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

Rami Mansour,Artem Kulachenko,Wei Chen,Mårten Olsson

doi:10.3390/ma12030538

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.

Highlights

IntroductionMaterials are characterized by certain degrees of random variations in their mechanical properties
Materials are characterized by certain degrees of random variations in their mechanical properties.This is true for all materials but especially pronounced in disordered materials such as thin fiber networks [1]
The eight parameters in the stochastic constitutive model, n, c1, c2, s R, `1, `2, ρ12, and12 are dependent on the choice of stochastic volume elements (SVEs) size, see Table 5

Summary

Introduction

Materials are characterized by certain degrees of random variations in their mechanical properties This is true for all materials but especially pronounced in disordered materials such as thin fiber networks [1]. Such variations can be the cause of unexplained occasional failures that cannot be predicted by deterministic material models [2,3,4]. The mechanical behavior of randomly generated networks was investigated using detailed direct micromechanical simulations [5,6,7,8] (see Section 2.1) Such simulations can capture the complicated mechanisms of failure, they cannot yet be employed for product development due to the overwhelming computational costs required to capture the relevant product sizes. Simulation of the uniaxial mechanical response up to strain localization and failure of a 24 mm × 24 mm fiber network takes two days on a modern 28-core, 128 GB RAM supercomputer

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