Computational simulation of fabric armour subjected to ballistic impacts

In computational simulations of ballistic impacts on woven polymeric fabric armour, specialized fabric models are normally used. Attempts have also been made to use commercial finite element packages for such purposes. However, such attempts normally result in either overly simplified models or prohibitively detailed finite element discretization of the fabric to capture the unique properties of woven fabric. This paper presents an FE model of woven fabric that reflects the orthotropic properties of the fabric, the viscoelastic nature of the yarns, the crimping of the yarns, the sliding contact between yarns and yarn breakage using an assembly of viscoelastic bar elements. Excellent agreement between simulation and ballistic test data is obtained in terms of the deformation of the fabric during impact, residual velocity of the projectile and the energy absorbed by the fabric. This is achieved despite the modest number of degrees of freedom employed by the model.     

Nonlinear Multi-Scale Modelling,Simulation and Validation of 3D Knitted Textiles

Three-dimensionally (3D) knitted technical textiles are spreading into industrial applications, since their geometric, structural and functional performance can be tailored and optimized on fibre-, yarn- and fabric levels by customizing yarn materials, knit patterns and geometric shapes. The ability to simulate their complex mechanical behaviour is thus an essential ingredient in the development of a digital workflow for optimal design and manufacture of 3D knitted textiles. Here, we present a multi-scale modelling and simulation framework for the prediction of the nonlinear orthotropic mechanical behaviour of single jersey knitted textiles and its experimental validation. On the meso-scale, representative volume elements (RVEs) of the fabric are modelled as single, interlocked yarn loops and their mechanical deformation behaviour is homogenized using periodic boundary conditions. Yarns are modelled as nonlinear 3D beam elements and numerically discretized using an isogeometric collocation method, where a frictional contact formulation is used to model inter-yarn interactions. On the macro-scale, fabrics are modelled as membrane elements with nonlinear orthotropic material behaviour, which is parameterized by a response surface constitutive model obtained from the meso-scale homogenization. The input parameters of the yarn-level simulation, i.e., mechanical properties of yarns and geometric dimensions of yarn loops in the fabrics, are determined experimentally and subsequent meso- and macro-scale simulation results are evaluated against reference results and mechanical tests of knitted fabric samples. Good agreement between computational predictions and experimental results is achieved for samples with varying stitch values, thus validating our novel computational approach combining efficient meso-scale simulation using 3D beam modelling of yarns with numerical homogenization and nonlinear orthotropic response surface constitutive modelling on the macro-scale.     

Analysis on failure mechanisms of an interlock woven fabric under ballistic impact

In this paper, damage mechanisms of a 3D interlock woven fabric subjected to ballistic impact were analyzed using a numerical model. Two impact configurations were carried out in order to validate the numerical model with experimental observations: perforation (900 m/s) and no-perforation (90 m/s). Global deformation of the fabric during impact is determined continuously to detail fabric impact behavior. Also, in this study, the effects of boundary conditions on failure mechanisms have been investigated. Boundary conditions are divided into two cases: (1) only warp yarns fixed and (2) only weft yarns fixed. Basing on continuous evolutions of global deformation, projectile velocity, different energies and reaction force onto projectile, the influence of both these fixation conditions is investigated.     

A continuum shell finite element model for impact simulation of woven fabrics

A new computational approach is developed to predict the impact behaviour of fabric panels based on the detailed response of the smallest repeating unit (unit cell) in the fabric. The unit cell is constructed and calibrated using measured geometrical (weave architecture, crimp, voids, etc.) and mechanical properties of the fabric. A pre-processor is developed to create a 3D finite element mesh of the unit cell using the measured fabric cross-sectional micro-images. To render an efficient method for simulation of multi-layer packs, these unit cells are replaced with orthotropic shell elements that have similar macroscopic (smeared) mechanical properties as the unit cell. The aim is to capture the essence of the response of a unit cell in a single representative shell element, which would replace the more complicated and numerically costly 3D solid model of the yarns in a crossover. The 3D finite element analysis of the unit cell is used to provide a baseline mechanical response for calibrating the constitutive model in the equivalent shell representation. This shell element takes advantage of a simple physics-based analytical relationship to predict the behaviour of the fabric's warp and weft yarns under general applied displacements in these directions. The analytical model is implemented in the commercial explicit finite element code, LS-DYNA, as a user material routine (UMAT) for shell elements. Layers of fabric constructed from these specialized elements are stacked together to create fabric targets that are then analysed under projectile impact. This approach provides an efficient numerical model for the dynamic analysis of multi-layer fabric structures while taking into account several geometrical and material attributes of the yarns and the fabric.     

纤维织物FEM-SPH耦合单胞模型及超高速碰撞特性

目前,对纤维织物超高速碰撞过程中的变形、断裂、破碎等力学行为已有较广泛的研究,但对碰撞过程中纱线间接触问题的分析尚未见公开文献报道。考虑纱线间的相互作用,建立了纤维织物的FEM-SPH耦合单胞模型,该模型不仅能够进行纤维织物超高速碰撞过程中的穿孔断裂、破碎、碎片云扩展等损伤行为分析,还能够进行纱线间的接触作用过程分析。结果表明,该模型分析结果与试验结果具有较好的一致性。      

隔振橡胶本构建模研究

提出适合描述隔振橡胶在宽频振动时力学行为的本构模型。本构模型包含超弹性和粘弹性两个部分，超弹性部分表征橡胶材料的静态特性；非线性粘弹性部分描述橡胶材料在振动、冲击载荷下的动态响应。基于该本构模型，对橡胶材料在宽应变率范围内进行试验，九个材料参数通过高、低应变率下的试验数据拟合确定。模型预测结果与试验结果是相当吻合的。     

Multi-Scale Modeling the Mechanical Properties of Biaxial Weft Knitted Fabrics for Composite Applications

In this paper a multi-scale numerical model for simulating the mechanical behavior of biaxial weft knitted fabrics produced based on 1×1 rib structure is presented. Fabrics were produced on a modern flat knitting machine using polyester as stitch yarns and nylon as straight yarns. A macro constitutive equation was presented to model the fabric mechanical behavior as a continuum material. User defined material subroutines were provided to implement the constitutive behavior in Abaqus software. The constitutive equation needs remarkable tensile tests on the fabric as the inputs. To solve this drawbacks meso scale modeling of the fabric was used to predict stress–strain curves of the fabric in three different directions (course, wale and 45°). In these simulations only the yarn properties are needed. To evaluate the accuracy of the proposed macro and meso models, fabric tensile behavior in 22.5 and 67.5° directions were simulated by the calibrated macro model and compared with experimental results. Spherical deformation was also simulated by the multi scale model and compared with experimental results. The results showed that the multi-scale modeling can successfully predict the tensile and spherical deformation of the biaxial weft knitted fabric with least required experiments. This model will be useful for composite applications.     

Design optimization of non-linear structures with rate-dependent and rate-independent constitutive models

A design optimization process for non-linear structures with history-dependent materials modelled using the endochronic constitutive theory is described. This constitutive model does not use the concept of a yield surface and describes plastic, viscoplastic and viscoelastic behaviour with one set of equations. Therefore, development of the yield surface is not traced in numerical calculations, simplifying the implementation of response and sensitivity analyses. The total Lagrangian formulation incorporating both geometric and material non-linear effects is used. Shape, non-shape and material design parameters are treated simultaneously using the control volume concept, and static and dynamic problems are treated. A simple structure is optimized for several cases of static and impact loading conditions to demonstrate the procedure. Plastic and viscoplastic material behaviour as well as shape and non-shape design parameters are treated in the example problems.     

Computational micro‐mechanical model of flexible woven fabric for finite element impact simulation

This work presents a computational material model of flexible woven fabric for finite element impact analysis and simulation. The model is implemented in the non‐linear dynamic explicit finite element code LSDYNA. The material model derivation utilizes the micro‐mechanical approach and the homogenization technique usually used in composite material models. The model accounts for reorientation of the yarns and the fabric architecture. The behaviour of the flexible fabric material is achieved by discounting the shear moduli of the material in free state, which allows the simulation of the trellis mechanism before packing the yarns. The material model is implemented into the LSDYNA code as a user defined material subroutine. The developed model and its implementation is validated using an experimental ballistic test on Kevlar woven fabric. The presented validation shows good agreement between the simulation utilizing the present material model and the experiment. Copyright © 2001 John Wiley & Sons, Ltd.     

Three-scale modeling and numerical simulations of fabric materials

Based on the underlying structure of fabric materials, a three-scale model is developed to describe the mechanical behavior of fabric materials. The current model assumes that fabric materials take on an overall behavior of anisotropic membranes, thus the membrane-scale is taken as the macroscopic scale of the model. Since fabric materials exist only as thin structures and there is no corresponding bulk material having a similar constitutive property, the direct approach of the mechanics of surfaces is employed. Following the membrane-scale, a yarn-scale is introduced, in which yarns and their weaving structure are accounted for explicitly. Yarns are modeled as an extensible elasticae. A unit cell consisting of two overlapping yarns is used to formulate the weaving patterns and the interaction between the yarns, which governs the nonlinear constitutive behavior of fabric materials. The third scale, named fibril-scale, accounts for the fibrils constituting a yarn and incorporates their mechanical properties. Via a coupling (handshake) process between these three scales a couple model is introduced. The overall behavior and performance of various fabric products becomes predictable by the knowledge of the material properties of a single fibril and the weaving structure of the fabrics. In addition, potential damage during deformation is also captured in the current model through breakage of fibrils in the fibril-scale.     

Effect of Mesoscale and Multiscale Modeling on the Performance of Kevlar Woven Fabric Subjected to Ballistic Impact: A Numerical Study

In this study, an optimal finite element model of Kevlar woven fabric that is more computational efficient compared with existing models was developed to simulate ballistic impact onto fabric. Kevlar woven fabric was modeled to yarn level architecture by using the hybrid elements analysis (HEA), which uses solid elements in modeling the yarns at the impact region and uses shell elements in modeling the yarns away from the impact region. Three HEA configurations were constructed, in which the solid element region was set as about one, two, and three times that of the projectile’s diameter with impact velocities of 30 m/s (non-perforation case) and 200 m/s (perforation case) to determine the optimal ratio between the solid element region and the shell element region. To further reduce computational time and to maintain the necessary accuracy, three multiscale models were presented also. These multiscale models combine the local region with the yarn level architecture by using the HEA approach and the global region with homogenous level architecture. The effect of the varying ratios of the local and global area on the ballistic performance of fabric was discussed. The deformation and damage mechanisms of fabric were analyzed and compared among numerical models. Simulation results indicate that the multiscale model based on HEA accurately reproduces the baseline results and obviously decreases computational time.     

Engineering Design and Mechanical Property Characterisation of 3D Warp Interlock Woven Fabrics

3D warp interlock fabrics have been used both in composite materials as fibrous reinforcement as well as in protective solutions against impact mainly due to their improved capacity to absorb energy by higher intra-ply resistance to delamination. However, depending on the type of architecture used, the binding warp yarns may provide different types of mechanical behaviour. By the same, the choice of the yarn raw material coupled with the suited 3D warp interlock architecture is still a challenge to solve due to the lack of knowledge on the optimized fabric parameters to be chosen. Thus, to fill this gap, we have designed, produced on same dobby loom and tested different types of 3D warp interlock architectures (O-T 4 3–4 Basket 3–3 and A-T 4 5–4 Twill 6) with different types of raw material (E-glass EC9 900 Tex, para-aramid 336 Tex and flax Tex 500 yarns). Thanks to these tests, it has been highlighted different mechanical behaviours of 3D warp interlock fabrics with the same weave pattern but with different types of yarns (E-glass, flax and para-aramid) both in the warp and weft directions. It has been also revealed that the warp shrinkage of warp yarns inside the woven structure has a major influence on the whole fabric behaviour.     

Ballistic impact behaviour of woven fabric composites: Formulation

Resistance to high velocity impact is an important requirement for high performance structural materials. Even though, polymer matrix composites are characterized by high specific stiffness and high specific strength, they are susceptible to impact loading. For the effective use of such materials in structural applications, their behaviour under high velocity impact should be clearly understood. In the present study, investigations on the ballistic impact behaviour of two-dimensional woven fabric composites have been presented. Ballistic impact is generally a low-mass high velocity impact caused by a propelling source. The analytical method presented is based on wave theory. Different damage and energy absorbing mechanisms during ballistic impact have been identified. These are: cone formation on the back face of the target, tension in primary yarns, deformation of secondary yarns, delamination, matrix cracking, shear plugging and friction during penetration. Analytical formulation has been presented for each energy absorbing mechanism. Energy absorbed during each time interval and the corresponding reduction in velocity of the projectile has been determined. The solution is based on the target material properties at high strain rate and the geometry and the projectile parameters. Using the analytical formulation, ballistic limit, contact duration at ballistic limit, surface radius of the cone formed and the radius of the damaged zone have been predicted for typical woven fabric composites. The analytical predictions have been compared with the experimental results. A good correlation has been observed.     

Dynamic mechanical properties of fabric armour

Twaron^®, a fabric made from aramid fibres and somewhat similar to the commonly known Kevlar^®, is also often used in flexible armour applications and hence subjected to high rates of loading. The dynamic mechanical properties of Twaron^® fabric are examined via high-speed tensile tests on specimens using a split Hopkinson bar. The load-deformation and failure characteristics at different rates of stretching are determined, from which constitutive equations representing its viscoelasticity and strain-rate dependence are formulated. This facilitates modelling of the material response to impact and perforation. Experimental results indicate that Twaron^® is highly strain-rate dependent; the tensile strength and modulus increase with strain rate while the failure strain decreases. Twaron^® specimens are also observed to fail in a more brittle fashion as the strain rate increases; this phenomenon significantly reduces the amount of energy absorbed at high strain rates. An analysis based on the morphology and fracture mechanisms of poly(p-phenylene-terephthalamide) (PPTA) fibres, the main constituent of Twaron^®, is formulated to account for the experimental observations. The proposed constitutive equation, based on a three-element linear viscoelastic model is able to describe reasonably accurately the experimental stress–strain response over a range of strain rates.     

碳纤维织物力学性能和冲压成形实验研究

在实际成形过程中,碳纤维复合材料往往处于复杂的应力状态,开展近于真实载荷环境下的力学试验分析,能够更准确地认识实际应用中材料的成形性能和变形机理.为获得碳纤维织物的基本力学特性,设计了平纹碳纤维织物拉伸试样及成形试样,进行了单轴拉伸、双轴拉伸、镜框剪切试验和方盒冲压成形实验研究,对比了不同双拉比及纱线取向对力学性能及成形性能的影响.研究结果表明:碳纤维织物具有高度的非线性、各向异性和双拉耦合特性,即经纬向纤维的力学性能会相互影响;剪切变形是成形过程中的主要变形模式,当剪切角达到临界锁死角时,织物发生起皱现象;同种织物不同纱线取向试样表现出不同的成形性能,因此可以根据零件几何形状选择合适纤维取向的织物,从而减少缺陷,优化成形零件的力学性能.研究结果为后续建立碳纤维织物本构模型和成形仿真奠定了基础.     

Characterization and constitutive modeling of aramid fibers at high strain rates

The quasi-static and rate-dependent mechanical properties of aramid yarns are presented together with a study on different methods of securing yarn specimens in tensile tests. While capstans were found to be suitable for quasi-static tests, they either were not strong enough or had too high inertia for dynamic tests in a Split Hopkinson Pressure Bar setup. Instead, specially designed clamps were used. A viscoelastic material model to describe the mechanical behavior of the yarns, including failure, is also presented. The material model was employed in the computational simulation of ballistic penetration of woven aramid fabrics. Comparison of the simulations and actual ballistic tests showed that predictions of the energy absorbed by the fabric were in good agreement with the experiments.     

Composite structures under ballistic impact

In the present study, investigations on the ballistic impact behaviour of two-dimensional woven fabric composites has been presented. Ballistic impact behaviour of plain weave E-glass/epoxy and twill weave T300 carbon/epoxy composites has been compared. The analytical method presented is based on our earlier work. Different damage and energy absorbing mechanisms during ballistic impact have been identified. These are: cone formation on the back face of the target, tensile failure of primary yarns, deformation of secondary yarns, delamination, matrix cracking, shear plugging and friction during penetration. Analytical formulation has been presented for each energy absorbing mechanism. Energy absorbed during each time interval and the corresponding reduction in velocity of the projectile has been determined. The solution is based on the target material properties at high strain rate and the geometry and the projectile parameters. Using the analytical formulation, ballistic limit, contact duration at ballistic limit, surface radius of the cone formed and the radius of the damaged zone have been predicted for typical woven fabric composites.     

Nonlinear tensile behaviour of elementary hemp fibres. Part II: Modelling using an anisotropic viscoelastic constitutive law in a material rotating frame

A 3D viscoelastic model is presented, based on the use of finite element method for the study of the nonlinear tensile behaviour of hemp fibres. On the basis of an experimental investigation, Part I of this study (Placet et al., 2014) proposed a scenario based on several physical mechanisms, in order to explain the nonlinear behaviour of such fibres. These mechanisms included viscoelastic strain, cellulose microfibril reorientation, and shear strain-induced crystallisation of the amorphous paracrystalline components. The second part of this ongoing study proposes to implement such mechanisms and the associated constitutive laws in a simplified 3D model, in order to evaluate the contribution of each mechanism to the macroscopic tensile behaviour of the fibre.The results show that the proposed anisotropic viscoelastic constitutive law, describing finite transformations through a material rotating frame formulation, is able to accurately simulate the shape of the experimentally observed tensile curves. This model is also used to investigate the influence of dislocation areas on the tensile behaviour and stress fields.     

Prediction on viscoelastic properties of three-dimensionally braided composites by multi-scale model

Three-dimensional viscoelastic properties of four-step three-dimensionally (3D) braided composites are studied in this paper. Based on the three-cell division scheme, a multi-scale model for 3D braided composites is proposed. A periodic boundary condition is applied to characterize the periodic structure of 3D braided composites and yarns. Given the viscoelastic parameters of resin matrix and the elastic constants of fibers, the viscoelastic properties of yarns are obtained by the finite element method and Prony Series fitting. The three-dimensional viscoelastic constitutive relationship of interior cells is derived based upon the viscoelastic properties of yarns and resin matrix. Moreover, the viscoelasticity of 3D braided composites is studied by creep experiment. The viscoelastic deformation obtained from the multi-scale method agrees well with the experimental results. The influence of the two independent micro-structural parameters, braiding angles, and fiber volume fractions, on the viscoelastic properties of 3D braided composites is investigated in detail.     

On the Poisson''s ratios of a woven fabric

Although it is undeniable that the Poisson's effect on the behavior of a woven fabric is crucial, there have been relatively few papers devoted to this subject. In this study, a 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. The prediction of Poisson's ratios in this paper will enable more rigorous studies on such important issues of fabric bending and draping behaviors.