Effect of density on in-plane material behavior: The case of laboratory paper and commercial paperboard

Paper and paperboard are highly regarded for their recyclability and sustainability, but their inherent inhomogeneity presents challenges for material characterization and modeling. Despite being pressed during production, they remain compressible in the thickness direction, making density a key factor in determining mechanical properties. This study examines the effect of density and thickness compression on the in-plane mechanical behavior of paper and paperboard through uniaxial tensile tests on both laboratory paper with different refining energies and commercial paperboard with anisotropy. The results confirm that density significantly affects stress-strain response, elasticity, and plastic deformation. To capture this effect systematically, an efficiency factor is introduced that provides a quantitative measure of the density-dependent mechanical behavior to model the influence of density using a linear function. Incorporating efficiency factors refines the material modeling approach and improves predictions of stiffness and plastic stress. Higher refining energies result in a more homogeneous structure, reducing density-related variations, while commercial paperboard is less affected by fiber orientation and surface coatings. The proposed efficiency factor provides a new framework for optimizing and modelling the influence of the pressure and density on material parameters of fiber-based materials.