A Shell Formulation to Model the Three-Dimensional Deformation Response of Woven Fabrics

We capture the out-of-plane mechanical response of woven fabrics through a nonlinear anisotropic shell implementation of a continuum constitutive model. For the membrane response, we rely on a previously developed model for the in-plane behavior of woven fabrics. This planar model captured both the macroscopic response and the interactions of the yarns at the structural level, but was limited to two dimensions. The two-dimensional model is here extended to capture three-dimensional modes of deformations through a shell formulation. We assume that the effects of out-of-plane bending and shear on the established in-plane behavior are negligible; however, we do consider the effects that in-plane deformation and the resulting evolution of the fabric structure have on the out-of-plane response. For example, the formulation accounts for the evolving anisotropy of the out-of-plane bending behavior, which reflects the changing orientations of the yarn families within the fabric surface. This three-dimensional model permits the analysis of complex modes of fabric deformation such as wrinkling at large shear strains or transverse identation. We present experiments and detailed finite element analyses used to understand and characterize the out-of-plane responses of the fabric, including bending and twist, and we discuss the underlying physical phenomena that control these responses. Finally, we compare model predictions of complex loading modes to experimental findings.

A Non-Continuum Model of Aligned, Long Fiber Composite Textile Preform Tensile Response

Stretch-broken fiber preforms provide composites with post-formable characteristics that may reduce the costs of manufacturing complex shapes. Research into fiber preform production methods provides a fiber length and dispersion predictor that is then used to predict forming inputs required to excite tensile elongation of the preform under the influence of various boundary conditions common to sheet-based forming. Fiber behavior is discussed separately from the influence of liquid-phase matrix material. A comparison is made between model results and tensile response measurements of performs for polyarylate-matrix composites.

Mathematical Clothing Modeling in a Digital Human Environment

A new motivation for mathematical clothing modeling, namely to quantify the impact of clothing on digital human models in virtual environments, is discussed. After a brief review of previous mathematical clothing modeling works, a nonlinear finite element approach with contact is exercised with good results on a variety of draping problems. A micromechanical approach for predicting fabric effective mechanical properties based on fiber properties and texture is proposed.

Tensile Load Deformation Behaviour of Woven Fabrics

This paper is concerned with the mechanics of woven fabrics under tensile loading. The yarns are treated as elastica. The yarns bent into shape for both warp and weft are assumed to be elastic, homogenous, and weightless. During deformation the yarns are subjected to bending, extension and transverse compression. The initial geometry of the yarns in the fabric, under no external loading, is first obtained using a force-equilibrium method based on Love’s ordinary approximate theory, a generalisation of the Bernoulli-Euler theory of elastic rods. A non-linear boundary-value problem with a system of five differential equations has been formulated and solved. Application of load will further change the shape of the bent yarns due to bending and stretching. For a yarn with given initial geometry, as obtained by the force-equilibrium method, the solution of the deformed configuration is obtained from the solution of two nonlinear differential equations using appropriate boundary conditions. The formulation of the latter problem is based on the energy method. The sum of the energy terms due to bending, stretching together with the potential energy due to the applied load provides an expression for the total energy of the system. The variation of the total energy in terms of the variations of two parameters is then obtained, using the techniques from calculus of variations. One parameter described the deviation of the bent yarn from a straight line while the other is the length as measured along the yarn axis. This leads to a set of differential equations that fully describe the deformed yarns. The models, initially developed for plain weave, are being currently extended to non-plain weaves and 3D woven fabrics.

Mechanical Behaviors of Woven Fabrics

This paper introducing some recent research progress consists of two parts: the shear deformation analysis and Poisson’s ratios for woven fabrics. The analytical methods of the shear moduli and Poisson’s ratios for woven fabrics will enable more rigorous studies on such important issues of fabric bending and draping behaviors. A new mechanical model is proposed in this paper to evaluate the shearing properties for woven fabrics during the initial slip region. Compared to the existing mechanical models for fabric shear, this model involves not only bending but also torsion of curved yarns. Analytical results show that this model provides better agreement with the experiments for both the initial shear modulus and the slipping angle than the existing models. Furthermore, another mechanical model for a woven fabric made of extensible yarns is developed to calculate the fabric Poisson’s ratios. Theoretical results are compared with the available experimental data. A thorough examination on the influences of various mechanical properties of yarns and structural parameters of fabrics on the Poisson’s ratios of a woven fabric is given.

Finite Element Analysis of Transverse Impact on a Woven Textile

High-strength textiles are widely used in soft impact threat shield systems. During the past several decades, a lot of experiments and theoretical work were conducted to understand the transverse impact behavior of textile structures. As a continuation of those efforts, this paper presents finite element modeling of transverse impact of a rigid right circular cylinder into a square patch of plain-woven textile. Two boundary conditions are applied on the woven textile: four edges clamped; two opposite edges clamped and the other two edges left free. Results show that during the initial stage of the impact, there exists an abrupt momentum/energy transfer from the projectile to the local textile in the impact region. The modeling results also show that the textile boundary condition plays an important role in the impact. It significantly affects the textile transient deformation, stress distribution, energy absorption, and failure modes. The textile absorbs energy more quickly when all its four edges are clamped.

A Model for the Onset of Tearing at Slits in Stressed Coated Woven Fabrics

Coated woven fabrics are often used as stressed membranes in inflatable and tension structures. When the stressed fabrics in such structures are damaged locally, the damage site often provides a starting point for the propagation of a tear. In this paper, a micromechanical model is developed for predicting the onset of tearing at slit-like damage sites in biaxially stressed coated woven fabrics. The stress concentration in the first intact yarn adjacent to the slit is determined as a function of increasing remote stress, and predictions for tearing onset are made assuming that tearing initiates through the rupture of the first intact yarn when the maximum tension in the yarn reaches the yarn ultimate breaking load. A crucial aspect of the model is the treatment of inelastic deformation involving yielding and/or separation of the coating and relative slip between interlaced yarns near the slit tip. Inelastic deformation near the slit tip leads to significant reduction in the stress concentration compared with the elastic deformation case and, therefore, acts to inhibit the onset of tearing. A single dimensionless parameter is shown to govern the stress concentration at tearing versus slit length behavior of particular fabrics. The parameter may be interpreted as a measure of the slit damage tolerance of coated fabrics and shows how particular microstructural properties of the fabric (coating yield stress, coating shear stiffness, yarn axial stiffness, etc.) affect tearing onset. A series of experiments on various coated nylon and polyester fabrics are conducted using slit-damaged cruciform specimens in a simple biaxial test frame. Initial slit lengths in these tests ranged from five to 61 consecutive yarn breaks. The model is shown to capture the onset of tearing in these fabrics over a range of slit lengths quite well.

Effects of Coupled Biaxial Tension and Shear Stresses on Decrimping Behavior in Pressurized Woven Fabric

Tension structures continue to be of increasing importance to military applications requiring both minimum weight, small packing volumes and enhanced deployment operations. However, in the case of inflated fabric structures, present design methods are not well established. Analytical tools required to efficiently design these structures lag behind those for conventional structures and materials. This is partly due to nonlinearities resulting from changes in fabric architecture upon loading. In particular, constitutive relationships need to be developed to establish the pressure-dependence and coupling effects of biaxial tension and shear loads. Through analysis and experiment, the present research addresses the changes in fabric architecture and, more specifically, the combined effects of biaxial tension, shear and crimp interchange on the global behavior of woven fabrics. Engineering test standards need to be prepared that capture the fabric’s mechanical behavior under a variety of coupled loading environments. A novel fixture is introduced for use in experimental testing of fabrics subjected to combined biaxial tension and shear loads.

Filtration Model of Aerosol Particles by Fibrous Filters

Aerosol filtration by fibrous filters is one of the most common methods of separating and removing particles in micro and sub-micro size ranges. The statistical genesis of this process can be regarded as the interactions and the resulting equilibrium among particle and fiber cells that comprise the system. Therefore a statistical mechanics approach, the Ising’s model, combined with Monte Carlo simulation, is employed in studying the process of the aerosol filtration through fibrous filters. The process is modeled as consisting of numerous cell state exchanges driven by the difference of system energy after and before a particle moves from one cell to the other and/or deposits on a fiber cell. With the use of a simpler binary algorithm, this approach is capable of realistically simulating the complicated mechanisms involved in the filtration process. For verification, simulations are carried out for the behaviors of aerosol particles of different sizes through isotropic fiber filters with various volume fractions. Simulation results are in good agreements with reported experimental data.