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

doi:10.1016/j.euromechsol.2018.10.005

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

Institute of Bioproducts and Paper Technology (6610)

Research output: Contribution to journal › Article › peer-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.

Original language	English
Pages (from-to)	516-531
Number of pages	16
Journal	European Journal of Mechanics, A/Solids
Volume	75
DOIs	https://doi.org/10.1016/j.euromechsol.2018.10.005
Publication status	Published - 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

Access to Document

10.1016/j.euromechsol.2018.10.005

Cite this

Godinho, P. M. J. S., Jajcinovic, M., Wagner, L., Vass, V., Fischer, W. J., Bader, T. K., Hirn, U., Bauer, W., Eberhardsteiner, J., & Hellmich, C. (2019). A continuum micromechanics approach to the elasticity and strength of planar fiber networks: Theory and application to paper sheets. European Journal of Mechanics, A/Solids, 75, 516-531. https://doi.org/10.1016/j.euromechsol.2018.10.005

Godinho, PMJS, Jajcinovic, M, Wagner, L, Vass, V, Fischer, WJ, Bader, TK, Hirn, U , Bauer, W, Eberhardsteiner, J & Hellmich, C 2019, 'A continuum micromechanics approach to the elasticity and strength of planar fiber networks: Theory and application to paper sheets', European Journal of Mechanics, A/Solids, vol. 75, pp. 516-531. https://doi.org/10.1016/j.euromechsol.2018.10.005

@article{60b645bd11984f14b30de256fbbbf2d3,

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

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.",

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",

author = "Godinho, {Pedro Miguel J.S.} and Marina Jajcinovic and Leopold Wagner and Viktoria Vass and Fischer, {Wolfgang J.} and Bader, {Thomas K.} and Ulrich Hirn and Wolfgang Bauer and Josef Eberhardsteiner and Christian Hellmich",

year = "2019",

month = may,

day = "1",

doi = "10.1016/j.euromechsol.2018.10.005",

language = "English",

volume = "75",

pages = "516--531",

journal = "European Journal of Mechanics, A/Solids",

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T1 - A continuum micromechanics approach to the elasticity and strength of planar fiber networks

T2 - Theory and application to paper sheets

AU - Godinho, Pedro Miguel J.S.

AU - Jajcinovic, Marina

AU - Wagner, Leopold

AU - Vass, Viktoria

AU - Fischer, Wolfgang J.

AU - Bader, Thomas K.

AU - Hirn, Ulrich

AU - Bauer, Wolfgang

AU - Eberhardsteiner, Josef

AU - Hellmich, Christian

PY - 2019/5/1

Y1 - 2019/5/1

N2 - 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.

AB - 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.

KW - Continuum micromechanics

KW - Linear elasticity

KW - Planar fiber networks

KW - Strength

KW - Two-dimensional representation

KW - Wood pulp fiber experiments

KW - Wood pulp fiber-to-wood pulp fiber bond experiments

KW - Wood pulp-based paper sheet experiments

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U2 - 10.1016/j.euromechsol.2018.10.005

DO - 10.1016/j.euromechsol.2018.10.005

M3 - Article

AN - SCOPUS:85061483302

SN - 0997-7538

VL - 75

SP - 516

EP - 531

JO - European Journal of Mechanics, A/Solids

JF - European Journal of Mechanics, A/Solids

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

Fields of Expertise

Access to Document

Other files and links

Fingerprint

CD-Laboratory for Fiber Swelling and Paper Performance

DokIn Holz - Projekt P1 - PhD School DokInHolz-Project P1: Experimental Evaluation and numerical modelling of strenght properties of single fibers and fiber-fiber bonds in paper

Cite this

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

Abstract

Keywords

ASJC Scopus subject areas

Fields of Expertise

Access to Document

Other files and links

Fingerprint

Projects

CD-Laboratory for Fiber Swelling and Paper Performance

DokIn Holz - Projekt P1 - PhD School DokInHolz-Project P1: Experimental Evaluation and numerical modelling of strenght properties of single fibers and fiber-fiber bonds in paper

Cite this