Mechanical multiscale modelling of fibrous materials with application to electrospun networks

Abstract

Fibrous materials are ubiquitous in nature and technical applications, owing to their many advantages including their lightweight and porous multi-scale structure, their high surface-to-volume ratio and their flexibility in properties, which can be adapted to different environments and requirements. A key question concerns the relation between mechanical properties at the macro- and microscale. Fibrous structures consist of single fibres interacting with each other at their contact points. Their macroscopic mechanical behaviour differs from their solid counterparts as, besides the base material, also the fibre arrangement, shape and interaction properties have a major impact. Here, suitable experiments and modelling approaches are exploited to shed light on the multi-scale mechanical behaviour of fibrous materials. Electrospun networks (ESNs), a class of synthetic nonwovens with cost-efficient large scale production capabilities, serve as reference structure for modelling and experimental studies. A 3D discrete network model was developed in this thesis and utilised to investigate the mechanical behaviour of ESNs on the fibre, network and macroscopic material scale. To this end, first the computational generation of 2D random networks was investigated. The study reveals that common algorithms for modelling the planar distribution of fibres lead to unintended inhomogeneity and anisotropy, especially for long fibres much larger than the modelling domain. To generate truly random planar networks, an improved algorithm is proposed and validated by an analytical approach and Monte Carlo simulations. In a next step, the complete 3D network structure is generated by a finite element based computation of the fibre deposition process inspired by the network formation in electrospinning. The low out-of-plane curvature of fibres in ESNs and other nonwovens motivated reduced modelling approaches assuming a planar fibre distribution and a negligible out-of-plane deformation aiming for better computational efficiency. A 3D approach was used as a tool to assess typical assumptions of planar models, giving access to micro scale properties of the network. Good agreement was observed between 3D and planar models in terms of macroscopic network response for high porosities (>\,90\%), validating the planar approach as an efficient alternative with regard to the in-plane macroscopic response of ESNs. However, independent of the porosity, the local fibre kinematics show a mismatch due to the restrictive assumptions of planarity in a 2D model. The 3D model reveals a significant out-of-plane deformation of single fibres which cannot be considered in planar models. These results suggest in general to use a 3D approach for modelling the multi-scale mechanical behaviour of fibrous materials, even if they display a nearly planar fibre structure but especially if microscopic mechanics of the network play an important role. The 3D discrete modelling approach provides the possibility for bottom-up computations. Characterised only by microstructural fibre information, sample weight and dimension, an assessment of the model's predictive capability was conducted. The single fibres' mechanical properties were extracted from AFM-based three-point bending and micromechanical testing. An inverse finite element routine and an appropriate analytical approach based on a Timoshenko beam and torsional springs was derived, overcoming uncertainties in the treatment of boundary conditions for the extraction of single fibre material parameters. The study shows a clear dependence of single fibre mechanical properties on fibre diameter and a correlation of the Young's modulus with morphological changes of the polymer. Further information on the shape of single fibres was extracted from scanning electron micrographs. The final 3D model, describing ESNs in a statistically representative manner, was used for mechanical simulations and the effective material response was compared with tensile experiments of the respective samples. Direct prediction by the discrete model shows good qualitative agreement with the experiments. The network's yield stress, however, was overestimated. Comparison with computed tomography data of the sample ruled out a significant difference in fibre disposition between model and sample material. Specific adjustments of the material properties and number of connections between fibres were identified as sufficient to obtain a sound agreement with macroscopic experimental data of two distinct samples, demonstrating the predictive capabilities of the model. Furthermore, the discrete network approach was utilised to access single fibre deformations, revealing non-affine kinematics and stretch distributions. A comparison of the DNM to an affine analytic approach showed that the mismatch on the microscale and the good match on the macroscale are no contradiction. Finally, the out-of-plane kinematics of single fibres and their influence on whole network deformation were investigated in detail. An analytic planar model equipped with an out-of-plane buckling component predicted a possible major increase of thickness in uniaxial tension of planar fibrous structures. Dedicated experiments confirmed the auxetic effect with unprecedented Poisson's ratios, and the fibre segments' aspect ratio as the main network property to tune this behaviour. Buckling instability as main driver for the auxetic effect was confirmed by top and side view scanning electron micrographs and by results of the 3D multi-scale modelling approach capable of tracking each fibre segment. Compressed fibre segments buckle out-of-plane and increase the distance between layers of fibres on the network scale leading to an overall thickness increase. In summary, the access to microscale information, predictive bottom-up simulations, and the rationalisation of the auxetic effect in ESNs demonstrate the value of experiments and models developed and used in this dissertation to understand and tailor the multi-scale mechanics of fibrous materials.