4 - Stochastic constitutive model of thin fibre networks

Abstract

Thin fibre networks are characterised by a certain degree of randomness in their mechanical response. This randomness can be seen as one of the main reasons for unexplained occasional failures that cannot be predicted by deterministic materials models. Direct fibre-level mechanical simulations can provide insights into the role of the constitutive components of such networks as well as capture the mechanisms of failure. However, these direct simulations are limited to small fibre networks due to overwhelming computational costs and cannot be employed for product development. Therefore, a stochastic multiscale approach for predicting the random mechanical response for thin fibre networks of arbitrary size is necessary. In such a model, the randomness in the network is mathematically described by spatial fields of material properties characterised using stochastic volume elements. In this book chapter, the steps involved in three-dimensional (3D)-fibre network characterisation, random generation, and finite-element simulation are described. This is followed by a description of the stochastic continuum modelling approach with a quantitative comparison to direct numerical simulation with respect to mechanical response and strain localisation pattern. The mathematical preliminaries and advanced topics related to stochastic continuum modelling using spatial field representations are presented in detail.