Computational homogenization of micromorphic continua for random fiber networks

3 - Generalised continuum mechanics of random fibrous media

Mechanical response of composite fiber networks subjected to local contractile deformation

Design and thermal conductivity of 3D artificial cross-linked random fiber networks

Negative and positive Poynting effects in tendon under simple shear.

The analysis of fibrous structures using micro-computer tomography (µCT) is becoming more important as it provides an opportunity to characterise the mechanical properties and performance of materials. This study is the first attempt to provide computations of fibre crimp for various random fibrous networks (RFNs) based on µCT data. A parametric algorithm was developed to compute fibre crimp in fibres in a virtual domain. It was successfully tested for six different X-ray µCT models of nonwoven fabrics. Computations showed that nonwoven fabrics with crimped fibres exhibited higher crimp levels than those with non-crimped fibres, as expected. However, with the increased fabric density of the non-crimped nonwovens, fibres tended to be more crimped. Additionally, the projected fibre crimp was computed for all three major 2D planes, and the obtained results were statistically analysed. Initially, the algorithm was tested for a small-size, nonwoven model containing only four fibres. The fraction of nearly straight fibres was computed for both crimped and non-crimped fabrics. The mean value of the fibre crimp demonstrated that fibre segments between intersections were almost straight. However, it was observed that there were no perfectly straight fibres in the analysed RFNs. This study is applicable to approach employing a finite-element analysis (FEA) and computational fluid dynamics (CFD) to model/analyse RFNs.

Microstructural insights into the enigmatic network of random fibers: van Wyk’s notions revisited

The deformation of dense random fiber networks is important in a variety of applications including biological and nonliving systems. In this paper it is shown that semiflexible fiber networks exhibit long-range power-law spatial correlations of the density and elastic properties. Hence, the stress and strain fields measured over finite patches of the network are characterized by similar spatial correlations. The scaling is observed over a range of scales bounded by a lower limit proportional to the segment length and an upper limit on the order of the fiber length. If the fiber bending stiffness is reduced below a threshold, correlations are lost. The issue of solving boundary value problems defined on large domains of random fiber networks is also addressed. Since the direct simulation of such systems is impractical, the network is mapped into an equivalent continuum with long-range correlated elastic moduli. A technique based on the stochastic finite element method is used to solve the resulting stochastic continuum problem. The method provides the moments of the distribution function of the solution (e.g., of the displacement field). It performs a large dimensionality reduction which is based on the scaling properties of the underlying elasticity of the material. Two examples are discussed in closure.

Organic and inorganic fiber reinforced composites with various fiber orientation distributions and fiber geometries are abundantly available in several natural and synthetic structures. Inorganic glass fiber composites have been introduced to numerous applications due to their economical fabrication and tailored structural properties. Numerical characterization of such composite materials is necessitated due to their intrinsic statistical nature, since elaborate experiments are prohibitively costly and time consuming. In this work, representative volume elements of unidirectional random filaments and fibers are numerically developed in PYTHON to enhance accuracy and efficiency of complex geometric representations encountered in random fiber networks. A modified random sequential adsorption algorithm is applied to increase the volume fraction of the representative volume elements, and a spatial segment shortest distance algorithm is introduced to construct a 3D random fiber composite with high fiber aspect ratio (100:1) and high volume fraction (31.8%). For the unidirectional fiber networks, volume fractions as high as 70% are achieved when an assortment of circular fiber diameters are used in the representative volume element.

Random filamentous networks and their response to the applied load can be considered as a model to study the mechanical properties of biological systems such as cytoskeleton of a cell and connective tissues. A mathematical model for the actual and complex deformation of these networks under stress is developed using a micromechanics approach. We recently studied the effect of various micro-structural parameters such as fiber length, mean segment length and fiber flexibility on the network deformation field at various length scales. The network elasticity is mapped into a two dimensional heterogeneous continuum domain in order to show that the elastic fields of dense fiber networks show long range correlations over a range of scales for which we gave the upper and lower bounds. It is concluded that the deformation of random networks is similar to that of highly heterogeneous continuum domains with stochastic distribution of moduli. We employed the stochastic finite element method to solve boundary value problems defined on the random fiber network domain. Here, we present a brief review of this methodology and report new results on scaling properties of the structure of fiber networks using box-counting method.

The shear-lag type model due to Cox (Br. J. Appl. Phys. 3, 72 (1952) is widely used to calculate the deformation properties of fibrous materials such as short fiber composites and random fiber networks. We compare the shear-lag stress transfer mechanism with numerical simulations at small, linearly elastic strains and conclude that the model does not apply to random fiber networks. Most of the axial stress is transferred directly from fiber to fiber rather than through intermediate shear-loaded segments as assumed in the Cox model. The implications for the elastic modulus and strength of random fiber networks are discussed.

Analysis of the basis weight for random fibrous networks is important to understand their microstructure, properties and performance. Two-dimensional microscopical images show in-plane fibers without giving any information on their distribution in three dimensions. This research introduces a fully parametric algorithm for computing the local basis weight of random fibrous networks using three-dimensional images because out-of-plane fiber orientation is important, especially for high-density or thick networks. Voxel models of real nonwoven webs were generated by an X-ray micro-computed tomography system. The developed algorithm could accurately estimate a local basis weight value for random fibrous networks produced with various manufacturing parameters. Numerical results computed with the developed method were compared with those obtained with a physical weight measurement technique. The algorithm was tested and validated for various nonwoven fabrics with different densities. It was observed that the developed method can be used to examine and/or compare the basis weight of a wide range of random fibrous networks. In addition, it can be used to predict the basis weight for fabrics, especially in a new product development process.

The study of fiber networks is essential in understanding the mechanical properties of many polymeric and biological materials. These systems deform non-affinely, i.e. the local deformation is different than the applied far-field. The degree of non-affinity increases with decreasing scale of observation. Here, we show that this relationship is a power law with a scaling exponent independent of the type of applied load. Preferential fiber orientation influences non-affinity in a significant way: this parameter generally increases upon increasing orientation. However, some components of non-affinity, such as that associated with the normal strain in the direction of the preferential fiber orientation, decrease. In random networks, the nature of the far-field has little influence on the level of non-affinity. This is not the case in oriented networks.

A mechanical behaviour of random fibrous networks is predominantly governed by their microstructure. This study examines the effect of microstructure on macroscopic deformation and failure behaviour of random fibrous networks and its practical implication for optimisation of its structure by using finite-element simulations. A subroutine-based parametric modelling approach—a tool to develop and characterise random fibrous networks—is also presented. Here, a thermally bonded polypropylene nonwoven fabric is used as a model system. Its microstructure is incorporated into the model by explicit introduction of fibres according to their orientation distribution in the fabric. The model accounts for main deformation and damage mechanisms experimentally observed and provides the meso- and macro-level responses of the fabric. The suggested microstructure-based approach identifies and quantifies the spread of stresses and strains in fibres of the network as well as its structural evolution during deformation and damage. Its simulations also predict a continuous shift in the distribution of stresses due to structural evolution and progressive failure of fibres.

We numerically investigate the propagation of small-amplitude elastic waves in random fiber networks. Our analysis reveals that the dynamic response of the system is not only controlled by its overall elasticity, but also by the local microstructure. In fact, we find that the longest fiber-segment plays a key role in dynamics when the network is excited with waves of short wavelength. In this case, the Bloch modes are highly non-affine as the longest segments oscillate close to their resonances. Based on this observation, we predict the low frequency dispersion curves of random fiber networks.

The interruption of cellular interactions in biological processes such as migration, differentiation, proliferation, and wound healing could lead to conditions such as fibrosis, muscular dystrophy, brain tumors, and cancer. The role of microstructural and mechanical properties of the surrounding fibrous extracellular matrix has been highlighted in facilitating cellular communications and long-range transmission of displacements and stresses. However, the role of prestress, which is commonly seen in biological materials, is largely overlooked. The primary objective of the present study is to address this existing gap by investigating the influence of prestress on the displacement propagation caused by a local contractile domain inside discrete fibrous media. In this regard, we first generate 2D random fiber networks with an average network connectivity of less than the isostatic threshold. We create a prestressed state in these networks by applying both compressive/tensile uniaxial and biaxial deformation. Then, we numerically characterize prestress effects on the displacement propagation caused by the local contractile deformation. In comparison with displacement transmission in random fiber networks under tensile prestress, the numerical simulations show that the displacement propagation due to a local contraction is more pronounced in networks with compressive prestress. The numerical findings are discussed in terms of prestress effects on microstructural and mechanical properties of random fiber networks.