotropic random network of interconnected fibres: non-triangulated network model. Acta Mater 52:1013–1022CrossRefGoogle Scholar
  15. 15.
    Neelakantan S, Bosbach W, Woodhouse J, Markaki AE (2014) Characterization and deformation response of orthotropic fibre networks with auxetic out-of-plane behaviour. Acta Mater 66:326–339CrossRefGoogle Scholar
  16. 16.
    Neelakantan S, Tan J-C, Markaki AE (2015) Out-of-plane auxeticity in sintered fibre network mats. Scr Mater 106:30–33CrossRefGoogle Scholar
  17. 17.
    Thirlwell BE, Treloar LRG (1965) Non-woven fabrics. Part VI: dimensional and mechanical anisotropy. Text Res J 35:827–835CrossRefGoogle Scholar
  18. 18.
    Hearle JWS, Purdy AT (1972) On the nature of deformation of needled fabrics. Fibre Sci Technol 5:113–128CrossRefGoogle Scholar
  19. 19.
    Verma P, Shofner ML, Griffin AC (2014) Deconstructing the auxetic behavior of paper. Phys Stat Sol B 251:289–296CrossRefGoogle Scholar
  20. 20.
    Verma P, Shofner ML, Lin A et al (2015) Inducing out-of-plane auxetic behavior in needle-punched nonwovens. Phys Stat Sol B 252:1455–1464CrossRefGoogle Scholar
  21. 21.
    Verma P, Shofner ML, Lin A et al (2016) Induction of auxetic response in needle-punched nonwovens: effects of temperature, pressure, and time. Phys Stat Sol B 253:1270–1278CrossRefGoogle Scholar
  22. 22.
    Åström JA, Mäkinen JP, Hirvonen H, Timonen J (2000) Stiffness of compressed fiber mats. J Appl Phys 88:5056–5061CrossRefGoogle Scholar
  23. 23.
    Rawal A, Lomov S, Ngo T et al (2007) Mechanical behavior of thru-air bonded nonwoven structures. Text Res J 77:417–431CrossRefGoogle Scholar
  24. 24.
    Hearle JWS, Sultan MAI (1967) A study of needled fabrics. Part I: experimental methods and properties. J Text Inst 58:251–265CrossRefGoogle Scholar
  25. 25.
    Watanabe A, Miwa M, Yokoi T, Merati AA (2004) Predicting the penetrating force and number of fibers caught by a needle barb in needle punching. Text Res J 74:417–425CrossRefGoogle Scholar
  26. 26.
    Hearle JWS, Sultan MAI (1968) A study of needled fabrics Part IV: the effects of stretch, shrinkage and reinforcement. J Text Inst 59:161–182CrossRefGoogle Scholar
  27. 27.
    Hearle JWS, Sultan MAI (1968) A study of needled fabrics Part V: the approach to theoretical understanding. J Text Inst 59:183–201CrossRefGoogle Scholar
  28. 28.
    Hearle JWS, Stevenson PJ (1964) Studies in nonwoven fabrics. Part IV: prediction of tensile properties. Text Res J 34:181–191CrossRefGoogle Scholar
  29. 29.
    Komori T, Makishima K (1977) Numbers of fiber-to-fiber contacts in general fiber assemblies. Text Res J 47:13–17Google Scholar
  30. 30.
    Pan N, Chen J, Seo M, Backer S (1997) Micromechanics of a planar hybrid fibrous network. Text Res J 67:907–925CrossRefGoogle Scholar
  31. 31.
    Kumar V, Rawal A (2014) A model for predicting uniaxial compression behavior of fused fibrous networks. Mech Mater 78:66–73CrossRefGoogle Scholar
  32. 32.
    Lee DH, Lee JK (1985) Initial compressional behaviour of fibre assembly. Objective measurements: application to product design and process control. The Textile Machinery Society of Japan, Osaka, pp 613–622Google Scholar
  33. 33.
    Giroud JP (2004) Poisson’s ratio of unreinforced geomembranes and nonwoven geotextiles subjected to large strains. Geotext Geomembr 22:297–305CrossRefGoogle Scholar
  34. 34.
    Hearle JWS, Sultan MAI, Choudhari TN (1968) A study of needled fabrics. Part II: effects of the needling process. J Text Inst 59:103–116CrossRefGoogle Scholar
  35. 35.
    Goswami BC, Suryadevara J, Vigo TL (1984) Determination of Poisson’s ratio in thermally bonded nonwoven fabrics. Text Res J 54:391–396CrossRefGoogle Scholar
  36. 36.
    Rawal A, Priyadarshi A, Kumar N et al (2010) Tensile behaviour of nonwoven structures: comparison with experimental results. J Mater Sci 45:6643–6652CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Amit Rawal
    • 1
    • 2
    • 3
  • Vijay Kumar
    • 4
  • Harshvardhan Saraswat
    • 5
  • Dakshitha Weerasinghe
    • 3
  • Katharina Wild
    • 3
  • Dietmar Hietel
    • 2
  • Martin Dauner
    • 3
  1. 1.Indian Institute of Technology DelhiNew DelhiIndia
  2. 2.Fraunhofer Institute for Industrial Mathematics (ITWM)KaiserslauternGermany
  3. 3.Institut für Textil- und VerfahrenstechnikDenkendorfGermany
  4. 4.University of BoråsBoråsSweden
  5. 5.MLV Textile & Engineering CollegeBhilwaraIndia

Personalised recommendations