Stochastic Constitutive Model of Isotropic Thin Fiber Networks Based on Stochastic Volume Elements

Abstract

Thin fiber networks are widely represented in nature and can be found in man-made materials such as paper and packaging. The strength of such materials is an intricate subject due to inherited randomness and size-dependencies. Direct fiber-level numerical simulations can provide insights into the role of the constitutive components of such networks, their morphology, and arrangements on the strength of the products made of them. However, direct mechanical simulation of randomly generated large and thin fiber networks is characterized by overwhelming computational costs. Herein, a stochastic constitutive model for predicting the random mechanical response of isotropic thin fiber networks of arbitrary size is presented. The model is based on stochastic volume elements (SVEs) with SVE size-specific deterministic and stochastic constitutive law parameters. The randomness in the network is described by the spatial fields of the uniaxial strain and strength to failure, formulated using multivariate kernel functions and approximate univariate probability density functions. The proposed stochastic continuum approach shows good agreement when compared to direct numerical simulation with respect to mechanical response. Furthermore, strain localization patterns matched the one observed in direct simulations, which suggests an accurate prediction of the failure location. This work demonstrates that the proposed stochastic constitutive model can be used to predict the response of random isotropic fiber networks of arbitrary size.

Modeling and simulation of anisotropic cross-linked cellulose fiber networks with an out-of-plane topography

“…More details on the DEM formulations can be found in [30,44]. The performance of the implemented technique is compared with other forming models [39,47] elsewhere [30]. A detailed explanation of the fiber, and bond properties, fabric specifications, and underlying assumptions in the deposition model are discussed in the next subsections.…”

Humidity influence on mechanics of paper materials: joint numerical and experimental study on fiber and fiber network scale

“…Less information is available on the critical separations of fiber joints in experimental context, due to difficult experimental realizations as mentioned. As for the numerical simulation using cohesive zone models, work by Magnusson (2016) set the cohesive final separations to be 1 lm for both normal and tangential direction, and in Borodulina et al (2018), Mansour et al (2019), they are assumed to be 1.56 lm and 0.35 lm, respectively. Given the variation in the reported values in the literature, a range of parameters were therefore checked to study their influence on the mechanical response of the fiber network.…”

A Review of Recent Trends and Challenges in Computational Modeling of Paper and Paperboard at Different Scales

“…Alternatively, anisotropic 3D material models can be obtained from 1D material models accounting for orientation distribution functions by applying the unit sphere approach suggested in [178], which has already been adapted successfully to model composites with consideration of fiber misalignment [145]. Instead, stochastic continuum models can also be constructed by applying Gaussian fields to the 1D formulation [172]. However, independent of the method utilized, it is crucial to account for the anisotropy of paper on the sheet scale.…”