A finite element simulation approach to the mechanical behaviour of 3D angle-interlock fabrics at the scale of their internal components, using an implicit scheme, is presented in this paper. Based on the determination of the static equilibrium of assemblies of fibres, this approach is used first to find the unknown initial configuration of a unit cell of angle-interlock fabric, by implementing an original method to gradually separate initially inter-penetrating yarns. This method, only based on the weaving pattern, does not require any geometrical pre-processor. Various loading cases can then be simulated to characterize the non-linear behaviour of such fabrics. Applications to the determination of the initial configuration of the unit cell of a typical example of a 5-layer angle-interlock fabric, and to the simulation of a transverse compression test and a forming test are presented.

Abstract. In this paper we develop a multiple scattering model for elastic waves in random anisotropic media. It relies on a kinetic approach of wave propagation phenomena pertaining to the situation whereby the wavelength is comparable to the correlation length of the weak random inhomogeneitiesthe so-called weak coupling limit. The waves are described in terms of their associated energy densities in the phase space position × wave vector. They satisfy radiative transfer equations in this scaling, characterized by collision operators depending on the correlation structure of the heterogeneities. The derivation is based on a multi-scale asymptotic analysis using spatio-temporal Wigner transforms and their interpretation in terms of semiclassical operators, along the same lines as Bal [Wave Motion 43, 132-157 (2005)]. The model accounts for all possible polarizations of waves in anisotropic elastic media and their interactions, as well as for the degeneracy directions of propagation when two phase speeds possibly coincide. Thus it embodies isotropic elasticity which was considered in several previous publications. Some particular anisotropic cases of engineering interest are derived in detail.