Representative Volume Element Of Composite Research Articles

The lateral confinement effect on the interfacial crack in hybrid composites under uniaxial compression

The effect of hybridization on the interface crack growth along the fiber is predicted from numerical and analytical modelling approaches. A three-phase hybrid composite representative volume element (RVE) with an adjustable hybrid ratio and an initial interfacial crack is modelled. The fracture parameters and composite strength are computed from finite element analysis using VCCT approach in Ansys Workbench. A fracture energy-based mathematical model with a steady state crack growth is implemented to compute the hybrid composite splitting failure strength. The results show an enhancement in the compressive splitting strength with hybridization due to lateral confinement effect on the interfacial crack.

Representative volume element: Existence and extent in cracked heterogeneous medium

Acknowledging the ever-increasing demand for composites in the engineering industry, this paper focuses on the failure of composites at the microscale and augmenting the use of multiscale modelling techniques to make them better for various applications. This work aims to increase the representativeness of the volume element by attenuating the mesh and size sensitivities in representative volume element (RVE) modelling. A technique to alleviate mesh sensitivity in RVE modelling is proposed, which equalises the fracture energy observed from computational analysis with the real phenomenon, thereby keeping the response independent of the bandwidth of strain localisation. Based on the hypothesis that ensuring periodicity of strain, in addition to displacement periodicity across the domain boundary and supplementing the capability of periodic boundary conditions (PBCs) to attenuate the size dependency in RVE modelling, a set of modified PBCs (MPBCs) are formulated. One thousand two hundred RVE samples falling into combinations of five fibre volume fractions and four RVE sizes are analysed under transverse loading, and the ability of MPBCs to attenuate the effect of RVE size on the precision of material response, particularly in the softening regime, is verified. This work also focuses on various factors affecting damage initiation in 2D composite RVEs. The arrangement of a pair of fibres with their members placed close to each other, such that the angle between the direction of loading and an imaginary line drawn between their centres is less, is observed to make the region between them more favourable to damage.

Physically recurrent neural networks for path-dependent heterogeneous materials: Embedding constitutive models in a data-driven surrogate

Driven by the need to accelerate numerical simulations, the use of machine learning techniques is rapidly growing in the field of computational solid mechanics. Their application is especially advantageous in concurrent multiscale finite element analysis (FE2) due to the exceedingly high computational costs often associated with it and the high number of similar micromechanical analyses involved. To tackle the issue, using surrogate models to approximate the microscopic behavior and accelerate the simulations is a promising and increasingly popular strategy. However, several challenges related to their data-driven nature compromise the reliability of surrogate models in material modeling. The alternative explored in this work is to reintroduce some of the physics-based knowledge of classical constitutive modeling into a neural network by employing the actual material models used in the full-order micromodel to introduce non-linearity. Thus, path-dependency arises naturally since every material model in the layer keeps track of its own internal variables. For the numerical examples, a composite Representative Volume Element with elastic fibers and elasto-plastic matrix material is used as the microscopic model. The network is tested in a series of challenging scenarios and its performance is compared to that of a state-of-the-art Recurrent Neural Network (RNN). A remarkable outcome of the novel framework is the ability to naturally predict unloading/reloading behavior without ever seeing it during training, a stark contrast with popular but data-hungry models such as RNNs. Finally, the proposed network is applied to FE2 examples to assess its robustness for application in nonlinear finite element analysis.

Investigation on mechanical properties of ZTA+ Cr3C2 + Ni reinforced EN31 steel-based composite material: Micromechanical finite-element analysis

The present investigation deals with the development of EN31 steel-based metal matrix composite material under the ultrasonic vibration effect by providing 20 kHz frequency. In the process of the development of composite material, primary and secondary reinforcement has been taken as zirconia toughened alumina (ZTA) and Cr3C2 (chromium (II) carbide), respectively. The Ni has also been taken as dissolving reinforcement material and its weight percentage (wt.%) is kept constant at 2.5%. The variation in ZTA weight percentage was selected between 1.25% and 10%. Furthermore, the weight percentage of Cr3C2 has been kept constant (2.5 wt.%) throughout the development of different composite samples. The microstructural investigation indicated the fair distribution of reinforcement particles up to the 3.75 wt.% of ZTA, developed with the ultrasonic vibration effect. Furthermore, the addition of 2.5 wt.% of nickel in the EN31 steel has improved the wettability of ZTA and Cr3C2 particles. The best values of hardness (254.22 BHN) and tensile strength (892.15 MPa) were achieved with the composition of EN31/3.75 wt.% ZTA/2.5 wt.% Cr3C2/2.5 wt.% Ni composite material sample. Furthermore, the tensile strength and hardness of EN31 steel matrix material were improved by about 45.065% and 100.36% respectively. The addition of ZTA and Cr3C2 decreases the ductility of EN31 steel matrix material. The addition of 2.5wt.% Ni powder with ZTA+ Cr3C2 improved the ductility of EN31 steel. The results revealed that the mechanical properties (tensile strength, hardness, and ductility) of the developed composite material were further improved after performing the heat treatment process. Furthermore, an approach has been made to investigate the micro-mechanical deformation of EN31/3.75 wt.% ZTA/2.5 wt.% Cr3C2 metal matrix composite representative volume element (size: 225 × 225 × 225 nm) with finite-element analysis (FEA). The maximum stress (895.60 MPa) is generated at matrix–particle interfaces, which is the main reason for failure. The percentage difference between FEA and experimental results was less than 10%.

Concurrent n-scale modeling for non-orthogonal woven composite

Concurrent analysis of composite materials can provide the interaction among scales for better composite design, analysis, and performance prediction. A data-driven concurrent n-scale modeling approach (\(\text {FExSCA}^\text {n-1}\)) is adopted in this paper for woven composites utilizing a mechanistic reduced order model (ROM) called Self-consistent Clustering Analysis (SCA). We demonstrated this concurrent multiscale modeling theory with a \(\text {FExSCA}^2\) approach to study the 3-scale woven carbon fiber reinforced polymer (CFRP) laminate structure. \(\text {FExSCA}^2\) significantly reduced expensive 3D nested composite representative volume element (RVE) computation for woven and unidirectional (UD) composite structures by developing a material database. The modeling procedure is established by integrating the material database into a woven CFRP structural numerical model, formulating a concurrent 3-scale modeling framework. This framework provides an accurate prediction for the structural performance (e.g., nonlinear structural behavior under tensile load), as well as the woven and UD physics field evolution. The concurrent modeling results are validated against physical tests that link structural performance to the basic material microstructures. The proposed methodology provides a comprehensive predictive modeling procedure applicable to general composite materials aiming to reduce laborious experiments needed.

An Accuracy Comparison of Micromechanics Models of Particulate Composites against Microstructure-Free Finite Element Modeling.

Micromechanics models of composite materials are preferred in the analysis and design of composites for their high computational efficiency. However, the accuracy of the micromechanics models varies widely, depending on the volume fraction of inclusions and the contrast of phase properties, which have not been thoroughly studied, primarily due to the lack of complete and representative experimental data. The recently developed microstructure-free finite element modeling (MF-FEM) is based on the fact that, for a particulate-reinforced composite, if the characteristic size of the inclusions is much smaller than the composite representative volume element (RVE), the elastic properties of the RVE are independent of inclusion shape and size. MF-FEM has a number of advantages over the conventional microstructure-based finite element modeling. MF-FEM predictions have good to excellent agreement with the reported experiment results. In this study, predictions produced by MF-FEM are used in replace of experimental data to compare the accuracy of selected micromechanics models of particulate composites. The results indicate that, only if both the contrasts in phase Young’s moduli and phase Poisson’s ratios are small, the micromechanics models are able to produce accurate predictions. In other cases, they are more or less inaccurate. This study may serve as a guide for the appropriate use of the micromechanics models.

Pore tortuosity and diffusivity of porous composite RVEs composed of random sequential additions of polydisperse superellipsoidal particles

Understanding the effects of particle configurations on their surrounding pore tortuosity and the diffusivity of porous composites is very critical to the durability evaluations of fuel cell electrodes, filtration membranes, polymer foams, ceramics, and powder beds. It has been a key but unresolved issue how to accurately probe the tortuosity of pore space interstitial to non-spherical particles and its influence on the diffusivity of porous composites. This work proposes two powerful numerical strategies that one is a direction-guided rapidly exploring random tree (DGRRT) method and another is a dual-probability-Brownian motion (DP-BM) scheme, to respectively explore the nonlinear pore tortuosity and the effective diffusivity of porous composites, the representative volume element (RVE) of which is regarded as a two-phase composite composed of the random sequential addition (RSA) of superellipsoidal particles with polydispersity in size under periodic boundary conditions and their supplementary set as complex pore space at a microscopic level. Both numerical models are validated to be capable of accurately obtaining the pore tortuosity and the effective diffusivity of porous composites by comparing with extensive theoretical data reported in the literature, which can be viewed as general strategies suitable for detecting the pore tortuosity and diffusivity-like transport properties of porous composites. Moreover, we utilize the proposed strategies to investigate the effects of superellipsoidal particle shapes, volume fraction, maximum particle size, and particle size distribution, on the pore tortuosity and the effective diffusivity of porous composites. The derived results show the affinity to particle component-pore tortuosity-diffusivity of porous composites, which can provide sound guidance for the design and optimization of composites.

Optimization of weight and elastic properties for unidirectional glass fiber reinforced composites

Glass fibers reinforcing composites (GFRC) are the most common industrial materials due to their low weight and superior strength. Microstructure modeling provides a practical approach for predicting the behavior of the composite based on the constituent's property. The weight and mechanical properties of composite materials play a significant role in various applications such as aviation, marines, and vehicles industries. In this study, a microstructure model of (GFRC) is developed for a multi-objective optimization problem involving trade-offs between weight minimizing and material stiffness-enhancing. A finite element model of a representative volume element (RVE) of a material's microstructure is used to predict the elastic properties of the fiber and the matrix composites. Composite properties such as elasticity and density can be obtained directly from the RVE and extrapolated to a larger scale. The representative volume element (RVE) is generated by using commercial software (Abaqus); then, the non-GUI mode is called by Isight Software to solve multi-objective optimization by using Archive based Micro Genetic (AMGA) Algorithm to obtain optimum design of composite RVE.

Numerical prediction of elastic properties for carbon nanotubes reinforced composites using a multi-scale method

The main aim of this research was to investigate longitudinal elastic and effective modulus of composites reinforced with zigzag and armchair single-walled (CNT) and multi-walled carbon nanotubes (MWCNT) with different volume fractions and aspect ratios via finite element simulation. A three-phased volume element was adopted for the modeling of nanocomposite behavior and nonlinear spring elements were used to model interphase part joints and the effective force between nanotubes and resin were determined based on Lennard-Jones potential. After the evaluation and validation of the model, elastic modulus and Poisson’s ratio of composites reinforced with zigzag and armchair CNTs with different volume fractions and aspect ratios were extracted. It was found that by increasing volume fraction and aspect ratio, elastic modulus of representative volume element of composite was increased and its Poisson’s ratio was decreased. At similar aspect ratio and volume fraction, the elastic modulus of composites reinforced with armchair CNTs and Poisson’s ratio of those reinforced with zigzag CNTs were higher. Also, results showed that elastic modulus of composite was independent from elastic modulus of interphase.

Evaluation and Modeling of the Fatigue Damage Behavior of Polymer Composites at Reversed Cyclic Loading.

Understanding the composite damage formation process and its impact on mechanical properties is a key step towards further improvement of material and higher use. For its accelerated application, furthermore, practice-related modeling strategies are to be established. In this collaborative study, the damage behavior of carbon fiber-reinforced composites under cyclic loading with load reversals is analyzed experimentally and numerically. The differences of crack density evolution during constant amplitude and tension-compression block-loading is characterized with the help of fatigue tests on cross-ply laminates. For clarifying the evolving stress-strain behavior of the matrix during static and fatigue long-term loading, creep, and fatigue experiments with subsequent fracture tests on neat resin samples are applied. The local stress redistribution in the composite material is later evaluated numerically using composite representative volume element (RVE) and matrix models under consideration of viscoelasticity. The experimental and numerical work reveals the strong influence of residual stresses and the range of cyclic tension stresses to the damage behavior. On the microscopic level, stress redistribution dependent on the mean stress takes place and a tendency of the matrix towards embrittlement was found. Therefore, it is mandatory to consider stress amplitude and means stress as inseparable load characteristic for fatigue assessment, which additionally is influenced by production-related and time-dependent residual stresses. The phenomenological findings are incorporated to a numerical simulation framework on the layer level to provide an improved engineering tool for designing composite structures.

The effect of mesh morphologies on the mesoscale Finite Element modelling of woven composites

Mesoscale Finite Element (FE) modelling methods of woven and braided composites have attracted great attention in recent years as they can provide high accuracy, especially in describing damage behaviour. One of the key factors that affects the results of such kind of simulations is the choice of the mesh morphology. The two most widely-applied meshing approaches at present are the voxel- and the volume-mesh; however, these two models have not been compared in detail with experimental data. Therefore, in the present work, both volume- and voxel-mesh models have been used to build a composite Representative Volume Element (RVE) made of glass-fibre woven fibre with Epoxy Ampreg 26. These FE models have been built in order to investigate the effects of the mesh morphology on the simulations under quasi-static tensile and shear loading conditions. The volume-mesh model provides a well correlated stress-strain relationship in comparison with the test results, while the voxel-mesh model predicts higher tension and shear properties. However, computational issues, such as negative volume and the stress concentration caused by the mesh, are observed in the volume-mesh model while the voxel-mesh is computationally more efficient, i.e. less time-consuming, in replicating the tension and shear tests with acceptable results.

Stress field and effective elastic moduli of periodic spheroidal particle composite with Gurtin-Murdoch interface

The periodic spheroidal particle nanocomposite with Gurtin-Murdoch type interface stress is considered. A complete semi-analytical solution to the unit cell model problem has been obtained by the multipole expansion method. To this end, the displacement perturbation field of the periodic array of inhomogeneities is expanded over a set of the periodic vector solutions of Lamé equation in spheroidal basis. An accurate fulfilling the interface conditions reduces the model boundary value problem to an infinite set of linear algebraic equations for the multipole strengths. The obtained solution provides evaluation of the displacement, strain and stress in every point of the unit cell being, at the same time, the representative volume element of composite. Surface averaging the local strain and stress fields yields an exact expression of the effective stiffness tensor of composite in terms of the induced dipole moment of spheroidal inhomogeneity. Numerical examples demonstrate an accuracy and computational efficiency of the developed approach and shows significant combined effect of the geometry and elastic properties of interface on the elastic fields and macroscopic stiffness of periodic nanocomposite.

A novel approach to impose periodic boundary condition on braided composite RVE model based on RPIM

Periodic boundary condition for the representative volume element (RVE) model of the 3D braided composite is required to predict the braided composite properties in the framework of mean field homogenization. Meanwhile, generating periodic mesh is quite challenging due to complicated mesoscopic features for 3D braided composites. This paper presents a novel approach for the 3D braided composite RVE model by introducing radial point interpolation method (RPIM) to impose periodic boundary condition either on periodic or non-periodic mesh. Applied to a homogeneous and isotropic block and a 3D four-directional braided RVE model, it is demonstrated that the novel method is accurate for predicting FE results involving stress/strain values under 6 kinds of monotonic loading conditions and elastic constants for the braided composites.

Multi-scale computational homogenisation to predict the long-term durability of composite structures

A coupled hygro-thermo-mechanical computational model is proposed for fibre reinforced polymers, formulated within the framework of Computational Homogenisation (CH). At each macrostructure Gauss point, constitutive matrices for thermal, moisture transport and mechanical responses are calculated from CH of the underlying representative volume element (RVE). A degradation model, developed from experimental data relating evolution of mechanical properties over time for a given exposure temperature and moisture concentration is also developed and incorporated in the proposed computational model. A unified approach is used to impose the RVE boundary conditions, which allows convenient switching between linear Dirichlet, uniform Neumann and periodic boundary conditions. A plain weave textile composite RVE consisting of yarns embedded in a matrix is considered in this case. Matrix and yarns are considered as isotropic and transversely isotropic materials respectively. Furthermore, the computational framework utilises hierarchic basis functions and designed to take advantage of distributed memory high performance computing.

Maxwell homogenization scheme as a rigorous method of micromechanics: Application to effective conductivity of a composite with spheroidal particles

Maxwell’s homogenization scheme (MHS) is formulated in terms of the dipole moments and property contribution tensors of the representative volume element (RVE) of actual composite and of the equivalent inclusion. Provided interactions between the inclusions taken into account, this scheme is rigorous in the sense that the effective properties converge to their exact values with increasing RVE size. To demonstrate its potential, the conductivity problem for a composite with aligned spheroidal inclusions is considered. The convergence of the solution is explored and an effect of structural parameters on the effective conductivity of the composite has been evaluated. The methodological issues of MHS application are discussed including an appropriate shape of the composite RVE and of the equivalent inclusion. It is shown that intelligent (accounting for microstructure of composite) shape choice accelerates convergence of the solution. Practical importance of the developed approach consists in its direct applicability to the images of microstructure obtained by the experimental methods. This makes MHS a convenient tool for estimating effective properties of composites from the observed fragments of microstructure.

Uncertainty in effective elastic properties of particle filled polymers by the Monte-Carlo simulation

The main issue of this paper is to present statistical computational procedure for a determination of the effective elastic parameters for polymers filled with rubber particles. The homogenized elasticity tensor components are derived both as the variational upper and lower bounds as well as the solution for the cell problem on the composite Representative Volume Element. Probabilistic simulation is provided using both Monte-Carlo simulation technique and the generalized stochastic perturbation technique implemented in the symbolic computer algebra system MAPLE and, separately, together with the FEM-oriented code MCCEFF. Finally, up to fourth order probabilistic moments and coefficients of the homogenized tensor for the elastomers are computed as functions of the polymer’s and particles’ Young’s moduli coefficients of variation. This study gives the basis for further homogenization-based experiments, where the hyperelastic constitutive model will replace the classical Hookean one applied here.

Investigation of stress transfer in carbon nanotube reinforced composites using a multi-scale finite element approach

This paper describes a micromechanical hybrid finite element approach to study the stress transfer in single-walled carbon nanotube reinforced composites. A three-dimensional representative volume element of composite has been considered in this analysis. The nanotube is modeled taking into account its atomistic microstructure. The matrix material is modeled as continuum utilizing appropriate solid finite elements. Spring-based elements are used to describe the behavior of the single-walled carbon nanotubes. The interfacial effects between the two materials are simulated by appropriate stiffness variations defining a heterogeneous region. The model presents a reasonable behavior, with respect to composite effective mechanical properties, comparing with results available in the literature. The effects of carbon nanotube volume fraction, interfacial stiffness and elastic modulus of matrix on stresses are analyzed in details.

Design sensitivity analysis for the homogenized elasticity tensor of a polymer filled with rubber particles

The main purpose of this work is the computational simulation of the sensitivity coefficients of the homogenized tensor for a polymer filled with rubber particles with respect to the material parameters of the constituents. The Representative Volume Element (RVE) of this composite contains a single spherical particle, and the composite components are treated as homogeneous isotropic media, resulting in an isotropic effective homogenized material. The sensitivity analysis presented in this paper is performed via the provided semi-analytical technique using the commercial FEM code ABAQUS and the symbolic computation package MAPLE. The analytical method applied for comparison uses the additional algebraic formulas derived for the homogenized tensor for a medium filled with spherical inclusions, while the FEM-based technique employs the polynomial response functions recovered from the Weighted Least-Squares Method. The homogenization technique consists of equating the strain energies for the real composite and the artificial isotropic material characterized by the effective elasticity tensor. The homogenization problem is solved using ABAQUS by the application of uniform deformations on specific outer surfaces of the composite RVE and the use of tetrahedral finite elements C3D4. The energy approach will allow for the future application of more realistic constitutive models of rubber-filled polymers such as that of Mullins and for RVEs of larger size that contain an agglomeration of rubber particles.

A Coupled Fiber-Matrix Model Demonstrates Highly Inhomogeneous Microstructural Interactions in Soft Tissues Under Tensile Load

A soft tissue's macroscopic behavior is largely determined by its microstructural components (often a collagen fiber network surrounded by a nonfibrillar matrix (NFM)). In the present study, a coupled fiber-matrix model was developed to fully quantify the internal stress field within such a tissue and to explore interactions between the collagen fiber network and nonfibrillar matrix (NFM). Voronoi tessellations (representing collagen networks) were embedded in a continuous three-dimensional NFM. Fibers were represented as one-dimensional nonlinear springs and the NFM, meshed via tetrahedra, was modeled as a compressible neo-Hookean solid. Multidimensional finite element modeling was employed in order to couple the two tissue components and uniaxial tension was applied to the composite representative volume element (RVE). In terms of the overall RVE response (average stress, fiber orientation, and Poisson's ratio), the coupled fiber-matrix model yielded results consistent with those obtained using a previously developed parallel model based upon superposition. The detailed stress field in the composite RVE demonstrated the high degree of inhomogeneity in NFM mechanics, which cannot be addressed by a parallel model. Distributions of maximum/minimum principal stresses in the NFM showed a transition from fiber-dominated to matrix-dominated behavior as the matrix shear modulus increased. The matrix-dominated behavior also included a shift in the fiber kinematics toward the affine limit. We conclude that if only gross averaged parameters are of interest, parallel-type models are suitable. If, however, one is concerned with phenomena, such as individual cell-fiber interactions or tissue failure that could be altered by local variations in the stress field, then the detailed model is necessary in spite of its higher computational cost.

Parametric Modeling Method for Composite Microstructure Virtual Testing

A method of parametric modeling composite microstructure is proposed. It can be used for composite microstructure virtual testing and optimization procedure. Considering the fiber random distribution features of composite microstructure and the flaw distribution in the fibers, a three dimensional parametric model has been built in this paper. Then, the sizes of the composite representative volume element (RVE) generated by the method are determined by moving-window function method. These models are close to reality and can be used for further virtual testing. Finally, numerical experiment is presented by the secondary development of the finite element packages (ABAQUS) via Python language programming to verify the proposed method. The following conclusions are obtained: (i) fiber volume fraction of the composite structure model reaches 65% by the modeling method, which meets the majority engineering demands; (ii) stress distribution feature of RVE generated by using moving-window function method coincides with general prediction.