Skip to main content

Advertisement

SpringerLink
Log in

Analysis of creep and modulus loss of the wood cell wall

  • Original Paper
  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

This paper proposes a nonlinear constitutive model for the wood cell wall based on the nonequilibrium thermodynamics. The wood cell wall is modeled as a long fiber-reinforced composite with cellulose microfibril enclosed by hemicellulose and lignin. An internal variable is introduced into the Helmholtz free energy of the cell wall system, to describe the modulus loss of hemicellulose due to moisture absorption. The viscoelastic behavior of the wood cell wall changes with its moisture content, which leads to different creep evolutions even under the same loading level. To account for this phenomenon, another internal variable is introduced to depict the creep behavior of the wood cell wall, which is correlated with the irreversible energy dissipation processes such as stick–slip mechanism in the wood cell wall. Based on five elastic coefficients of transverse isotropy predicted by the present model, the creep behaviors of the wood cell wall with different microfibril angles are theoretically analyzed and show good agreements with experiment results.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Burgert I., Keckes J., Fratzl P.: Mechanics of the wood cell wall. Charact. Cellul. Cell Wall 30, 7 (2006)

    Google Scholar 

  2. Holmberg S., Persson K., Petersson H.: Nonlinear mechanical behaviour and analysis of wood and fibre materials. Comput. Struct. 72, 459–480 (1999)

    Article  MATH  Google Scholar 

  3. Hofstetter K., Hellmich C., Eberhardsteiner J.: Development and experimental validation of a continuum micromechanics model for the elasticity of wood. Eur. J. Mech. A Solids 24, 1030–1053 (2005)

    Article  MATH  Google Scholar 

  4. Hofstetter K., Hellmich C., Eberhardsteiner J.: Micromechanical modeling of solid-type and plate-type deformation patterns within softwood materials. A review and an improved approach. Holzforschung 61, 343–351 (2007)

    Article  Google Scholar 

  5. Qing H., Mishnaevsky L. Jr: 3D hierarchical computational model of wood as a cellular material with fibril reinforced, heterogeneous multiple layers. Mech. Mater. 41, 1034–1049 (2009)

    Article  Google Scholar 

  6. Qing H., Mishnaevsky L.: Moisture-related mechanical properties of softwood: 3D micromechanical modeling. Comput. Mater. Sci. 46, 310–320 (2009)

    Article  Google Scholar 

  7. Smith I.: Fracture and Fatigue in Wood. Wiley, New York (2003)

    Google Scholar 

  8. Tashiro K., Kobayashi M.: Theoretical evaluation of three-dimensional elastic constants of native and regenerated celluloses: role of hydrogen bonds. Polymer 32, 1516–1526 (1991)

    Article  Google Scholar 

  9. Kojima Y., Yamamoto H.: Effect of moisture content on the longitudinal tensile creep behavior of wood. J. Wood Sci. 51, 462–467 (2005)

    Article  Google Scholar 

  10. Salmén L.: Micromechanical understanding of the cell-wall structure. C. R. Biol. 327, 873–880 (2004)

    Article  Google Scholar 

  11. Cousins W.: Elastic modulus of lignin as related to moisture content. Wood Sci. Technol. 10, 9–17 (1976)

    Article  Google Scholar 

  12. Cousins W., Armstrong R., Robinson W.: Young’s modulus of lignin from a continuous indentation test. J. Mater. Sci. 10, 1655–1658 (1975)

    Article  Google Scholar 

  13. Flores E.S., de Souza Neto E., Pearce C.: A large strain computational multi-scale model for the dissipative behaviour of wood cell-wall. Comput. Mater. Sci. 50, 1202–1211 (2011)

    Article  Google Scholar 

  14. Kojima Y., Yamamoto H.: Effect of microfibril angle on the longitudinal tensile creep behavior of wood. J. Wood Sci. 50, 301–306 (2004)

    Article  Google Scholar 

  15. Keckes J., Burgert I., Frühmann K., Müller M., Kölln K., Hamilton M. et al.: Cell-wall recovery after irreversible deformation of wood. Nat. Mater. 2, 810–813 (2003)

    Article  Google Scholar 

  16. Perré P., Keey R.: Drying of wood: principles and practices. Handb. Ind. Dry. 822, 872 (2006)

    Google Scholar 

  17. Chow C., Xing X., Li R.: Moisture absorption studies of sisal fibre reinforced polypropylene composites. Compos. Sci. Technol. 67, 306–313 (2007)

    Article  Google Scholar 

  18. Hu R.-H., Sun M., Lim J.-K.: Moisture absorption, tensile strength and microstructure evolution of short jute fiber/polylactide composite in hygrothermal environment. Mater. Des. 31, 3167–3173 (2010)

    Article  Google Scholar 

  19. Lei Y., Wu Q., Yao F., Xu Y.: Preparation and properties of recycled HDPE/natural fiber composites. Compos. Part. A 38, 1664–1674 (2007)

    Article  Google Scholar 

  20. Peng X., Guo G., Zhao N.: An anisotropic hyperelastic constitutive model with shear interaction for cord–rubber composites. Compos. Sci. Technol. 78, 69–74 (2013)

    Article  Google Scholar 

  21. Guo Z., Peng X., Moran B.: Large deformation response of a hyperelastic fibre reinforced composite: theoretical model and numerical validation. Compos. Part. A 38, 1842–1851 (2007)

    Article  Google Scholar 

  22. Peng X., Guo Z., Moran B.: An anisotropic hyperelastic constitutive model with fiber-matrix shear interaction for the human annulus fibrosus. J. Appl. Mech. 73, 815–824 (2006)

    Article  MATH  Google Scholar 

  23. Guo Z., Peng X., Moran B.: A composites-based hyperelastic constitutive model for soft tissue with application to the human annulus fibrosus. J. Mech. Phys. Solids 54, 1952–1971 (2006)

    Article  MATH  Google Scholar 

  24. Pan Y., Zhong Z.: A nonlinear constitutive model of unidirectional natural fiber reinforced composites considering moisture absorption. J. Mech. Phys. Solids 69, 132–142 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  25. Pan, Y., Zhong, Z.: Modeling of the mechanical degradation induced by moisture absorption in short natural fiber reinforced composites. Compos. Sci. Technol. 103, 22–27 (2014)

  26. Pan, Y., Zhong, Z.: The effect of hybridization on moisture absorption and mechanical degradation of natural fiber composites: an analytical approach. Compos. Sci. Technol. 110, 132–137 (2015)

  27. Pan, Y., Zhong, Z.: A micromechanical model for the mechanical degradation of natural fiber reinforced composites induced by moisture absorption. Mech. Mater. 85, 7–15 (2015)

  28. Wang W., Sain M., Cooper P.: Study of moisture absorption in natural fiber plastic composites. Compos. Sci. Technol. 66, 379–386 (2006)

    Article  Google Scholar 

  29. Hong W., Zhao X., Zhou J., Suo Z.: A theory of coupled diffusion and large deformation in polymeric gels. J. Mech. Phys. Solids 56, 1779–1793 (2008)

    Article  MATH  Google Scholar 

  30. Spencer, A.J.M.: Constitutive theory for strongly anisotropic solids. Contin. Theory Mech. Fibre Reinf. Compos. 282, 1–32 (1984)

  31. Moon P., Spencer D.E.: Field Theory Handbook. Springer, New York (1971)

    Book  Google Scholar 

  32. Qiu G.Y., Pence T.J.: Remarks on the behavior of simple directionally reinforced incompressible nonlinearly elastic solids. J. Elast. 49, 1–30 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  33. Merodio J., Ogden R.W.: Mechanical response of fiber-reinforced incompressible non-linearly elastic solids. Int. J. Nonlinear Mech. 40, 213–227 (2005)

    Article  MATH  Google Scholar 

  34. Dhakal H., Zhang Z., Richardson M.: Effect of water absorption on the mechanical properties of hemp fibre reinforced unsaturated polyester composites. Compos. Sci. Technol. 67, 1674–1683 (2007)

    Article  Google Scholar 

  35. Pandey J.K., Ahn S.H., Lee C.S., Mohanty A.K., Misra M.: Recent advances in the application of natural fiber based composites. Macromol. Mater. Eng. 295, 975–989 (2010)

    Article  Google Scholar 

  36. Laiarinandrasana L., Piques R., Robisson A.: Visco-hyperelastic model with internal state variable coupled with discontinuous damage concept under total Lagrangian formulation. Int. J. Plast. 19, 977–1000 (2003)

    Article  MATH  Google Scholar 

  37. Holzapfel G.A.: Nonlinear Solid Mechanics: A Continuum Approach for Engineering. Wiley, New York (2000)

    MATH  Google Scholar 

  38. Karra S., Rajagopal K.R.: A model for the thermo-oxidative degradation of polyimides. Mech. Time-Depend. Mater. 16, 329–342 (2011)

    Article  Google Scholar 

  39. Guo Z.Y., Peng X.Q., Moran B.: Mechanical response of Neo–Hookean fiber reinforced incompressible nonlinearly elastic solids. Int. J. Solids Struct. 44, 1949–1969 (2007)

    Article  MATH  Google Scholar 

  40. Reddy J.N.: Mechanics of Laminated Composite Plates and Shells: Theory and Analysis. CRC Press, Boca Raton (2004)

    MATH  Google Scholar 

  41. Rajagopal K.R., Srinivasa A.R., Wineman A.S.: On the shear and bending of a degrading polymer beam. Int. J. Plast. 23, 1618–1636 (2007)

    Article  MATH  Google Scholar 

  42. Soares J.S., Rajagopal K.R., Moore J.E.: Deformation-induced hydrolysis of a degradable polymeric cylindrical annulus. Biomech. Model. Mechanobiol. 9, 177–186 (2009)

    Article  Google Scholar 

  43. Xu Y., Wu Q., Lei Y., Yao F.: Creep behavior of bagasse fiber reinforced polymer composites. Bioresour. Technol. 101, 3280–3286 (2010)

    Article  Google Scholar 

  44. Lee S.-Y., Yang H.-S., Kim H.-J., Jeong C.-S., Lim B.-S., Lee J.-N.: Creep behavior and manufacturing parameters of wood flour filled polypropylene composites. Compos. Struct. 65, 459–469 (2004)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, 200092, People’s Republic of China

    Yihui Pan & Zheng Zhong

Authors
  1. Yihui Pan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zheng Zhong
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zheng Zhong.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Pan, Y., Zhong, Z. Analysis of creep and modulus loss of the wood cell wall. Acta Mech 227, 3191–3203 (2016). https://doi.org/10.1007/s00707-015-1532-y

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-015-1532-y

Keywords

Search

Navigation