3 - Generalised continuum mechanics of random fibrous media

Abstract

In this chapter, we focus our interest on the dynamic analysis of random fibre networks in the frame of generalised continua. The stochastic fibre networks in general and particularly random ones have many applications in the mechanical vibration area because of their submission to different dynamical loading conditions. We begin by developing and identifying two different equivalent continuum models for the random fibre networks at the mesoscopic level of windows of analysis in order to avoid the difficulty and complexity of the microscopic computations of the discrete structure; we next analysed the size effects of such random networks on their dynamic properties. Thanks to the finite element simulation performed over the window of analysis under mixed boundary conditions, the static mechanical properties that are the basis of the dynamic analysis are computed so that the classical and non-classical effective moduli are identified. Acoustic characteristics are captured by the dispersion and phase velocity diagrams. The effects of fibre bending length, the size of the window of analysis and fibre network density on the dynamic characteristics are analysed. The influence of these mechanical and geometrical parameters is evaluated for couple-stress and strain-gradient continuum models. By comparing the acoustic properties of the two provided effective media, we conclude that the couple-stress model behaves like a non-dispersive medium for the longitudinal mode and dispersive for the shear mode, whereas the strain-gradient model behaves in a dispersive manner for both modes.