Prediction of the Effective Mechanical Properties of Regular and Random Fibrous Materials Based on the Mechanics of Generalized Continua

Abstract

The micromechanics of regular fibrous materials is first investigated to evaluate the large strains effective elastic response of repetitive fibrous microstructures at the level of a repetitive unit cell. This is representative for instance of 3D interlocks subjected to complex macroscopic loadings leading to internal stresses; unit cell based analyses are convenient to derive an effective constitutive law at the intermediate scale which can be used to perform macroscopic scale computations at a reasonable computational cost. A dedicated discrete homogenization approach has been developed to derive the effective mechanical response of the unit cell successively in a small and large transformations framework. The proposed micromechanical approach is particularly appealing, due to the difficulty to measure the effective properties for textiles considering their discreteness. The computed full set of effective ansotropic properties of fibrous media structures in the small strains regime reflect the influence of the geometrical and mechanical micro-parameters of the fibrous architecture on the overall response of the chosen equivalent continuum. Internal scale and microstructural effects are captured by a micropolar effective continuum model, capturing the pronounced rotations of fibers responsible for the large shape capacity of fibrous materials. The setting up of such computational homogenization methods allows to identify hyperelastic models for fibrous media. The same methodology for the identification of the overall properties has been extended to the more complex random fibrous media. The deformation of random fibrous networks is extremely non-affine (the motion of the fibers do in general not follow the imposed strain over the boundary of the WOA), especially for such structures that store energy predominantly in the bending deformation mode of fibers. The degree of non-affinity increases rapidly with decreasing bending stiffness of the filaments, the importance of which being quantified by the internal bending length, the ratio of the fiber bending modulus to its axial stiffness. We especially analyze the mechanical response of such RFN in both affine and non affine deformation regimes, depending on the network density and window size. The ability of such generalized continua to reach a response that become independent of the size of the window of analysis is one objective of the performed analyses.