NONLINEAR MICRO－MECHANICAL MODEL FOR PLAIN WOVEN FABRIC

The warp yarns and weft yarns of plain woven fabric which, being the principal axes of material of fabric, are orthogonal in the original configuration, but are obliquely crossed in the deformed configuration in general. The orthotropic constitutive model is unsuitable for fabric. In the oblique principal axes system the relations between loaded stress vectors and stress tensor are investigated, the stress fields of micro-weaving structures of fabric due to pure shear are carefully studied and, finally, a nonlinear micro-mechanical model for plain woven fabric is proposed. This model can accurately describe the nonlinear mechanical behavior of fabric observed in experiments. Under the assumption of small deformation and linearity of mechanical properties of fabric the model will degenerate into the existing linear model.     

INCREMENTAL MICRO-MECHANICAL MODEL OF PLAIN WOVEN FABRIC

I. INTRODUCTION Previous research on woven fabric ignored the micro-weaving structures in fabric and modeled thewoven fabric as a ?exible orthotropic plate[1??3]. However, such a model is unable to predict certainbuckling phenomena of fabric commonly ob…     

倾斜内锁型三维机织陶瓷基复合材料的细观力学模型

利用平均化方法提出了倾斜内锁型三维机织陶瓷基复合材料弹性性能分析的三维细观力学模型,对材料的弹性性能进行了预测。这个力学模型考虑了倾斜内锁型三维机织陶瓷基复合材料经向纤维束的弯曲和纬向纤维束的平直,纤维束的横截面形状尺寸和相邻纤维束之间的孔洞以及材料制造过程中碳纤维性能下降对弹性性能的影响。基于层合板理论,提出两种单胞应变状态假设分别对材料的九个弹性常数进行了推导计算,结果表明两种方法理论的预测值非常接近。计算结果与实验值比较吻合,表明所提出的细观力学模型是合理的,可以为纺织陶瓷基复合材料的优化设计提供有价值的参考。     

An analytical model to predict residual thermal stress in 2D orthogonal plain weave fabric composites

This paper seeks to address a practical rectangular truss model to predict residual thermal stress in a 2 D plain weave fabric (PWF) composite. The two orthogonal yarns in a micromechanical unit cell are idealized as straight rods subjected to tensile or compression loading resulting in extension or shortening deformation. The residual thermal stresses and equivalent thermal expansion coefficients in a PWF layer are derived from the thermal constitutive equations and the deformation compatibility condition. Based on the deformation compatibility equations, the thermal constitutive relationships for PWF composites are obtained to derive the residual thermal stresses between PWF plies and pure resin. In order to validate the model, experiments have been performed to investigate the mechanical properties of two-dimensional (2D) orthogonal EW220/5284 PWF composites fabricated by resin transfer moulding (RTM). It is shown that the experimental results correlate well with predictions from the new model.     

ELASTIC BEHAVIOR ANALYSIS OF 3D ANGLE-INTERLOCK WOVEN CERAMIC COMPOSITES

A micromechanical model for elastic behavior analysis of angle-interlock woven ceramic composites is proposed in this paper. This model takes into account the actual fabric structure by considering the fiber undulation and continuity in space, the cavities between adjacent yarns and the actual cross-section geometry of the yarn. Based on the laminate theory, the elastic properties of 3D angle-interlock woven ceramic composites are predicted. Different numbers of interlaced wefts have almost the same elastic moduli. The thickness of ceramic matrix has little effect on elastic moduli. When the undulation ratio increases longitudinal modulus decreases and the other Young's moduli increase. Good agreement between theoretical predictions and experimental results demonstrates the feasibility of the proposed model in analyzing the elastic properties of 3D angle-interlock woven ceramic composites. The results of this paper verify the fact that the method of analyzing polyester matrix composites is suitable for woven ceramic composites.     

Materially and geometrically non-linear woven composite micro-mechanical model with failure for finite element simulations

A computational micro-mechanical material model of woven fabric composite material is developed to simulate failure. The material model is based on repeated unit cell approach. The fiber reorientation is accounted for in the effective stiffness calculation. Material non-linearity due to the shear stresses in the impregnated yarns and the matrix material is included in the model. Micro-mechanical failure criteria determine the stiffness degradation for the constituent materials. The developed material model with failure is programmed as user-defined sub-routine in the LS-DYNA finite element code with explicit time integration. The code is used to simulate the failure behavior of woven composite structures. The results of finite element simulations are compared with available test results. The model shows good agreement with the experimental results and good computational efficiency required for finite element simulations of woven composite structures.     

三维机织复合材料的弹性性能预报模型

建立了基于等效响应比拟技术的三维机织复合材料弹性性能预报模型．首先将三维机织物的结构单元分解为4个子元(经纱、纬纱、填充纱和接结纱),用几何模型去估算这些子元的体积分数．然后依据不同的外载形式,将复合材料的应力-应变关系等效地表达为3组诸子元所组成的三维弹簧网络．根据刚度系数的物理意义,采用不同的弹簧网络连接形式,并按体积平均化方法获得材料总体刚度矩阵中相应的刚度系数,进而计算得到三维机织复合材料的9个弹性系数．该模型考虑了层内交织经纱、层间交织接结纱的弯曲以及材料内部纯树脂区对三维机织复合材料弹性性能的影响．试验结果与模型的理论预测值进行比较,表明这个模型是有效的。     

编织复合材料弹性性能的细观力学模型

提出了编织复合材料弹性性能分析的细观力学模型，这个力学模型考虑了实际编织结构中的纬向和经向纤维束的曲屈，相邻纤维束之间的间隙和纤维束的横截面尺寸对编织复合材料弹性性能的影响，并探讨了在纤维束间纯树脂区内孔隙的含量和两种叠层结构对材料弹性性能的影响．理论计算结果与实测值的比较，表明所提出的细观力学模型是合理的．根据理论分析的结果，提出了优化单层和叠层编织结构的结构参数选择方法     

A continuum constitutive model for the mechanical behavior of woven fabrics

We propose a new approach for developing continuum models for the mechanical behavior of woven fabrics in planar deformation. We generate a physically motivated continuum model that can both simulate existing fabrics and predict the behavior of novel fabrics based on the properties of the yarns and the weave. The approach relies on the selection of a geometric model for the fabric weave, coupled with constitutive models for the yarn behaviors. The fabric structural configuration is related to the macroscopic deformation through an energy minimization method, and is used to calculate the internal forces carried by the yarn families. The macroscopic stresses are determined from the internal forces using equilibrium arguments. Using this approach, we develop a model for plain weave ballistic fabrics, such as Kevlar®, based on a pin-joined beam geometry. We implement this model into the finite element code ABAQUS and simulate fabrics under different modes of deformation. We present comparisons between model predictions and experimental findings for quasi-static modes of in-plane loading.     

Equivalent properties of monolayer fabric from mesoscopic modelling strategies

A general and systematic approach for the development of mesostructurally-based continuum model of woven fabrics has been elaborated, relating the fabric behavior at the macroscopic continuum scale to the response and geometry of the fabric’s mesostructure (geometrical configuration of the weave and the yarn properties). Mesoscopic discrete models of dry fabric have been developed based on a discretization of the yarn geometry, accounting for the yarn–yarn interactions at the yarns crossing points. The yarns are modeled within a unit cell consisting of the repetitive fabric pattern as curved planar beams submitted to the reaction forces of the transverse yarns at discrete crossover points. Those reaction forces are expressed in semi-analytical form versus the yarn geometry and mechanical properties for general armour from beam theory. The equilibrium shape of the woven fabric is obtained by minimizing its total potential energy, accounting for the work of the reaction forces due to the transverse yarns. The absolute minimum of the structure’s total potential energy is achieved by a classical genetic algorithm. Simulation results show that plain weave presents a nonlinear response in the early deformation stage due to the crimp change, whereas twill shows a quasi linear response due to yarn extension being the dominant deformation mechanism. Plain weave fabric overall exhibits an orthotropic constitutive law, as biaxial simulations show. The transverse behavior of plain weave fabric is presently evaluated in terms of Poisson’s ratio, based on virtual simulations at the mesoscopic scale of analysis. Simulation results show that Poisson’s ratio first increases towards a maximum due to the rapid shrinkage of the sample in the transverse direction, and decreases thereafter when the crimp changes become limited by the reaction forces of the transverse yarns. The influence of the mechanical properties of both warp and weft on Poisson’s coefficient is assessed. The predictions of the mesoscopic models regarding the impact of yarn geometry and mechanical properties on the overall behavior provide a guideline for the design of woven fabrics.     

Finite element modelling of woven composite failure modes at the mesoscopic scale: deterministic versus stochastic approaches

Textile composites are composed of 3D complex architecture. To assess the durability of such engineering structures, the failure mechanisms must be highlighted. Examinations of the degradation have been carried out thanks to tomography. The present work addresses a numerical damage model dedicated to the simulation of the crack initiation and propagation at the scale of the warp yarns. For the 3D woven composites under study, loadings in tension and combined tension and bending were considered. Based on an erosion procedure of broken elements, the failure mechanisms have been modelled on 3D periodic cells by finite element calculations. The breakage of one element was determined using a failure criterion at the mesoscopic scale based on the yarn stress at failure. The results were found to be in good agreement with the experimental data for the two kinds of macroscopic loadings. The deterministic approach assumed a homogeneously distributed stress at failure all over the integration points in the meshes of woven composites. A stochastic approach was applied to a simple representative elementary periodic cell. The distribution of the Weibull stress at failure was assigned to the integration points using a Monte Carlo simulation. It was shown that this stochastic approach allowed more realistic failure simulations avoiding the idealised symmetry due to the deterministic modelling. In particular, the stochastic simulations performed have shown several variations of the stress as well as strain at failure and the failure modes of the yarn.     

纤维增强陶瓷基复合材料疲劳迟滞回线模型研究

纤维增强陶瓷基复合材料初始加载到疲劳峰值应力时, 基体出现裂纹, 纤维/基体界面发生脱粘. 在疲劳载荷作用下, 纤维相对基体在界面脱粘区往复滑移使得陶瓷基复合材料出现疲劳迟滞现象. 建立了纤维陶瓷基复合材料疲劳迟滞回线细观力学模型, 采用断裂力学方法确定了初始加载纤维/基体界面脱粘长度、卸载界面反向滑移长度与重新加载新界面滑移长度, 分析了4种不同界面滑移情况的疲劳迟滞回线. 假设正交铺设与编织陶瓷基复合材料疲劳迟滞回线主要受0°铺层、轴向纱线内纤维/基体界面滑移的影响, 预测了单向、正交铺设与编织陶瓷基复合材料在不同峰值应力与不同循环的疲劳迟滞回线, 与试验结果吻合.      

INVESTIGATION ON FATIGUE HYSTERESIS LOOPS MODELS OF FIBRE-REINFORCED CERAMIC-MATRIX COMPOSITES

纤维增强陶瓷基复合材料初始加载到疲劳峰值应力时, 基体出现裂纹, 纤维/基体界面发生脱粘. 在疲劳载荷作用下, 纤维相对基体在界面脱粘区往复滑移使得陶瓷基复合材料出现疲劳迟滞现象. 建立了纤维陶瓷基复合材料疲劳迟滞回线细观力学模型, 采用断裂力学方法确定了初始加载纤维/基体界面脱粘长度、卸载界面反向滑移长度与重新加载新界面滑移长度, 分析了4种不同界面滑移情况的疲劳迟滞回线. 假设正交铺设与编织陶瓷基复合材料疲劳迟滞回线主要受0°铺层、轴向纱线内纤维/基体界面滑移的影响, 预测了单向、正交铺设与编织陶瓷基复合材料在不同峰值应力与不同循环的疲劳迟滞回线, 与试验结果吻合.     

Buckling analysis of fibers in composite materials by wave propagation analogy

The analogy between the governing equations for the analysis of buckling in elastic structures and the elastodynamic equations of motion for wave propagation is presented. By employing this analogy, the exact and approximate buckling stresses of periodic layered materials and continuous fiber composites, respectively, are established. This is performed by utilizing micromechanically based dispersion relations for elastic wave propagating in the composite materials, which provide for a given wave length the corresponding phase velocity. By a specific change of variables in these dispersion relations, the corresponding buckling stresses can be determined. Results are presented and compared with solutions based on the mechanics of materials approach as well as with the well known Rosen’s fiber buckling predictions.     

Woven fabric composite material model with material nonlinearity for nonlinear finite element simulation

The objective of the current investigation is to develop a simple, yet generalized, model which considers the two-dimensional extent of woven fabric, and to have an interface with nonlinear finite element codes. A micromechanical composite material model for woven fabric with nonlinear stress-strain relations is developed and implemented in ABAQUS for nonlinear finite element structural analysis. Within the model a representative volume cell is assumed. Using the iso-stress and iso-strain assumptions the constitutive equations are averaged along the thickness direction. The cell is then divided into many subcells and an averaging is performed again by assuming uniform stress distribution in each subcell to obtain the effective stress–strain relations of the subcell. The stresses and strains within the subcells are combined to yield the effective stresses and strains in the representative cell. Then this information is passed to the finite element code at each material point of the shell element. In this manner structural analysis of woven composites can be performed. Also, at each load increment global stresses and strains are communicated to the representative cell and subsequently distributed to each subcell. Once stresses and strains are associated to a subcell they can be distributed to each constituent of the subcell i.e. fill, warp, and resin. Consequently micro-failure criteria (MFC) can be defined for each constituent of a subcell and the proper stiffness degradation can be modeled if desired. This material model is suitable for implicit and could be modified for explicit finite element codes to deal with problems such as crashworthiness, impact, and failure analysis under static loads.     

对二维编织复合材料弹性、热、强度及失效分析模型的评论

纺织结构作为聚合物复合材料的增强相在许多工业应用中变得非常重要,例如在航海与航空 领域中,由于其刚度及强度与其重量的高比值而倍受欢迎.由于工业及工程应用的需求, 研究纺织复合材料的弹性性质及失效行为变得非常重要.这篇文章重点评论了关于二维编织复合材料弹性、热、强度及失效分析的数值及解析模型,给出了主要的建模技术及方法. 同时也简单给出了编织复合材料从最初的一维模型到最近三维模型的发展.本文的目的不是对所 论模型的数学方法进行详细分析,而是告知研究者关于先前工作的主要思想. 这篇评论总共引用了122篇文献.      

Explicit solutions for shearing and radial stresses in curved beams

In this paper the formulae for the shearing and radial stresses in curved beams are derived analytically based on the solution for a Volterra integral equation of the second kind. These formulae satisfy both the equilibrium equations and the static boundary conditions on the surfaces of the beams. As some applications, the resulting solutions are used to calculate the shearing and radial stresses in a cantilevered curved beam subjected to a concentrated force at its free end. The numerical results are compared with other existing approximate solutions as well as the corresponding solutions based on the theory of elasticity. The calculations show a better agreement between the present solution and the one based on the theory of elasticity. The resulting formulae can be applied to more general cases of curved beams with arbitrary shapes of cross-sections.     

Equivalent mechanical properties of textile monolayers from discrete asymptotic homogenization

The determination of the effective mechanical moduli of textiles from mechanical measurements is usually difficult due to their discrete architecture, which makes micromechanical analyses a relevant alternative to access those properties. Micropolar continuum models describing the effective mechanical behavior of woven fabric monolayers are constructed from the homogenization of an identified repetitive pattern of the textile within a representative unit cell. The interwoven yarns within the textile are represented as a network of trusses connected by nodes at their crossover points. These trusses have extensional and bending rigidities to allow for yarn stretching and flexion, and a transverse shear deformation is additionally considered. Interactions between yarns at the crossover points are captured by beam segments connecting the nodes. The woven fabric is modeled after homogenization as an anisotropic planar continuum with two preferred material directions in the mean plane of the textile. Based on the developed methodology, the effective mechanical properties of plain weave and twill are evaluated, including their bending moduli and characteristic flexural lengths. A satisfactory agreement is obtained between the effective moduli obtained by homogenization and numerical values obtained by finite element simulations performed over periodic unit cells.     

Convexity of the Strain-Energy Function in a Two-Scale Model of Ideal Fabrics

A two-scale model is used to generate the macro-scale constitutive response of a sheet of woven fabric from a micro-scale model of interacting yarns regarded as crossed elasticae in contact. The model furnishes a macro-scale strain-energy function for an orthotropic membrane idealized as being weak in shear compared to the extensional resistance of material curves representing the yarns. The operative Legendre–Hadamard inequality for the membrane is derived and shown to be satisfied by a suitably relaxed version of the computed strain-energy function.     

Strain-rate effect on initial crush stress of irregular honeycomb under dynamic loading and its deformation mechanism

The seemingly contradictory understandings of the initial crush stress of cellular materials under dynamic loadings exist in the literature, and a comprehensive analysis of this issue is carried out with using direct information of local stress and strain. Local stress/strain calculation methods are applied to determine the initial crush stresses and the strain rates at initial crush from a cell-based finite element model of irregular honeycomb under dynamic loadings. The initial crush stress under constant-velocity compression is identical to the quasi-static one, but less than the one under direct impact, i.e. the initial crush stresses under different dynamic loadings could be very different even though there is no strain-rate effect of matrix material. A power-law relation between the initial crush stress and the strain rate is explored to describe the strain-rate effect on the initial crush stress of irregular honeycomb when the local strain rate exceeds a critical value, below which there is no strain-rate effect of irregular honeycomb. Deformation mechanisms of the initial crush behavior under dynamic loadings are also explored. The deformation modes of the initial crush region in the front of plastic compaction wave are different under different dynamic loadings.