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

Research output: Contribution to journalArticleResearchpeer-review

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.

LanguageEnglish
Pages516-531
Number of pages16
JournalEuropean Journal of Mechanics, A/Solids
Volume75
DOIs
StatusPublished - 1 May 2019

Fingerprint

micromechanics
Micromechanics
Circuit theory
Elasticity
elastic properties
continuums
fibers
Fibers
Pulp
stiffness
Stiffness
porosity
homogenizing
Tensors
Porosity
inclusions
tensors
shear
matrices
Experiments

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

Cite this

A continuum micromechanics approach to the elasticity and strength of planar fiber networks : Theory and application to paper sheets. / Godinho, Pedro Miguel J.S.; Jajcinovic, Marina; Wagner, Leopold; Vass, Viktoria; Fischer, Wolfgang J.; Bader, Thomas K.; Hirn, Ulrich; Bauer, Wolfgang; Eberhardsteiner, Josef; Hellmich, Christian.

In: European Journal of Mechanics, A/Solids, Vol. 75, 01.05.2019, p. 516-531.

Research output: Contribution to journalArticleResearchpeer-review

Godinho, Pedro Miguel J.S. ; Jajcinovic, Marina ; Wagner, Leopold ; Vass, Viktoria ; Fischer, Wolfgang J. ; Bader, Thomas K. ; Hirn, Ulrich ; Bauer, Wolfgang ; Eberhardsteiner, Josef ; Hellmich, Christian. / A continuum micromechanics approach to the elasticity and strength of planar fiber networks : Theory and application to paper sheets. In: European Journal of Mechanics, A/Solids. 2019 ; Vol. 75. pp. 516-531.
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