Application of decohesive model with mixed damage scale in fracture analysis of composite materials

A decohesive model using a mixed damage scale and using the total fracture energy to simulate the fracture process of composite materials has been developed in this article. The model assumes a bilinear interfacial decohesion function and is incorporated into an interface finite element developed as a user subroutine in the commercial FEA package ABAQUS. In comparison with traditional numerical methods in fracture mechanics, this approach can automatically predict the failure load, crack path and the residual stiffness of bodies undergoing the fracture process. Applications given in this paper are simulation of a typical fracture test with a double cantilever beam (DCB) specimen; modelling a stiffened composite laminated panel under four-point bending and modelling a repaired composite sandwich panel under four-point bending. Good correlation was seen between modelling predictions and experimental results.     

Low-velocity impact-induced damage of continuous fiber-reinforced composite laminates. Part I. An FEM numerical model

A numerical model for simulating the process of low-velocity impact damage in composite laminates using the finite element method is presented in this paper, i.e. Part I of this two part series on the study of impact. In this model, the 9-node Lagrangian element of the Mindlin plate with consideration of large deformation analysis is employed. To analyze the transient response of the laminated plates, a modified Newmark time integration algorithm previously proposed by the authors is adopted here. We also proved that the impact process between a rigid ball and laminated plates is a stiff system, therefore a kind of A(α) stable method has been advocated here to solve the motion equation of the rigid ball. Furthermore, various types of damages including delamination, matrix cracking and fiber breakage, etc. and their mutual influences are modeled and investigated in detail. To overcome the difficulty of numerical oscillation or instability in the analysis of the dynamic contact problem between delaminated layers using the traditional penalty methods, we have employed dynamic spring constraints to simulate the contact effect, which are added to the numerical model by a kind of continuous penalty function. Moreover, an effective technique to calculate the strain energy release rate based on the Mindlin plate model is proposed, which can attain high precision. Finally, some techniques of adaptive analyses have been realized for improving the computational efficiency. Based on this model, a program has been developed for numerically simulating the damage process of cross-ply fiber-reinforced carbon/epoxy composite laminates under low-velocity impact load. In Part II, this numerical model will be verified by comparing with the experimental results. Also the impact damage will be investigated in detail using this numerical approach.     

Numerical analysis of size effects on open-hole tensile composite laminates

The tensile strength of open-hole fibre reinforced composite laminates depends on in-plane, thickness and ply lay-up scaling. Translaminar (fibre direction) mode I fracture toughness has recently been experimentally determined to be thickness dependent. This paper presents a computational study of the tensile strength prediction of open-hole laminates using a cohesive zone model. To the authors’ knowledge, it is for the first time in the literature that the thickness-dependence of translaminar fracture toughness is accounted for in the numerical modelling of composites. The thickness size effect in the strength of open-hole composite laminates failed by pull-out is accurately predicted for the first time by a deterministic model. It is found that neglecting delamination in the numerical models will lead to mesh-dependency and over-estimation on the predicted strength. Smeared crack model with cohesive elements to model delamination is able to predict the correct failure mode; but it is found not suitable for accurate strength predictions for laminates failed by delamination.     

Fracture statistics of single-fibre composite specimens

The failure of unidirectional composite materials is subject to wide dispersion owing to the occurrence of flaws or imperfections in the fibres. Fracture modelling requires the use of statistical models to deal with this variability in stength. We are currently developing an original and general approach that combines random models of defects with mechanical models and tests on composite materials. The present study is devoted to the problem of the characterisation of single fibres.

The fragmentation test is used to study the flaw population along the fibre as a function of applied stress. Each fracture is to a flaw in the fibre with a critical stress, σ_c, less than the applied stress σ. We can means of a multifragmentation test. Various density estimate the flaw distribution as a function of stress by means of a multifragmentation test. Various density functions are proposed and tested and good agreement is found between the experimental data and theoretical results. Following the proposed model, which has been verified experimentally, numerical simulations were carried out to study the validity of the parameters of the model.     

基于弹塑性损伤本构模型的复合材料层合板破坏荷载预测

在连续损伤力学和塑性力学框架内,建立一个同时考虑塑性效应和损伤累积导致材料属性退化的复合材料弹塑性损伤本构模型。基于最近点投影回映算法,开发本构模型的应变驱动隐式积分算法以更新应力及与解答相关的状态变量,并推导与所开发算法相应的数值一致性切线刚度矩阵,保证有限元分析采用NewtonRaphson迭代法解答非线性问题的计算效率。采用断裂带模型对已开发的本构模型软化段进行规则化,以减轻有限元分析结果的网格相关性问题。对损伤变量进行粘滞规则化,并推导出相应的粘滞规则化数值一致性切线刚度张量,解决了在有限元隐式计算程序中采用含应变软化段本构关系的数值分析由于计算困难而提前终止的问题。开发包含数值积分算法的用户材料子程序UMAT,并嵌于有限元程序Abaqus v6.14中。通过对力学行为展现显著塑性效应的AS4/3501-6V型开口复合材料层合板的渐进失效分析,验证本文提出的材料本构模型的有效性。结果显示,预测结果与已报道的试验结果吻合良好,并且预测精度高于其他已有弹性损伤模型。表明已建立的弹塑性损伤本构模型能够准确预测力学行为,展现显著塑性效应的复合材料层合板的破坏荷载,为其构件和结构设计提供一种有效的分析方法。     

Theoretical modelling of laminated composite plates

Formulation of appropriate governing equations, simpler than the three-dimensional equations of elasticity yet capable of predicting, fairly accurately, all important response parameters such as stress and strain, is attempted in modelling a structural component. Several theoretical models are available in the literature for the analyses of plates. The emergence of fibre-reinforced plastics as an attractive form of structural construction, added a new complexity to the modelling considerations of laminates by requiring the estimation of the interlaminar stresses and strains. In this paper, modelling considerations of laminated composite plates are discussed. The classical laminated plate theory and higher-order shear deformation models are reviewed to bring out their interlaminar stress predictive capabilities, and some new modelling possibilities are indicated. This work has been supported by the Aeronautics Research and Development Board, Ministry of Defence, Government of India.     

A coupled thermo-chemo-mechanical reduced-order multiscale model for predicting process-induced distortions,residual stresses,and strength

We study residual stresses and part distortion induced by a manufacturing process of a polymer matrix composite and its effect on the component strength. Unlike most of the thermo-chemo-mechanical models in the literature where governing multiphysics equations are directly formulated on the macroscale, we present a multiscale-multiphysics approach. To address the enormous computational complexity involved, a reduced-order homogenization was originally developed for a single physics problem is employed. The proposed reduced-order two-scale thermo-chemo-mechanical model has been validated for predicting part distortion beam strength in three-point bending test. It is shown that while macroscopic stresses are relatively low, and therefore often ignored in practice, stresses at the scale of microconstituents are significant and may have an effect on the overall composite component strength.     

Parametric constitutive model of plain-weave fabric reinforced composite ply

A computational model that allows to explicitly determine orthotropic elastic constants of plain-weave fabric-reinforced composite ply as functions of microstructure parameters has been developed in this study. These relationships are not given in the form of analytical formulae (as it is in the case of approximate analytical models) but in the form of an extensive database of numerically evaluated results for different microstructure instances and a numerical scheme that interpolates the results. To build the database, a standard finite-element-based homogenization technique of a periodic representative volume element is employed. As a result, a numerical algorithm is provided that may be easily employed in FE codes as a part of a regular constitutive subroutine. Sensitivity of the composite elastic constants with respect to the microstructure parameters is also directly available from the model.     

Adaptive neuro-fuzzy inference system in modelling fatigue life of multidirectional composite laminates

Adaptive neuro-fuzzy inference system (ANFIS) has been successfully used for the modelling of fatigue behaviour of a multidirectional composite laminate. The evaluation of the neuro-fuzzy model has been performed using a data base containing 257 valid fatigue data points. Coupons were cut at 0° on-axis and 15°, 30°, 45°, 60°, 75°, and 90° off-axis directions from an E-glass/polyester multidirectional laminate with a stacking sequence of [0/(±45)₂/0]_T. Constant amplitude fatigue tests at different tensile and compressive conditions were conducted for the determination of the 17 S–N curves. The modelling accuracy of this novel, in this field, computational technique is very high. For all cases studied, it has been proved that a portion of around 50% of the available data are adequate for accurate modelling of the fatigue behaviour of the material under consideration. The new technique is a stochastic process which leads to the derivation of a multi-slope S–N curve based on the available experimental data without the need for any assumptions. Employment of this technique can lead to a substantial decrease of the experimental cost for the determination of reliable fatigue design allowables.     

Quantification of uncertainty modelling in stochastic analysis of FRP composites

The extensive use of FRP composite materials in a wide range of industries, and their inherent variability, has prompted many researchers to assess their performance from a probabilistic perspective. This paper attempts to quantify the uncertainty in FRP composites and to summarise the different stochastic modelling approaches suggested in the literature. Researchers have considered uncertainties starting at a constituent (fibre/matrix) level, at the ply level or at a coupon or component level. The constituent based approach could be further classified as a random variable based stochastic computational mechanics approach (whose usage is comparatively limited due to complex test data requirements and possible uncertainty propagation errors) and the more widely used morphology based random composite modelling which has been recommended for exploring local damage and failure characteristics. The ply level analysis using either stiffness/strength or fracture mechanics based models is suggested when the ply characteristics influence the composite properties significantly, or as a way to check the propagation of uncertainties across length scales. On the other hand, a coupon or component level based uncertainty modelling is suggested when global response characteristics govern the design objectives. Though relatively unexplored, appropriate cross-fertilisation between these approaches in a multi-scale modelling framework seems to be a promising avenue for stochastic analysis of composite structures. It is hoped that this review paper could facilitate and strengthen this process.     

An automated finite element analysis of the initiation and growth of damage in carbonfibre composite materials

The analysis and prediction of the development of damage in composite materials up to the point of final failure is important in the assessment of whether composite structures and components are fit for their purpose. Progressive damage modelling, using finite element analysis, has demonstrable potential as a tool for this.

If this approach is to be of real value, it needs to be automated so that the application of specialist knowledge is minimized. The ABAQUS finite element (FE) code has been used to develop fully-automated, threedimensional modelling of damage development in carbon fibre composites under tensile loading.

This paper describes the approach used in the development of these models. It covers work on the development of suitable FE meshes, the identification of suitable criteria to control the onset and effects of local damage, and the extension of the methodology to real component geometries.     

Application of a dynamic-mixture shock-wave model to the metal-matrix composite materials

The so-called “dynamic mixture” model is applied to a prototypical metal matrix composite (MMC) system (consisting of an aluminum matrix and SiC particulates) in order to investigate the propagation of planar (i.e. one directional), longitudinal (i.e. uniaxial strain), steady (i.e. time-invariant) structured shock waves. Waves of this type are typically generated during blast-wave loading or ballistic impact and play a major role in the way blast/ballistic impact loads are introduced into a structure. Hence, the knowledge of their propagation behavior is critical for designing structures with superior blast and impact protection capacities.To validate the computational procedure used, the structured shock-wave analysis is first applied to a homogeneous (i.e. single component) metallic system (commercially pure niobium). Next, the analysis is applied to the aforementioned MMC (in the limit of intermediate to strong shocks) when the contribution of the stress deviator to the total stress state can be neglected. Finally, the computational results are compared with their experimental counterparts available in the open literature in order to validate the dynamic-mixture method used.     

A highly efficient user-defined finite element for load distribution analysis of large-scale bolted composite structures

This paper presents the development of a highly efficient user-defined finite element for modelling the bolt-load distribution in large-scale composite structures. The method is a combined analytical/numerical approach and is capable of representing the full non-linear load-displacement behaviour of bolted composite joints both up to, and including, joint failure. In the elastic range, the method is generic and is a numerical extension of a closed-form method capable of modelling the load distribution in single-column joints. A semi-empirical approach is used to model failure initiation and energy absorption in the joint and this has been successfully applied in models of single-bolt, single-lap joints. In terms of large-scale applications, the method is validated against an experimental study of complex load distributions in multi-row, multi-column joints. The method is robust, accurate and highly efficient, thus demonstrating its potential as a time/cost saving design tool for the aerospace industry and indeed other industries utilising bolted composite structures.     

A new damage model for composite laminates

Aircraft composite structures must have high stiffness and strength with low weight, which can guarantee the increase of the pay-load for airplanes without losing airworthiness. However, the mechanical behavior of composite laminates is very complex due the inherent anisotropy and heterogeneity. Many researchers have developed different failure progressive analyses and damage models in order to predict the complex failure mechanisms. This work presents a damage model and progressive failure analysis that requires simple experimental tests and that achieves good accuracy. Firstly, the paper explains damage initiation and propagation criteria and a procedure to identify the material parameters. In the second stage, the model was implemented as a UMAT (User Material Subroutine), which is linked to finite element software, ABAQUS™, in order to predict the composite structures behavior. Afterwards, some case studies, mainly off-axis coupons under tensile or compression loads, with different types of stacking sequence were analyzed using the proposed material model. Finally, the computational results were compared to the experimental results, verifying the capability of the damage model in order to predict the composite structure behavior.     

A new estimator for sensitivity analysis of model output: An application to the e-business readiness composite indicator

In this paper we propose and test a generalisation of the method originally proposed by Sobol’, and recently extended by Saltelli, to estimate the first-order and total effect sensitivity indices. Exploiting the symmetries and the dualities of the formulas, we obtain additional estimates of first-order and total indices at no extra computational cost. We test the technique on a case study involving the construction of a composite indicator of e-business readiness, which is part of the initiative “e-Readiness of European enterprises” of the European Commission “e-Europe 2005” action plan. The method is used to assess the contribution of uncertainties in (a) the weights of the component indicators and (b) the imputation of missing data on the composite indicator values for several European countries.     

Simulating crack growth and failure in a composite: A vector model for a layered composite material

Summary A model has been proposed for a layered composite having an inhomogeneous microstructure. It is represented as the union of vector spaces for the mechanical characteristics of the material and the volume contents of the layers. The elastic parameters for each layer are considered as random functions of an arbitrarily defined volume. For a microscopically inhomogeneous material, one can consider a base volume such that the elastic properties of the material are retained and for which one can apply effective elastic moduli.The state of stress and strain in such a material is described by the components of the macrostress and macrostrain tensors with respect to a certain (structural) volume, which exceeds the base volume. The justification for that approach is demonstrated for a microscopically inhomogeneous orthotropic composite.Translated from Fiziko-Khimicheskaya Mekhanika Materialov, Vol. 26, No. 1, pp. 22–26, January–February, 1990.     

A parametric cubic modelling system for general solids of composite material

A new approach to modelling solids that are anisotropic and heterogeneous is presented with applications to structures of composite material. A parametric cubic modelling system is presented for lines, surfaces, volumes, and physical data that uses construction-in-context to generate numerical data. This system automates the construction of discrete element models and can reduce input data requirements by more than an order of magnitude. A tricubic isoparametric discrete element is presented that does not require displacement derivatives to define connectivity. This element is capable of exact displacement and strain continuity over a surface while permitting strain discontinuities at heterogeneous material interfaces. The shape of an element can be any hexahedron, pentahedron, or tetrahedron and the material properties are allowed to vary over the volume. Evaluation of modelling error with respect to closed-form solutions for curved geometries indicate a single element can model up to 90-degree segments with stresses accurate to 1 per cent. Applications of the system to composite structures are presented for interlaminar edge effects and attachment stresses in a sandwich panel.     

A patient-specific computational model of hypoxia-modulated radiation resistance in glioblastoma using 18F-FMISO-PET

Glioblastoma multiforme (GBM) is a highly invasive primary brain tumour that has poor prognosis despite aggressive treatment. A hallmark of these tumours is diffuse invasion into the surrounding brain, necessitating a multi-modal treatment approach, including surgery, radiation and chemotherapy. We have previously demonstrated the ability of our model to predict radiographic response immediately following radiation therapy in individual GBM patients using a simplified geometry of the brain and theoretical radiation dose. Using only two pre-treatment magnetic resonance imaging scans, we calculate net rates of proliferation and invasion as well as radiation sensitivity for a patient''s disease. Here, we present the application of our clinically targeted modelling approach to a single glioblastoma patient as a demonstration of our method. We apply our model in the full three-dimensional architecture of the brain to quantify the effects of regional resistance to radiation owing to hypoxia in vivo determined by [¹⁸F]-fluoromisonidazole positron emission tomography (FMISO-PET) and the patient-specific three-dimensional radiation treatment plan. Incorporation of hypoxia into our model with FMISO-PET increases the model–data agreement by an order of magnitude. This improvement was robust to our definition of hypoxia or the degree of radiation resistance quantified with the FMISO-PET image and our computational model, respectively. This work demonstrates a useful application of patient-specific modelling in personalized medicine and how mathematical modelling has the potential to unify multi-modality imaging and radiation treatment planning.     

Integrated dopaminergic neuronal model with reduced intracellular processes and inhibitory autoreceptors

Dopamine (DA) is an important neurotransmitter for multiple brain functions, and dysfunctions of the dopaminergic system are implicated in neurological and neuropsychiatric disorders. Although the dopaminergic system has been studied at multiple levels, an integrated and efficient computational model that bridges from molecular to neuronal circuit level is still lacking. In this study, the authors aim to develop a realistic yet efficient computational model of a dopaminergic pre‐synaptic terminal. They first systematically perturb the variables/substrates of an established computational model of DA synthesis, release and uptake, and based on their relative dynamical timescales and steady‐state changes, approximate and reduce the model into two versions: one for simulating hourly timescale, and another for millisecond timescale. They show that the original and reduced models exhibit rather similar steady and perturbed states, whereas the reduced models are more computationally efficient and illuminate the underlying key mechanisms. They then incorporate the reduced fast model into a spiking neuronal model that can realistically simulate the spiking behaviour of dopaminergic neurons. In addition, they successfully include autoreceptor‐mediated inhibitory current explicitly in the neuronal model. This integrated computational model provides the first step toward an efficient computational platform for realistic multiscale simulation of dopaminergic systems in in silico neuropharmacology.Inspec keywords: neurophysiology, organic compounds, brain, medical disordersOther keywords: integrated dopaminergic neuronal model, reduced intracellular processes, inhibitory autoreceptors, neurotransmitter, multiple brain functions, dysfunctions, neurological disorders, neuropsychiatric disorders, computational model, molecular level, neuronal‐circuit level, dopaminergic presynaptic terminal, relative dynamical timescales, steady perturbed states, reduced fast model, spiking neuronal model, autoreceptor‐mediated inhibitory current, integrated computational model, efficient computational platform, realistic multiscale simulation, in silico neuropharmacology     

Variational multiscale approach to enforce perfect bond in multiple-point constraint applications when forming composite beams

Composite laminates that consist of two or more layers find widespread applications in a variety of engineering structures. In the computational modelling of composite laminates, the layers can be stacked together and connected conveniently at the nodes by using multiple-point constraints (MPCs). However, this type of modelling leads to weakening of the kinematic constraint conditions imposed by the bond between the juxtaposed layers and as a consequence, MPCs application at the nodes produces behaviour that is softer than the perfectly bonded composite beam behaviour. The work herein shows that when kinematic conditions for composite action are weakly imposed in the variational form, they can be enforced in the point-wise sense by proper selection of the interpolation field or otherwise reinforced by using variational multiscale approach without modifying the kinematic model. The originality of the approach presented herein is in the interpretation of the MPCs application as the solution in a superfluously extended space because of the weakening in the kinematic constraints. It is shown that the perfect bond between the composite beam layers can be recovered by excluding the identified fine-scale effect from the solution of the multiple point constraint application. The convergence characteristic of the finite element formulation is also improved by using the variational multi-scale approach. It is also shown that the fine-scale effects can be represented by using extra fictitious elements and springs, which offers a direct correction technique in modelling of composite beams that is especially useful when access to the numerical procedure is limited.