Finite element analysis of viscoelastic structures using Rosenbrock-type methods

The consistent application of the space-time discretisation in the case of quasi-static structural problems based on constitutive equations of evolutionary type yields after the spatial discretisation by means of the finite element method a system of differential-algebraic equations. In this case the resulting system of differential-algebraic equations with the unknown nodal displacements and the evolution equations at all spatial quadrature points of the finite element discretisation are solved by means of a time-adaptive Rosenbrock-type methods leading to an iteration-less solution scheme in non-linear finite element analysis. The applicability of the method will be studied by means of a simple example of a viscoelastic structure.     

Buckling analyses of viscoelastic structures considering ageing and damage effects

The durability of structures made of composite materials is affected by diverse factors, among which creep deformation, ageing and damage. Ageing is related to elapsed time (with different effects in different environmental conditions); damage is related to microstructural modifications due stress and/or strain inputs.The formal definition of these effects and the corresponding constitutive formulations are presented. These formulations are used to obtain analytical solutions and also to implement a Finite Element programme for viscoelastic analysis of laminar structures in a large displacement with small strains context. Then, the effects of ageing and damage on both the short and the long term stability of beam columns are analyzed. Some examples for verification of the formulation and for the comparison of effect are presented.     

Finite element analysis of micromechanical failure modes in a heterogeneous ceramic material system

A micromechanical model that provides explicit accounts for arbitrary microstructures and arbitrary fracture patterns is developed and used. The approach uses both a constitutive law for the bulk solid constituents and a constitutive law for fracture surfaces. The model is based on a cohesive surface formulation of Xu and Needleman and represents a phenomenological characterization for atomic forces on potential crack/microcrack surfaces. This framework of analysis does not require the use of continuum fracture criteria which assume, for example, the existence of K-fields. Numerical analyses carried out concern failure in the forms of crack propagation and microcrack formation. Actual microstructures of brittle alumina/titanium diboride (Al₂O₃/TiB₂) composites are used. The results demonstrate the effects of microstructure and material inhomogeneities on the selection of failure modes in this material system. For example, the strength of interfaces between the phases is found to significantly influence the failure characteristics. When weak interfacial strength exists, interfacial debonding and microcrack initiation and growth are the principal mode of failure. When strong interfacial strength is derived from material processing, advancement of a dominant crack and crack branching are observed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Finite element simulations of poly-crystalline shape memory alloys based on a micromechanical model

We present a finite element implementation of a micromechanically motivated model for poly-crystalline shape memory alloys, based on energy minimization principles. The implementation allows simulation of anisotropic material behavior as well as the pseudo-elastic and pseudo-plastic material response of whole samples. The evolving phase distribution over the entire specimen is calculated. The finite element model predicts the material properties for a relatively small number of grains. For different points of interest in the specimen the model can be consistently evaluated with a significantly higher number of grains in a post-processing step, which allows to predict the re-orientation of martensite at different loads. The influence of pre-texture on the material’s properties, due to some previous treatment like rolling, is discussed.     

Limit analysis of composite materials with anisotropic microstructures: A homogenization approach

A nonlinear mathematical programming approach together with the finite element method and homogenization technique is developed to implement kinematic limit analysis for a microstructure and the macroscopic strength of a composite with anisotropic constituents can be directly calculated. By means of the homogenization theory, the classical kinematic theorem of limit analysis is generalized to incorporate the microstructure - Representative Volume Element (RVE) chosen from a periodic composite/heterogeneous material. Then, using an associated plastic flow rule, a general yield function is directly introduced into limit analysis and a purely-kinematic formulation is obtained. Based on the mathematical programming technique, the finite element model of microstructure is finally formulated as a nonlinear programming problem subject to only one equality constraint, which is solved by a direct iterative algorithm. The calculation is entirely based on a purely-kinematical velocity field without calculation of stress fields. Meanwhile, only one equality constraint is introduced into the nonlinear programming problem. So the computational cost is very modest. Both anisotropy and pressure-dependence of material yielding behavior are considered in the general form of kinematic limit analysis. The developed method provides a direct approach for determining the macroscopic strength domain of anisotropic composites and can serve as a powerful tool for microstructure design of composites.     

A three-dimensional micromechanical model to predict the viscoelastic behavior of woven composites

Polymer matrix based cloth composites are increasingly used in engineering applications. For such composites, significant viscoelastic behavior can be observed for dynamic load conditions. The viscoelastic effect is primarily due to the polymeric matrix used as most of the fibers used in structural applications are elastic. Matrix does not show a major contribution in the axial properties of composites, thus in the traditional modeling its viscoelastic nature is often ignored. However, the effective out of plane properties are influenced by the matrix material and exhibit significant damping characteristics. Therefore, a complete three-dimensional (3-D) model considering the viscoelastic nature of matrix is needed for better understanding of cloth composites. An analytical 3-D micromechanical model based on classical laminate theory (CLT) is verified, in this paper for the prediction of effective elastic and viscoelastic properties of a cloth composite. The method is shown to be accurate. This model is extended to the viscoelastic regime with the use of Laplace transform and correspondence principle. Prony series coefficients for composite cloth are obtained for different volume fractions of fibers in yarn. It is observed from the hysteresis plots that dissipation in out of plane normal and shear modes is significantly higher than the normal directions.     

Finite element analysis of creep fracture initiation in a model superalloy material

Detailed finite element analyses were performed for a single edge-cracked specimen geometry under both plane stress and plane strain constraint for a superalloy material that obeys a power-law creep relationship. The objectives of these analyses were to elucidate the stationary creep crack-tip fields and to provide guidance for the experimental measurement of crack-tip deformations. New results demonstrate that, for both plane stress and plane strain, the angular variations in the creep strain fields do not agree with HRR-type predictions, although the radial variations are in agreement with HRR-type creep strain field predictions in a zone very near the crack tip. Thus, the use of experimental measurement of surface displacement and/or strain data for the location of HRR-type fields may not be possible, unless modifications to the existing HRR-type theory are made. It is also noted that the size of the stress-based HRR-dominance zone is only a fraction of the creep zone size in plane stress, and is very small (especially along =0°) compared to the creep zone size in plane strain. Furthermore, the dominance of the singular strain fields are at least two orders of magnitude smaller than the corresponding stress dominance zones. As such, unless the microstructural features of the material are smaller than the dimensions of the dominance zones, the basis for using stress or strain-based fracture parameters derived from the HRR-type fields for prediction of creep fracture initiation is unclear.     

Implementation of a constitutive micromechanical model for damage analysis in glass mat reinforced composite structures

A micromechanical model based on a probabilistic approach is implemented in the finite element code CASTEM 2000 to develop numerical simulations that efficiently predict the overall damaged behaviour of random oriented fibre composites. The proposed damage constitutive model is based upon the generalised Mori and Tanaka scheme and Eshelby's equivalence theory. Damage mechanisms occurring at each composite constituent (fibres, matrix and interface) are associated to Weibull probabilistic functions to model their onset and progressive growth at the microscopic scale level. It is obvious that the damaged behaviour of the composite material depends widely on the microscopic material parameters (fibre length, fibre volume fraction, fibre orientation, …). On one hand, the micromechanical model uses homogenisation techniques which enabled us to link these microscopic parameters to the material behaviour and to evaluate explicitly their influences. On the other hand, the implementation of the derived behaviour law into a finite element code enabled us to reflect on the effect of these microscopic parameters on the overall response of a simple composite structure presenting heterogeneous stress fields. In fact, the damage evolution in each constituent (local scale) and the related stiffness reduction are estimated at any material point (integration point) or node of the considered structure subject to a specific loading. Numerical simulations of a composite plate with a hole under in-plane tension were performed to validate the implementation of the behaviour law. Numerical results have been compared to experimental curves and damage evolutions monitored by acoustic emission techniques. Simulations agree well with experimental results in terms of damage onset and growth.     

Viscoelastic failure analysis of composite plates and shells

The present paper describes a numerical method for modeling the failure behavior of composite laminates in the presence of large displacements and creep. Geometrical nonlinear finite elements are used for the discretization. The modeling of material behavior includes thermal, hygroscopic and viscoelastic effects, using an efficient state variable representation. Incremental damage is determined and used to calculate a modified stiffness matrix. Thus, the procedure can be used to analyze, for example, buckling, creep buckling and creep buckling including damage. A detailed formulation, computational procedures and examples to check the accuracy of the code are presented.     

Effective mechanical properties of EM composite conductors: an analytical and finite element modeling approach

An analytical model and numerical approach to predict the effective mechanical properties of a composite conductor consisting of metallic core and insulation layers are presented in this paper. The analytical model was developed based on a two-step homogenizations and mechanics analysis for composite unit cell. The Step 1 homogenization derives the effective properties of the out-wrapped composite insulation layers. The Step 2 homogenization further smears the metallic core and the effective composite insulation layers to develop homogenized mechanical properties for composite conductor according to appropriate homogenization sequences. The procedure of using numerical approach and finite element method to determine the unit cell effective constants were also described and the results of the FEA prediction were presented. The analytical predictions were compared well to the numerical results for the nine material constants that characterize the effective mechanical properties of the composite conductor.     

基于欧拉—拉格朗日方法的复合材料机翼前缘鸟撞模拟

复合材料大面积用于飞机结构后,其鸟撞问题变得更加突出。利用大型通用有限元程序ABAQUS,采用耦合欧拉—拉格朗日方法（CEL）对某型无人机复合材料机翼前缘的鸟撞问题进行模拟,研究了鸟体速度、密度和蒙皮铺层形式等对鸟撞动响应的影响,计算了机翼前缘填充泡沫后的鸟撞损伤,对复合材料蒙皮的鸟撞破坏机理进行了分析,所得结果对工程设计具有参考意义。     

Nonlinear hygro-thermo-elastic vibration analysis of doubly curved composite shell panel using finite element micromechanical model

Nonlinear free vibration behavior of laminated composite curved panel under hygrothermal environment is investigated in this article. The mathematical model of the laminated panel is developed using Green–Lagrange-type geometrical nonlinearity in the framework of higher-order mid-plane kinematics. The corrugated composite properties are evaluated through the micromechanical model and all the nonlinear higher-order terms are included in the present model for the sake of generality. The equation of vibrated panel is obtained using Hamilton's principle and discretized with the help of the finite element steps. The solutions are computed numerically using the direct iterative method. The effect of parameters on the nonlinear vibration responses is examined thoroughly by solving the wide variety of numerical examples.     

基于非线性本构关系的复合材料风机叶片有限元极限分析与设计

为了研究具有三维复杂构形的复合材料风机叶片的逐次破坏过程和极限承载能力, 将复合材料细观力学非线性本构理论桥联模型与有限元软件ABAQUS通过用户子程序UGENS结合起来对风力发电机叶片结构进行极限强度分析。只需提供纤维和基体的材料性能参数、 纤维体积含量以及蒙皮和增强筋的铺层数据包括铺设角、 层厚和铺层数, 就可预报出复合材料复杂叶片结构的整体承载能力以及叶片破坏所处的位置, 为正确评估和合理设计风机叶片结构提供了一种简便有效的分析方法。以一种20kW风机叶片为例, 用此方法实现了新型复合材料叶片结构的极限分析和合理设计, 提高了叶片的强度和刚度, 有效降低了叶片的重量。本文中的方法同样适用于其它复合材料复杂结构的极限分析与强度设计。      

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 substation composite insulators

Composite insulators are rapidly replacing their porcelain counterparts in electrical substation applications. These insulators consist of a glass-reinforced polymer (GRP) rod, with two metal end fittings radially crimped onto the ends of the rod during assembly. In this paper, axisymmetric finite element models are developed to evaluate the mechanical performance of composite insulators under externally applied axial compression. The analyses are performed by assuming both a perfectly bonded interface between the composite rod and the end fittings, and an imperfect interface which permits large relative sliding with Coulomb friction. Results indicate that the perfect interface model is unrealistic since it predicts singular stresses at the interface comer and an overall linear structural response. On the other hand, the imperfect interface model is found to simulate accurately the structural non-linearity caused by relative sliding of the GRP rod within the end fittings. The imperfect interface model has therefore been used to evaluate the effects of interface friction, and the extent of crimping, on the maximum load-bearing capacity of substation composite insulators.     

Finite element analysis of textile composite preform stamping

The forming or draping of a textile composite preform may result in large changes in the fibrous microstructure of the preform. This change in the local fiber orientation leads to significant changes in the fabric permeability as well as the mechanical properties of the ensuing composite structure. Therefore, this change in orientation of the tows of the preform needs to be known accurately to calculate the various effective properties of the composite. A new finite element approach for stamping analysis of a plain-weave textile composite preform has been developed. This model is simple, efficient and can be used in the existing finite element codes. The model represents the preform as a mesh of 3-D truss elements and 3-D shell elements. The truss elements model the tows, which are allowed to both scissor and slide relative to one another. The shell elements represent a fictitious material that accounts for inter-tow friction and fiber angle jamming. The model takes into account large strains and large deformations. In-plane uniaxial tension tests have been performed on plain-weave specimens for determining the constitutive law of the transforming medium and to show the inter-tow sliding. Application of the model is demonstrated by simulating the stamping of a preform by a spherical punch. The results from the simulation show good correlation with results from the experiments.     

Finite element analysis of composite revolution structures wound by wide plies

An isoparametric axisymmetrical finite element is developed for the analysis of multilayer composite structures wound by wide plies. This element takes into account the variation of angle along the width of a layer for a given parallel of a revolution structure. Evaluation of strain and stress tensors is performed in mean and extreme fibre directions of a ply. Moreover, this model can represent geometrical nonlinear behaviour and material nonlinearities. The extended possibilities of this model are illustrated for two aerospace structures: a spherical wound satellite tank and the composite head of a rocket motor.     

Free vibration analysis of anisotropic material structures using the boundary element method

This paper presents a formulation for the analysis of free vibration in anisotropic structures using the boundary element method. The fundamental solution for elastostatic is used and the inertial terms are treated as body forces providing domain integrals. The dual reciprocity boundary element method is used to reduce domain integrals to boundary integrals. Mode shapes and natural frequencies for free vibration of orthotropic structures are obtained and compared with finite element results showing good agreement.     

Finite element analysis of laminated composite plates using a higher-order displacement model

A C° continuous displacement finite element formulation of a higher-order theory for flexure of thick arbitrary laminated composite plates under transverse loads is presented. The displacement model accounts for non-linear and constant variation of in-plane and transverse displacement model eliminates the use of shear correction coefficients. The discrete element chosen is a nine-noded quadrilateral with nine degrees-of-freedom per node. Results for plate deformations, internal stress-resultants and stresses for selected examples are shown to compare well with the closed-form, the theory of elasticity and the finite element solutions with another higher-order displacement model by the same authors. A computer program has been developed which incorporates the realistic prediction of interlaminar stresses from equilibrium equations.     

Finite element analysis and optimization of composite wheelchair wheels

A methodology for the design of Paralympics wheelchair wheels has been developed and provided a framework for comparison between design solutions. Finite element analysis was used as a tool to develop an understanding of wheel design, provide a basis for evaluation of design solutions, and as a mean of design optimisation. A finite element model of an existing wheel design was created and analysed. It was found that the pushrim was significantly over designed for the application. As such, wheel improvement focused on redesign of this component. A number of design solutions were analysed and compared based on weight, rotational moment of inertia, side profile surface area, and wheel stiffness. From this, it was decided that a thin pushrim attached via spokes to the rim and the hub in a tangential spoking pattern would offer the best solution.