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Random formation, inelastic response and scale effects in paper.

Martin Ostoja-Starzewski¹, Jaime Castro

¹Department of Mechanical Engineering, McGill University, 817 Sherbrooke St. West, Montréal, Québec H3A 2K6, Canada.

Philosophical Transactions. Series A, Mathematical, Physical, and Engineering Sciences

|June 14, 2003

Summary

Paper

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Area of Science:

Materials Science
Solid Mechanics
Continuum Mechanics

Background:

Paper's mechanical properties are influenced by its spatially inhomogeneous structure, known as formation.
Understanding the relationship between paper structure and its constitutive law is crucial for material characterization.

Purpose of the Study:

To investigate the relationship between paper's random structure (formation) and its constitutive law under biaxial tensile loading.
To develop and validate a methodology for assessing paper's mechanical behavior based on its formation and material properties.

Main Methods:

Modeling paper as an elastic-plastic hardening material using a hyperbolic tangent law.
Utilizing basis-weight distribution to analyze paper formation and its correlation with strain/stress fields via finite-element simulation.
Employing a Boolean model and a computational-mechanics fibre-network model to study formation effects on strain fields and homogenization.

Main Results:

Higher basis-weight correlates with increased local stiffness and strength in paper on millimetre scales.
Formation significantly influences non-uniform strain fields, even in the elastic regime.
The representative volume element for paper homogenization is achieved at scales approximately 10 times larger than the floc size.

Conclusions:

The study establishes a direct link between paper's microstructural formation and its macroscopic mechanical properties.
The proposed methodology provides a framework for predicting paper's mechanical response based on its structural characteristics.
Scale-dependent homogenization is a key factor in understanding paper's bulk mechanical behavior.

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