  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.
