Discrete element modelling of unidirectional fibre-reinforced polymers under transverse tension

The mechanical behaviour of unidirectional fibre-reinforced polymer composites subjected to transverse tension was studied using a two dimensional discrete element method. The Representative Volume Element (RVE) of the composite was idealised as a polymer matrix reinforced with randomly distributed parallel fibres. The matrix and fibres were constructed using disc particles bonded together using parallel bonds, while the fibre/matrix interfaces were represented by a displacement-softening model. The prevailing damage mechanisms observed from the model were interfacial debonding and matrix plastic deformation. Numerical simulations have shown that the magnitude of stress is significantly higher at the interfaces, especially in the areas with high fibre densities. Interface fracture energy, stiffness and strength all played important roles in the overall mechanical performance of the composite. It was also observed that tension cracks normally began with interfacial debonding. The merge of the interfacial and matrix micro-cracks resulted in the final catastrophic fracture.     

Three‐dimensional meshfree‐enriched finite element formulation for micromechanical hyperelastic modeling of particulate rubber composites

A three‐dimensional microstructure‐based finite element framework is presented for modeling the mechanical response of rubber composites in the microscopic level. This framework introduces a novel finite element formulation, the meshfree‐enriched FEM, to overcome the volumetric locking and pressure oscillation problems that normally arise in the numerical simulation of rubber composites using conventional displacement‐based FEM. The three‐dimensional meshfree‐enriched FEM is composed of five‐noded tetrahedral elements with a volume‐weighted smoothing of deformation gradient between neighboring elements. The L₂‐orthogonality property of the smoothing operator enables the employed Hu–Washizu–de Veubeke functional to be degenerated to an assumed strain method, which leads to a displacement‐based formulation that is easily incorporated with the periodic boundary conditions imposed on the unit cell. Two numerical examples are analyzed to demonstrate the effectiveness of the proposed approach. Copyright © 2012 John Wiley & Sons, Ltd.     

陶瓷基复合材料多层界面相应力传递的有限元模拟

针对陶瓷基复合材料（CMCs）多层界面相的应力传递进行了有限元模拟。采用圆柱单胞模型描述CMCs的细观结构,按相应界面相亚层的实际厚度建立明确的界面相,并假设界面相亚层之间及界面相与纤维、基体之间初始完好结合,然后赋予各界面相亚层不同的材料参数,并采用轴对称有限元法进行求解,最终建立了多层界面应力传递的模拟方法。分别对比了不同厚度热解碳（PyC）界面相、PyC和SiC两种不同成分界面相及（PyC/SiC）和（SiC/PyC）两种结构界面相的应力传递模拟结果。从剪应力沿纤维方向分布及径向分布特点可以看出,通过合理配置CMCs内部多层界面相的结构、成分和厚度,可以实现界面相应力传递及失效模式的控制和优化。     

Finite element simulation of the micromechanics of interlayered polymer/fibre composites: A study of the interactions between the reinforcing phases

Finite element analysis has been applied to study the mechanical behaviour of composites with ductile thermoplastic and rubbery interlayers between fibres and matrix. The stress distribution in the transverse direction and the interactions between fibres was investigated with particular emphasis on the effect of varying the modulus and thickness of the interlayers. The results of the analysis show that the use of interlayers is more beneficial at higher fibre volume fractions in enhancing the energy absorbing capabilities of a polymer/fibre composite. In particular, ductile interlayers are clearly shown to have a less detrimental effect than rubbery interlayers on the modulus of coated fibre composites.     

梯度复合材料热传导分析的梯度单元法

给出了一种适用于梯度复合材料热传导分析的梯度单元, 采用细观力学方法描述材料变化的热物理属性, 通过线性插值和高阶插值温度场分别给出了4节点和8节点梯度单元随空间位置变化的热传导刚度矩阵。推导了在温度梯度载荷和热流密度载荷作用下, 矩形梯度板的稳态温度场和热通量场精确解。基于该精确解对比了连续梯度模型和传统的离散梯度模型的热传导有限元计算结果, 验证了梯度单元的有效性, 并讨论了相关参数对梯度单元的影响。结果表明, 梯度单元和均匀单元得到的温度场基本一致; 当热载荷垂直于材料梯度方向时, 梯度单元能够给出更加精确的局部热通量场; 当热载荷平行于材料梯度方向时, 4节点梯度单元性能恶化, 8节点梯度单元和均匀单元的计算结果与精确解吻合很好。     

Finite element modelling of creep deformation in fibre-reinforced ceramic composites

The tensile creep and creep-recovery behaviour of a unidirectional SiC fibre-Si₃N₄ matrix composite was analysed using finite element techniques. The analysis, based on the elastic and creep properties of each constituent, considered the influence of fibre-matrix bonding and processing-related residual stresses on creep and creep-recovery behaviour. Both two- and three-dimensional finite element models were used. Although both analyses predicted similar overall creep rates, three-dimensional stress analysis was required to obtain detailed information about the stress state in the vicinity of the fibre-matrix interface. The results of the analysis indicate that the tensile radial stress, which develops in the vicinity of the fibre-matrix interface after processing, rapidly decreases during the initial stages of creep. Both the predicted and experimental results for the composite show that 50% of the total creep strain which accumulated after 200 h at a stress of 200 MPa and temperature of 1200°C is recovered within 25 h of unloading.     

Finite element modelling of impact on preloaded composite panels

Composite aircraft structures are susceptible to impact damage during manufacture, maintenance and in-flight. Low energy impact damage is often internal and invisible, but can significantly reduce the stiffness and strength or cause catastrophic failure when the structure is under load during the impact event. This paper describes the development and application of an explicit finite element (FE) model, incorporating a bi-phase material degradation model, to predict the behaviour of loaded carbon/epoxy panels when impacted over a range of low energy levels. Overall, the trends predicted in the FE simulations were consistent with experimental data, although quantitatively the FE results were generally conservative. However, the model greatly underestimated the catastrophic failure boundary. The model was used to investigate the effect of various parameters including magnitude of preload, impact velocity and specimen geometry on the amount of damage and the residual strength of carbon/epoxy panels.     

Constitutive modelling of fibre-reinforced composites with unidirectional plies using a plasticity-based approach

This paper presents the development of a constitutive model able to accurately represent the full non-linear mechanical response of polymer-matrix fibre-reinforced composites with unidirectional (UD) plies under quasi-static loading. This is achieved by utilising an elasto-plastic modelling framework. The model captures key features that are often neglected in constitutive modelling of UD composites, such as the effect of hydrostatic pressure on both the elastic and non-elastic material response, the effect of multiaxial loading and dependence of the yield stress on the applied pressure.The constitutive model includes a novel yield function which accurately represents the yielding of the matrix within a unidirectional fibre-reinforced composite by removing the dependence on the stress in the fibre direction. A non-associative flow rule is used to capture the pressure sensitivity of the material. The experimentally observed translation of subsequent yield surfaces is modelled using a non-linear kinematic hardening rule. Furthermore, evolution laws are proposed for the non-linear hardening that relate to the applied hydrostatic pressure.Multiaxial test data is used to show that the model is able to predict the non-linear response under complex loading combinations, given only the experimental response from two uniaxial tests.     

Finite element micromechanical modelling of a unidirectional composite subjected to axial shear loading

A micromechanical model is presented which predicts the behaviour of a unidirectional composite subjected to axial shear load using standard finite elements. Only a three-dimensional model can handle the necessary shear loading boundary conditions when using such elements. These boundary conditions give shear stress components but no direct stress components within the composite. A parametric study is carried out on unidirectional carbon fibre/epoxy within the linear elastic regime of both constituents. The study reveals that the most critical parameters controlling the axial shear modulus of the composite are matrix modulus and fibre volume fraction whilst the stress state in the composite is mainly controlled by geometrical features of the composite, i.e., fibre volume fraction and fibre spacing. Comparison between the predicted axial shear modulus based on the concentric cylinder model and the current finite element model shows good agreement for low and intermediate fibre volume fractions. Both predictions lie within the Hashin bounds and the finite element prediction tends to be closer to the upper Hashin bound for fibre volume fractions greater than 60%. The initial tangent shear modulus predicted with the finite element model and that measured differ by less than 2.5%. The non-linear shear stress/strain response of the composite material is also predicted and agreement with the experimental results is good.     

Finite–element analysis of selectively SiC fibre–reinforced titanium composites (II)

Finite-element analysis has been carried out to predict the through-thickness stresses generated at the transition boundary between monolithic cladding layers and SiC fibre reinforced titanium matrix composite plates. Such stresses have been shown in studies elsewhere to promote premature transverse damage near the transition region ahead of a mode I crack propagating within the cladding layer. Results obtained in DEN tension are presented to demonstrate the influence of thermal residual stress, external loading, and the relative thicknesses of the cladding material and the composite regions, on the through-thickness stresses. A dimensionless parameter S has been constructed and is demonstrated to provide a useful tool for predicting the potential for through-thickness damage in a range of testpiece dimensions and levels of selective reinforcement. This revised version was published online in August 2006 with corrections to the Cover Date.     

3D机织复合材料多向接头有限元分析

为了探究3D机织复合材料桁架接头的机械性能,采用有限元软件ANSYS对3D机织复合材料多向接头所在桁架总体进行有限元模拟,模拟中根据纤维走向对多向接头不同轴向圆管建立相应坐标系,并赋予材料属性,使用MPC多点约束法施加载荷.求解分析后结果表明:模拟结果与实测结果中最大应变的位置与数值基本吻合,确定了模拟的有效性;将最大应力与破坏应力对比发现接头在当前载荷下可能发生轻微破坏,破坏位置应位于副管顶部;通过模拟判断了实测中发生轻微响声的原因;将4种角联锁结构的多向接头模拟结果对比发现,带有衬经结构的复合材料为多向接头最佳材料.此次模拟补充了实测中无法得到的数据,为接头的优化设计和实际使用提供一定的帮助.     

A micromechanical composite approach for finite element crashworthiness simulation

The present article deals with micromechanical composite modeling. Both analytical and computational micromechanics approaches are described as well as micromechanical modeling of damage. Based on micromechanics of failure theory, a user subroutine including a progressive damage algorithm is programmed for finite element analysis. Three theory-experiment correlations of tubes under a three-point bending test have been carried out using the bi-phase material model developed along with this project. These studies include three-ply schedules.     

Finite element modelling of fibre reinforced polymer sandwich panels exposed to heat

A finite element model that predicts temperature distribution in a composite panel exposed to a heat source, such as fire, is described. The panel is assumed to be composed of skins consisting of polymer matrix reinforced with fibres and a lightweight core (the paper concentrates on the crucial aspect of the problem, i.e. the behaviour of the ‘hot’ skin of the panel. The core is assumed not to decompose, and the ‘cold’ skin is treated exactly as the ‘hot’ skin.) It is assumed that the polymer matrix undergoes chemical decomposition. Such a model results in a set of coupled non‐linear transient partial differential equations. A Galerkin finite element framework is formulated to yield a fully implicit time stepping scheme. The crucial input parameters for the model are carefully identified for subsequent experimental determination. Copyright © 2004 John Wiley & Sons, Ltd.     

复合材料湿热弹性性能的变分渐近细观力学模型

基于变分渐近均匀化理论框架建立可预测复合材料有效湿热弹性性能和单胞内局部场分布的细观力学模型。从推导复合材料湿热弹性自由能泛函出发,利用细、宏观尺度比作为小参数对自由能泛函的主导变分项进行渐近分析,得到湿热弹性问题的系列细观力学模型和局部场分布的重构关系,并通过有限元数值方法实现。与ABAQUS有限元算例的对比表明:构建的细观力学模型可有效准确地预测复合材料有效湿热弹性属性和局部场分布。      

Finite element crash simulations of the human body: Passive and active muscle modelling

Conventional dummy based testing procedures suffer from known limitations. This report addresses issues in finite element human body models in evaluating pedestrian and occupant crash safety measures. A review of material properties of soft tissues and characterization methods show a scarcity of material properties for characterizing soft tissues in dynamic loading. Experiments imparting impacts to tissues and subsequent inverse finite element mapping to extract material properties are described. The effect of muscle activation due to voluntary and non-voluntary reflexes on injuries has been investigated through finite element modelling.     

Finite element modelling of solidification phenomena

The process of solidification process is complex in nature and the simulation of such process is required in industry before it is actually undertaken. Finite element method is used to simulate the heat transfer process accompanying the solidification process. The metal and the mould along with the air gap formation is accounted in the heat transfer simulation. Distortion of the casting is caused due to non-uniform shrinkage associated with the process. Residual stresses are induced in the final castings. Simulation of the shrinkage and the thermal stresses are also carried out using finite element methods. The material behaviour is considered as visco-plastic. The simulations are compared with available experimental data and the comparison is found to be good. Special considerations regarding the simulation of solidification process are also brought out. An erratum to this article is available at .     

A simplified micromechanical model for predicting effective mechanical behaviors of continuous bidirectional-fiber-reinforced composites

A simplified micromechanical model is proposed to estimate the macroscopic mechanical properties of continuous bidirectional-fiber-reinforced composites (CBFRCs) by ignoring Poisson's effect. The model is validated by results from a homogenized finite element approach. Based on the proposed analytical model, the influences of the ratios of fiber/matrix modulus and the fiber volume ratio on the effective modulus and the tensile strength are specifically investigated. The suggested theoretical method provides a convenient tool for estimating the effective mechanical behaviors of CBFRCs, which can be expressed as a function of fiber volume fraction and material parameters.     

陶瓷基复合材料界面结合强影响断裂过程的有限元研究

提出了纤维增强复合材料断裂有限元模型,该模型既用弹簧单元考虑了基体与纤维之间的分离,又用接触单元考虑了基体与纤维之间的摩擦,较真实地模拟了纤维增强复合材料的断裂过程。通过有限元计算,预测了基体与纤维之间的界面结合强度对整个复合材料断裂模式的影响。还对强弱两种不同基体弹性模量的材料进行进一步的探讨。对比其他文献 , 本文中预测结果与真实情况较为吻合。结果表明,对于纤维增强复合材料,不论是强基体还是弱基体,适中的界面结合强度有助于提高其韧性及整体抗拉强度。       

A low‐order,hexahedral finite element for modelling shells

A thin, eight‐node, tri‐linear displacement, hexahedral finite element is the starting point for the derivation of a constant membrane stress resultant, constant bending stress resultant shell finite element. The derivation begins by introducing a Taylor series expansion for the stress distribution in the isoparametric co‐ordinates of the element. The effect of the Taylor series expansion for the stress distribution is to explicitly identify those strain modes of the element that are conjugate to the mean or average stress and the linear variation in stress. The constant membrane stress resultants are identified with the mean stress components, and the constant bending stress resultants are identified with the linear variation in stress through the thickness along with in‐plane linear variations of selected components of the transverse shear stress. Further, a plane‐stress constitutive assumption is introduced, and an explicit treatment of the finite element's thickness is introduced. A number of elastic simulations show the useful results that can be obtained (tip‐loaded twisted beam, point‐loaded hemisphere, point‐loaded sphere, tip‐loaded Raasch hook, and a beam bent into a ring). All of the gradient/divergence operators are evaluated in closed form providing unequivocal evaluations of membrane and bending strain rates along with the appropriate divergence calculations involving the membrane stress and bending stress resultants. The fact that a hexahedral shell finite element has two distinct surfaces aids sliding interface algorithms when a shell folds back on itself when subjected to large deformations. Published in 2004 by John Wiley & Sons, Ltd.