A continuum micromechanics approach to the elasticity and strength of planar fiber networks: Theory and application to paper sheets

Pedro Miguel J.S. Godinho, Marina Jajcinovic, Leopold Wagner, Viktoria Vass, Wolfgang J. Fischer, Thomas K. Bader, Ulrich Hirn, Wolfgang Bauer, Josef Eberhardsteiner, Christian Hellmich*

*Corresponding author for this work

Research output: Contribution to journalArticle

Abstract

2D materials such as planar fibrous networks exhibit several mechanical peculiarities, which we here decipher through a 3D-to-2D transition in the framework of continuum micromechanics or random mean-field homogenization theory. Network-to-fiber concentration (or “downscaling”) tensors are derived from Eshelby–Laws matrix-inclusion problems, specified for infinitely long, infinitely flat fibers, and for infinitely flat spheroidal pores of vanishing stiffness. Overall material failure is associated with microscopic shear failure orthogonal to the fiber direction. Corresponding structure–property relations between porosity on the one hand, and in-plane stiffness as well as strength on the other hand, appear as linear. This is in good agreement with mechanical experiments carried out on pulp fibers, on pulp fiber-to-pulp fiber bonds, and on corresponding paper sheets.

Original languageEnglish
Pages (from-to)516-531
Number of pages16
JournalEuropean Journal of Mechanics, A/Solids
Volume75
DOIs
Publication statusPublished - 1 May 2019

Keywords

  • Continuum micromechanics
  • Linear elasticity
  • Planar fiber networks
  • Strength
  • Two-dimensional representation
  • Wood pulp fiber experiments
  • Wood pulp fiber-to-wood pulp fiber bond experiments
  • Wood pulp-based paper sheet experiments

ASJC Scopus subject areas

  • Materials Science(all)
  • Mechanics of Materials
  • Mechanical Engineering
  • Physics and Astronomy(all)

Fields of Expertise

  • Advanced Materials Science

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