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Advanced high-strength steel (AHSS) is of great technological interest in automotive lightweight applications. The dual-phase (DP) steel with a higher volume fraction of martensite has been rarely studied. In this work, the micromechanical deformation incompatibility of DP1180 steel was analyzed by a microstructure-based representative volume element (RVE) model. Via the electron-backscattered diffraction (EBSD) and the open-source software DREAM.3D, the statistically real microstructure-based RVE model was established. The flow curve of ferrite was obtained by the dislocation-based method. And the flow curve of martensite was obtained by the isostrain method (ISM) and the non-isostrain method (NISM). The simulation results showed good coincidence with the experiments. Furthermore, the ISM and the NISM were well clarified and improved. The microscale stress and strain in ferrite and martensite are approximately normal distributions due to the deformation incompatibility. The simulations verified that martensite carries much higher stress than ferrite. The mean value of strain in martensite is smaller than that in ferrite. And the strain variances of ferrite and martensite are similar. A larger variation range of stress triaxiality in ferrite indicates that the ferrite has gone through a more complex stress state. While the martensite has been approaching from the tension–compression state to the uniaxial-tension state. Consequently, the strain localization and damage initiation are predicted to be preferentially through ferrite compared to martensite, which is in good agreement with the results of the in situ tensile test. This paper provides a detailed analysis of the deformation incompatibility of the DP steel, especially in which the volume fraction of martensite is larger than that of ferrite. And it has theoretical significance for accurately predicting the micromechanical deformation behavior of multi-phase materials. [ABSTRACT FROM AUTHOR]

Semi-flexible pavement (SFP) material is a composite comprising cement, coarse aggregates and asphalt mortar, which has complex mechanical properties. Traditional experimental methods struggle to accurately quantify the effect of each phase and their interfaces on the SFP's mechanical properties. Micromechanical modelling based on finite element method offers a promising solution. In this study, a new micromechanical model for SFP is proposed, idealizing the material by representative volume elements. SFP mesostructure is represented as a simplified five element composite consisting of cement, asphalt mortar, aggregate, pore and cement-asphalt mortar interface. Periodic boundary conditions are used to simulate an infinite repetitive structure within a finite computational domain. The resulting model allows evaluating the stiffness and damage resistance of SFP in a computationally efficient manner. This model is utilized to explore the mechanical properties of SFPs and the results are compared with the experimental findings. The results show that the model captures the uniaxial compressive strength and stiffness for all materials examined. The model is further used to evaluate the effect of properties of individual elements of SFP on its stiffness and strength. The feasibility of using the proposed modelling approach to optimize the material design of SFP is discussed.

Austenitic stainless steel welds (ASSWs) of nuclear components undergo aging-related degradations caused by high temperature and neutron radiation. Since irradiation leads to the change of material characteristics, relevant quantification is important for long-term operation, but limitations exist. Although ion irradiation is utilized to emulate neutron irradiation, its penetration depth is too shallow to measure bulk properties. In this study, a systematic approach was suggested to estimate mechanical properties of ion irradiated 308 ASSW. First of all, weld specimens were irradiated by 2 MeV proton to 1 and 10 dpa. Microstructure evolutions due to irradiation in δ-ferrite and austenite phases were characterized and micropillar compression tests were performed. In succession, dislocation density based stress-strain (S–S) relationships and quantification models of irradiation defects were adopted to define phases in finite element analyses. Resultant microscopic S–S curves were compared to verify material parameters. Finally, macroscopic behaviors were calculated by multiscale simulations using real microstructure based representative volume element (RVE). Validity of the approach was verified for the unirradiated specimens such that the estimated S–S curves and 0.2% offset yield strengths (YSs) which was 363.14 MPa were in 10% agreement with test. For irradiated specimens, the estimated YS were 917.41 MPa in 9% agreement.

Herein, attempts are made to estimate the mechanical properties using microstructure‐based finite element (FE) modeling and validate these results with the experimental results. The two high‐carbon steel specimens are hot‐rolled and air‐cooled to develop ferrite–pearlite microstructures. Different characterizations are utilized to observe microstructures as well as Vickers hardness and tensile tests are carried out to determine the mechanical properties. Two high‐resolution scanning electron micrographs are chosen for representative volume element‐based FE analyses for modeling the mechanical behavior of ferrite–cementite microstructure. Object‐oriented finite elements (OOF2) and Abaqus FEA 6.14 software are used to estimate the elastic and elastoplastic behavior assuming plane stress conditions. The correlation between cementite lamellae orientation and the predicted elastoplastic properties is investigated and compared with the experimental results. The influence of image size and mesh size on the predicted true stress–true strain behavior is discussed. The hard and brittle cementite lamellae face maximum stress while the softer ferrite matrix experiences maximum strain. It is found that strain accumulation is maximum at the interfaces of ferrite and cementite. These findings are further validated by the microvoid and crack initiation spots in the fracture surface and subsurface micrographs of broken tensile specimens. [ABSTRACT FROM AUTHOR]

Inter-fibre failure analysis of carbon fibre-reinforced polymer (CFRP) composites, under biaxial loading conditions, has been a longstanding challenge and is addressed in this study. Biaxial failure analysis of IM7/8552 CFRP unidirectional (UD) composites is conducted under various stress states. Two widely accepted failure criteria, the interactive Tsai-Wu and non-interactive Hashin failure criteria, are comprehensively assessed with finite element-based micromechanical analysis. High-fidelity three-dimensional representative volume elements (RVEs) are subjected to biaxial loadings with imposed periodic boundary conditions. Carbon fibres are assumed to be transversely isotropic and linearly elastic. The Drucker-Prager plastic damage constitutive model and cohesive zone model are utilised to simulate the mechanical response of the matrix and fibre-matrix interface, respectively. Coulomb friction is assumed between the fibres and matrix after interface failure. Two sets of biaxial loading scenarios (i.e. transverse stress dominated and shear stress dominated) with the associated failure modes are selected for the failure analysis and assessment of these failure criteria. A data-driven failure envelope for the composites under biaxial loadings is developed using a univariate cubic spline function. Failure mode transition points are determined under biaxial loadings. It is found that the micromechanics-based numerical model is effective in assessing these two existing criteria. [ABSTRACT FROM AUTHOR]

The present study provides a thorough analysis of the influence of filament orientation on the tensile stiffness of 3D-printed structures. This exploration employs a combination of numerical simulations and experimental trials, providing an extensive understanding of additive manufacturing, particularly 3D printing. This process involves layer-by-layer material deposition to produce three-dimensional objects. The examination specifically targets PLA-based 3D printed structures created using Fused Filament Fabrication (FFF) technology and subjects them to rigorous evaluations using a universal tensile testing machine. Additionally, this approach combines Representative Volume Element (RVE) and Classical Lamination Theory (CLT) techniques to extrapolate the mechanical properties of the test material. Although the initial methodology faces challenges in determining the shear modulus with precision, an in-depth investigation results in enhanced accuracy. Furthermore, this study introduces a parametric RVE numerical method, demonstrating its resilience in handling sensitivity to shear modulus. A comparative study of results derived from both the analytical methods and experimental trials involving five series of samples with varied layups reveals that the newly proposed numerical method shows a stronger correlation with the experimental outcomes, delivering a relative error margin of up to 8%. [ABSTRACT FROM AUTHOR]

Computational approaches could provide a viable and cost-effective alternative to expensive experiments for accurately evaluating the nonlinear constitutive behavior of cementitious nanocomposite materials. In the present study, the mechanical properties of cement paste reinforced with multi-wall carbon nanotubes (MWCNTs) are examined experimentally and numerically. A multiscale computational approach is adopted in order to verify the experimental results. For this scope, a random sequential adsorption algorithm was developed to generate non-overlapping matrix-inclusion three-dimensional (3D) representative volume elements (RVEs), considering the inclusions as straight elements. Nonlinear finite element analyses (FEA) were performed, and the homogenized elastic and inelastic mechanical properties were computed. The use of a multiscale computational approach to accurately evaluate the nonlinear constitutive behavior of cementitious materials has rarely been explored before. For this purpose, the RVEs were analyzed both in pure tension and compression. Young's modulus as well compressive and tensile strength results were compared and eventually matched the experimental values. Moreover, the effect of MWCNTs on the nonlinear stress–strain behavior of reinforced cement paste was noted. Subsequently, three-point bending tests were conducted, and the stress–strain behavior was verified with FEA in the macro scale. The numerical modeling reveals a positive correlation between the concentration of MWCNTs and improved mechanical properties, assuming ideal dispersion. However, it also highlights the impact of practical limitations, such as imperfect dispersion and potential defects, which can deteriorate the mechanical properties that are observed in the experimental results. Among the different cases studied, that with a 0.1 wt% MWCNTs/CP composite demonstrated the closest agreement between the numerical model and the experimental measurements. The numerical model achieved the best accuracy in estimating the Young's modulus (underestimation of 13%), compressive strength (overestimation of 1%), and tensile strength (underestimation of 6%) compared to other cases. Overall, these numerical findings contribute significantly to understanding the mechanical behavior of the nanocomposite material and offer valuable guidance for optimizing cement-based composites for engineering applications. [ABSTRACT FROM AUTHOR]

The performance of fiber‐reinforced composites is not only determined by their constituents, but also by the spatial distribution of inclusions. The traditional random distribution algorithm only considers the randomness of its relative position, and every newly generated fiber has to be checked with all the existing fibers, which requires a large amount of calculation. In this paper, inspired by the spreading process that the fibers are not arranged randomly, but the forces acting on the upper and lower rows of fibers. A random fiber distribution algorithm based on partition randomness is proposed, and a microscopic model of in‐plane fibers with random distribution is established. The maximum volume fraction of fibers generated by the algorithm is 75%, and the generation time is less than 20s. Statistical characterization and finite element analysis of the structure generated by the algorithm are compared with the experimental data to verify the randomness and effectiveness of fibers. The algorithm overcomes the jamming limit of the traditional hard‐core method, and can efficiently generate random microstructure models with different volume fractions, which can be a promising alternative for modeling and analysis of unidirectional fiber‐reinforced composites. [ABSTRACT FROM AUTHOR]

In this work, a constitutive model is developed by incorporating precipitation strengthening into a dislocation-density-based crystal plasticity (CP) model to simulate the mechanical properties of 2024 aluminium alloy (AA). The proposed model considers the contributions of solid solution strengthening and strengthening from dislocation–precipitate interactions into the total slip resistance along with the forest hardening due to dislocation–dislocation interactions. A term accounting for the multiplication of dislocations due to their interactions with the non-shearable precipitates in the alloy is incorporated in the hardening law. The developed precipitation strengthening-based CP model is implemented into the crystal plasticity finite element method (CPFEM) for simulating the macroscopic mechanical behavior of AA2024-T3 alloy for uniaxial tension over various strain rates. The macroscopic response of the polycrystal representative volume element (RVE) used for simulations is computed using computational homogenization. The effect of meshing resolution on the RVE response is studied using four different mesh discretizations. Predictions of the macroscopic behavior by the developed model are in good agreement with the experimental findings. Additionally, the contribution of model parameters to the total uncertainty of the predicted stress has been assessed by conducting a sensitivity analysis. A parametric analysis with different precipitate radii and volume fractions has been done for finding the effect of precipitates on the macroscopic and localized deformation. [ABSTRACT FROM AUTHOR]

Multiscale FE 2 computations enable the consideration of the micro-mechanical material structure in macroscopical simulations. However, these computations are very time-consuming because of numerous evaluations of a representative volume element, which represents the microstructure. In contrast, neural networks as machine learning methods are very fast to evaluate once they are trained. Even the DNN-FE 2 approach is currently a known procedure, where deep neural networks (DNNs) are applied as a surrogate model of the representative volume element. In this contribution, however, a clear description of the algorithmic FE 2 structure and the particular integration of deep neural networks are explained in detail. This comprises a suitable training strategy, where particular knowledge of the material behavior is considered to reduce the required amount of training data, a study of the amount of training data required for reliable FE 2 simulations with special focus on the errors compared to conventional FE 2 simulations, and the implementation aspect to gain considerable speed-up. As it is known, the Sobolev training and automatic differentiation increase data efficiency, prediction accuracy and speed-up in comparison to using two different neural networks for stress and tangent matrix prediction. To gain a significant speed-up of the FE 2 computations, an efficient implementation of the trained neural network in a finite element code is provided. This is achieved by drawing on state-of-the-art high-performance computing libraries and just-in-time compilation yielding a maximum speed-up of a factor of more than 5000 compared to a reference FE 2 computation. Moreover, the deep neural network surrogate model is able to overcome load-step size limitations of the RVE computations in step-size controlled computations. [ABSTRACT FROM AUTHOR]

Crystal plasticity finite element (CPFEM) modeling of metals that can be age hardened consisting of second phase particles is extensively performed based on representative volume element (RVE) models. The RVE model is generated for ferritic low-carbon steel using the data obtained from microstructural observation through optical microscopy (OM) and electron backscatter diffraction (EBSD). The generated RVE is required to statistically represent the original material in terms of grain topology and texture in microscale, as well as the configuration of second phase particles in submicron scale. The multiscale, multi-phase nature of the generated RVE leads to a computationally expensive modeling procedure. To overcome this issue, an alternative multiscale modeling approach based on a homogenization scheme is proposed, in which the effect of second phase particles on deformation behavior is accounted for with no need for the explicit presence of particles in RVE. Lastly, a thorough parametric analysis is performed to investigate the sensitivity of the mechanical properties to the second phase particles in terms of size, volume fraction, geometrical distribution, and deformable or non-deformable properties of precipitates in the investigated material. The results show that the proposed multiscale modeling approach successfully accounts for the effect of second phase particles on deformation behavior, while the computational cost is reduced by more than 99%. In addition, the simulations show that the configuration of second phase particles at a microscale plays an important role in defining the mechanical behavior of the material. [ABSTRACT FROM AUTHOR]

Development of load-bearing fiber reinforced plastic (hereinafter referred to as FRP) composite structures in civil engineering, exploited under high temperatures, such as industrial chimneys and gas ducts, requires the knowledge of their long-term behavior under constant and cyclic mechanical and temperature loads. Such conditions mean that the viscoelasticity of FRP should be considered along with the thermal aging effect. This research is devoted to the effects of thermal aging on the viscoelastic behavior of polymers. Two sets of experiments were conducted: creep tensile tests and cyclic heating in a constrained state. The Kelvin–Voigt viscoelasticity model was used to determine the rheological parameters of binder from experimental creep curves. Cyclic heating was used to compare the behavior of normal and thermally aged binders and to evaluate the possibility of temperature stress accumulation. Fourier-transform infrared spectroscopy was used for polymer’s structural changes investigation. Both tests showed that non-aged glassed polymer (hereinafter referred to as GP) was prone to viscoelastic behavior, while the thermally aged GP lost viscosity and worked almost perfectly elastic. It was assumed that long heat treatment had caused changes in the inner structure of the GP, reducing the number of weak bonds and increasing the number of elastic ones. Therefore, the results show that the designing of FRP structures, exploited under thermomechanical load, requires using the elastic model while taking into account the properties of FRP after long-term heat treatment.

Abstract This study presents a new method to generate random fiber arrangements in a representative volume element model, which remains applicable at high fiber volume fractions. First of all, the fibers are arranged regularly to ensure accurate fiber volume fraction. Afterwards, disturbances are applied to all fibers to generate random arrangements. The image recognition technique and statistical analysis are used to quantitatively evaluate the randomness of the disturbed fiber arrangement. Eventually, the high efficiency of the method is verified by analyzing the consumption time of modeling, and its validity is also confirmed by comparing the calculated results with the tested results. [ABSTRACT FROM AUTHOR]

Abstract A micromechanical model implemented with the finite element method (FEM) using the representative volume element (RVE) approach is developed to investigate the creep compliance behavior of carbon nanotube (CNT)-polymer nanocomposites. Effects of the CNT waviness, orientation, volume fraction and aspect ratio on the creep compliance of the nanocomposite are examined. Contribution of the interphase region formed due to the interaction between CNTs and matrix to the nanocomposite creep behavior is considered. The nanocomposite creep behavior is affiliate on the waviness and orientation of CNTs. Increasing the volume fraction and length of CNT and interphase thickness improves the nanocomposite creep performance. [ABSTRACT FROM AUTHOR]

A homogenization method for the vibration analysis of periodic sandwich panels is presented. Periodic boundary conditions are applied to a representative volume element (RVE) of the structures. The complex responses of the RVE under eight sinusoidal excitations are calculated and the complex stiffness matrix of the sandwich panels is obtained by the direct-solution steady-state dynamic analysis (DSDA) using the finite element method (FEM) in the frequency domain. Based on equivalent single-layer (ESL) theory and finite element-modal strain energy (FE-MSE) method, the natural frequencies, the mode shapes and the loss factors of the structures are obtained by shell models. The effectiveness of the homogenization method is validated by using pyramidal lattice truss sandwich panels made of carbon fiber reinforced plastics (CFRP). The results obtained by the homogenization method are compared with those obtained by experiments and solid models. The effects of the number of cells and damping layers are discussed. [ABSTRACT FROM AUTHOR]

In this paper, a void closure model applicable to the general hot forming process has been proposed. Through the representative volume element (RVE) method, the influences of void shape, orientation, and stress state on void closure tendency were analysed. The void closure model was established so that it could consider these cross effects. The model calculates the changing void radius and orientation during deformation by considering the rate of change of the parameters affecting void deformation with respect to the effective strain. The model predicted the void closure tendency well on the RVE scale and predicted the void closure adequately in a multi-stage process with random voids. The results were compared with the stress-triaxiality-based (STB) model, which showed that the void closure model proposed in this study is applicable in general situations. A cogging process was analysed, and the degree of void closure at the end of each pass was compared with the calculated results of the void closure model. For the experimental verification of the proposed model, spherical and ellipsoid voids were placed in a rectangular specimen, and the radii of the voids after compression were measured. The measurement results were compared with the calculation results of the proposed model. [ABSTRACT FROM AUTHOR]

This work presents a computational study on the impact of carbon nanotube (CNT) enriched matrix on the performance of 1–3 lead-free piezoelectric periodic composites. Specifically, we investigate a piezoelectric composite system consisting of x 3 parallel aligned fibers of polycrystalline barium titanate (BaTiO3) embedded in a polydimethylsiloxane (PDMS) matrix doped with multiwalled CNT. The effective properties and several figures of merit have been obtained to evaluate the performance of this composite system as is typically done for these materials used for sensing, actuating, or harvesting applications. The results reveal that, in lead-free BaTiO3/PDMS piezocomposites, the addition of CNTs in the PDMS matrix should be f CNT ≈ 0. 5 f c "being f c the percolation threshold", but not higher. In another case, we will only improve the performance of the lead-free piezocomposite for sensing or actuating, but not for energy harvesting applications. This study provides insights into the use of multiwalled CNTs in lead-free piezocomposites and suggests the optimal concentration of CNTs to enhance their performance. The findings have potential implications for the development of new piezoelectric materials and devices for sensing and harvesting applications. [ABSTRACT FROM AUTHOR]

A new phase-field based method is proposed to represent the graphene reinforced composites and investigate the mechanical properties of the nanocomposites. The discrete graphene flakes are now represented with a continuous phase-field ϑ (x). Considering the extremely large aspect ratio of the graphene, both isotropic and anisotropic constitutions are used for the material at the transition region between the graphene and epoxy matrix. The present model is validated through comparison with shell based finite element model for the anisotropic constitution. The present model offers a simple way to model the thin flakes with a large aspect ratio reinforced composites in FEM software. [ABSTRACT FROM AUTHOR]

In this study, we investigate the relationship between interphase and Young's modulus influence in 3-phase composites for the design of graphene-based composites. We introduced the interphase concept for analyzes and developed a unidirectional unit cell based on RVE and varying the interphase thickness and Young's modulus. As a result, the presence of the interphase's affected the composites and graphene, which was related to stress and Young's modulus. Here, the effect of the interphase presence occurs depending on the thickness and also can observe through the stress-strain curve. Furthermore, we investigated that the interphase thickness determines the magnitude of the effects on graphene and composites, indicating a correlation proportional to the interphase thickness and Young's modulus. [ABSTRACT FROM AUTHOR]

In this paper, free vibration, modal and stress state analyses of honeycomb sandwich structures with different boundary conditions was investigated and major factors affecting the sandwich frequencies and stiffness due to material or parameter changes were determined. The representative volume element (RVE) method used in this work were analytically and numerically validated by comparing the obtained results to those available in literature. Firstly, unit cell method was used to capture the entire effects of different parameters on the free vibration of honeycomb sandwich structure in ANSYS. This study analyzed the natural frequencies of honeycomb sandwich structures with different core materials combination. The effects of foil thickness, boundary conditions, materials selection, density and presence of crack on sandwich structure were taken into consideration and examined. The proposed core had an inbuilt shaped reinforcement with different materials f [ABSTRACT FROM AUTHOR]

In this paper, a multiscale analysis method was proposed to simulate carbon nanoparticles (CNPs)−filled polymers which can be strain sensors applied in wearable electronic devices, flexible skin, and health monitoring fields. On the basis of the microstructure characteristics of the composite, a microscale representative volume element model of the CNPs−filled polymer was established using the improved nearest−neighbor algorithm. By finite element analysis, the variation of the junction widths of adjacent aggregates can be extracted from the simulation results. Then, according to the conductive mechanism of CNP−filled polymers, the composite was simplified as a circuit network composed of vast random resistors which were determined by the junction widths between adjacent aggregates. Hence, by taking junction widths as the link, the resistance variation of the CNPs−filled polymer with the strain can be obtained. To verify the proposed method, the electromechanical responses of silicone elastomer filled with different CNPs under different filling amounts were investigated numerically and experimentally, respectively, and the results were in good agreement. Therefore, the multiscale analysis method can not only reveal the strain−sensing mechanism of the composite from the microscale, but also effectively predict the electromechanical behavior of the CNPs−filled polymer with different material parameters. [ABSTRACT FROM AUTHOR]

The repeating nature of additive manufacturing (AM) translates into quasi-periodic repeating hierarchical microstructures, which vary depending on the working principle of the AM technology. The geometry and internal characteristics of these repeating microstructures affect the geometrical accuracy and mechanical properties of AM parts. We propose a modular and generic framework for AM microstructures to automatically determine a representative microstructural cell with average shape and microstructural information based on micrograph processing and morphological shape analyses. A general microstructural mapping procedure is presented to map and average different microstructural features inside the representative cell. Moreover, an extension of the method is proposed to recover a representative cell with a periodic shape as required for subsequent numerical micromechanical simulations under periodic boundary conditions to unravel process-structure–property relationships. The framework is demonstrated on a virtually generated microstructure and on the metallic and polymeric microstructure of two parts manufactured with different AM processes, showing the framework's versatility for different materials and AM technologies. The three test cases show the framework's modularity, where different procedures were applied to overcome the challenges of each particular case while keeping the primary method the same. We also discuss applications of the framework, such as enabling statistical investigations of spatial variations of the microstructural features across AM parts and providing essential input for microstructural and mechanical numerical simulations.

It is significant to determine the macroscopic mechanical properties of composite materials with complex microstructure efficiently and accurately in many fields. We propose a deep learning method based on three-dimensional convolutional neural network (3D CNN) to predict the elastic coefficients of composite materials with inclusions of arbitrary sizes, shapes and material parameters. 3D datasets are generated, and a storage algorithm is proposed to reduce great storage costs in 3D. A general framework for 3D CNN models is constructed, and numerical experiments are carried out using 3D CNNs of various scales. Our results demonstrate that the scale of full connection part is the key factor of prediction ability of 3D CNNs in this task. We also demonstrate that our method can effectively save computational time compared with traditional numerical methods such as the finite element method in large-scale prediction tasks. [ABSTRACT FROM AUTHOR]

Recent stochastic homogenization results for the Francfort–Marigo model of brittle fracture under anti-plane shear indicate the existence of a representative volume element. This homogenization result includes a cell formula which relies on Dirichlet boundary conditions. For other material classes, the boundary conditions do not effect the effective properties upon the infinite volume limit but may have a strong influence on the necessary size of the computational domain. We investigate the influence of the boundary conditions on the effective crack energy evaluated on microstructure cells of finite size. For periodic boundary conditions recent computational methods based on FFT-based solvers exploiting the minimum cut/maximum flow duality are available. In this work, we provide a different approach based on fast marching algorithms which enables a liberal choice of the boundary conditions in the 2D case. We conduct representative volume element studies for two-dimensional fiber reinforced composite structures with tough inclusions, comparing Dirichlet with periodic boundary conditions. [ABSTRACT FROM AUTHOR]

The Mechanical properties of composites are fundamental for the design of fiber composite structures. A new finite element analysis (FEA) technique is established to determine the effective properties of composite materials. The technique involves finite element analysis of Representative Volume Element (RVE). The boundary condition plays an important role in the analysis of composite RVE. It is important to predict the correct boundary conditions (BCs) to be applied on RVE before the analysis of composite RVE. In order for the deformation in RVE to accurately reflect the deformation within the composite structure, the BCs must be suitable. The appropriate boundary conditions to be applied are determined in this study using FE analysis of isotropic RVE. The composite RVE is subjected to the thusly acquired boundary conditions, and the resulting material property along that direction is given a unit displacement along the necessary direction. Averaging the stress - strain fields generated from the analysis yields the effective properties of unidirectional fibre reinforced composite material. [ABSTRACT FROM AUTHOR]

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In this paper, the modulus prediction of NP-C/C is completed by establishing a multiscale finite element model, and the influence weight analysis of the modulus is carried out by using the analytical homogenization method. Firstly, three Micro-RVE, including unidirectional composites, short fiber reinforced composites and porous matrix, are established to characterize the layers of NP-C/C. Then, the finite element model is used for homogenization and passed upward into Meso-RVE, and the modulus prediction is completed. Finally, the analytical homogenization method is used combined with the MATLAB® script to analyze the influence weight of the modulus by adjusting the parameters. The results show that the average errors of stiffness coefficient prediction values obtained based on the analytical homogenization method are only 6.0% relative to the experimental values, which are lower than 25.3% of the finite element model. The modulus prediction method given in this study does not need to establish a micromechanical model with complex structure, and can be directly completed by computer script when the prediction accuracy is met, which is simple and feasible. [ABSTRACT FROM AUTHOR]

It is well known that the inherent three‐dimensional and unsteady nature of turbulent flows is a stumbling block for all approaches aimed at resolving their spatial and temporal variability. The pseudo‐direct numerical simulation (P‐DNS) method for turbulent flows, proposed by the authors in a previous publication, focused on resolving the spatial variability, leaving the task of solving the temporal evolution to a highly simplified, parameter dependent model, to be adjusted in a case by case basis. Although some auspicious results were obtained, the applicability of P‐DNS for problems of industrial interest required a more sophisticated method to deal with the temporal variability. In this sense, the present work proposes a new, parameter free, data‐driven memory model for P‐DNS. The model is based on the study of off‐line DNS solutions of turbulent flows transitioning between statistically steady states in simple domains. The new P‐DNS model is tested and successfully compared against existing methods in selected three‐dimensional turbulent flows. [ABSTRACT FROM AUTHOR]

Due to the versatility of its implementation, additive manufacturing has become the enabling technology in the research and development of innovative engineering components. However, many experimental studies have shown inconsistent results and have highlighted multiple defects in the materials' structure thus bringing the adoption of the additive manufacturing method in practical engineering applications into question, yet limited work has been carried out in the material modelling of such cases. In order to account for the effects of the accumulated defects, a micromechanical analysis based on the representative volume element has been considered, and phase-field modelling has been adopted to model the effects of inter-fiber cracking. The 3D models of representative volume elements were developed in the Abaqus environment based on the fiber dimensions and content acquired using machine learning algorithms, while fulfilling both geometric and material periodicity. Furthermore, the periodic boundary conditions were assumed for each of the representative volume elements in transversal and in-plane shear test cases,. The analysis was conducted by adopting an open-source UMAT subroutine, where the phase-field balance equation was related to the readily available heat transfer equation from Abaqus, avoiding the necessity for a dedicated user-defined element thus enabling the adoption of the standard elements and features available in the Abaqus CAE environment. The model was tested on three representative volume element sizes and the interface properties were calibrated according to the experimentally acquired results for continuous carbon-fiber-reinforced composites subjected to transverse tensile and shear loads. This investigation confirmed the consistency between the experimental results and the numerical solutions acquired using a phase-field fracture approach for the transverse tensile and shear behavior of additively manufactured continuous-fiber-reinforced composites, while showing dependence on the representative volume element type for distinctive load cases. [ABSTRACT FROM AUTHOR]

The mechanical response of dual phase (DP) steel exhibits a complex dependence on the microstructure. The chemical composition and microstructure characteristics of the phases have significant effects on the contrast between the response of the phases, which affects, not only the strength and ductility, but also the anisotropic response of DP steel under strain path changes. In this work, extended dislocation-based models of the ferrite and martensite phases of DP steel are proposed and used in a finite element based representative volume element approach to account for the contrast between the local response of the phases. The flow stress of each phase is computed as a function of the amount of substitutional and interstitial solute elements and the microstructural characteristics of the phase. Particular attention is paid to the phase model of the martensite phase. The model parameter controlling the storage of dislocations is related to the carbon content, which appears to be the most important parameter affecting the strength of martensite and its contrast with the local response of the ferrite phase. The model predicts a significant effect of the contrast between the local responses of the phases and the microstructure characteristics of each phase on the yield locus after prestraining and on the stress–strain behaviour after strain path change, i.e., forward-reverse shear loading and cyclic uniaxial tension–compression loading. [ABSTRACT FROM AUTHOR]

The macroscopic properties of composite materials depend on the microscopic properties of the constituents and the geometric arrangement of their phases. Therefore, it is essential to predict heterogeneous materials’ mechanical properties by simulating microstructural finite element models. The present article aims to analyze particle reinforced composites composed of spherical alumina inclusions surrounded by a glass matrix using a tridimensional representative volume element. Herein, microstructures are artificially created considering a regular or random arrangement of the inclusions. Two materials systems previously studied in the literature were analyzed. The discretization of the models was performed to have periodic mesh, thus enabling the use of periodic boundary conditions. A finite element model is created using Abaqus software. Numerical results show that the macroscopic properties can be estimated with high accuracy for the temperature where linear matrix behavior stands. The predictions were compared to experimental data from the literature. The models with a regular arrangement of inclusions show a difference inferior to 10%, while random arrangements show a difference inferior to 3.9%. The developed numerical algorithms can be modified to include new features, such as other dispersed phase arrangements or nonlinear material behavior.

In this study, the aging performance of particle-filled polymer composites (PFPCs) under thermo-oxidative conditions was investigated on multiple scales. High-temperature-accelerated tests were conducted to analyze the effects of aging time and temperature. A representative volume element (RVE) model was established for the PFPCs using a random particle-filling algorithm. A predictive model for the crosslink density was conducted based on the closed-loop chain reaction of polymer oxidation. According to the theory of polymer physics, the relation between the crosslink density and matrix modulus was determined. The particle/matrix interface in the RVE model was represented by the cohesive zone model (CZM). The parameters of the CZM were determined by the inversion techniques. Then, a comprehensive multiscale RVE model was constructed, which was applied to predict the modulus and dewetting strain of the aged PFPCs. The predicted results show good agreement with the test results, which verifies the reliability of our model.

Improving the ductile deformation behavior of Mg-SiC nanocomposites without compromising strength is critical to enhancing their mechanical properties. Mg-SiC nanocomposites are produced through mechanical milling, cold isostatic pressing, sintering, and hot extrusion processes. This study investigates the uniaxial stress–strain response and deformation behavior of the Mg-SiC nanocomposite compared to pure Mg samples with and without the milling process. The deformation behavior was investigated by two-dimensional (2D) digital image correlation (DIC) at two macroscopic and microscopic scales, employing light micrographs and in situ loading samples, respectively, in the scanning electron microscope. Compared to the pure Mg samples, the mechanical test results demonstrated a significant improvement in strength (80 MPa) and fracture strain (23.5%) of the Mg-SiC nanocomposite. The three-dimensional (3D) representative volume element (RVE) model revealed the particle dispersion effect on the mechanical properties of the nanocomposite. The RVE results demonstrate ductile deformation behavior in the sample with homogenous dispersion of SiC particles compared with the heterogeneous dispersion of SiC particles in Mg-SiC nanocomposite. The results demonstrated a good agreement between DIC and RVE predictions for Mg-SiC nanocomposites across macro- and microscales.

Selective laser melting (SLM) is an additive manufacturing technique commonly used in the rapid prototyping of components. The complexity of the SLM microstructure poses a unique challenge to deriving effective mechanical properties at different length scales. Representative volume elements (RVEs) are often used to homogenize the material properties of composites. Instead of RVEs, we use statistical volume elements (SVEs) to homogenize the elastic and fracture properties of the material. This relates the inherent variation of a material’s microstructure to the variation in its mechanical properties at different observation scales. The convergence to the RVE limit is examined from two perspectives: the stability of the mean value as the SVE size increases for the mean-based approach, and the tendency of the normalized variation in homogenized properties to zero as the SVE size increases for the variation-based approach. Fracture properties tend to make the RVE limit slower than do elastic properties from both perspectives. There are also differences between vertical (normal to printing plane) and horizontal (in-plane) properties. While the elastic properties tend to make the RVE limit faster for the horizontal direction, i.e., having a smaller variation and more stable mean value, the fracture properties exhibit the opposite effect. We attributed these differences to the geometry of the melt pools.

A 3D representative volume element (RVE) model was developed to analyze the effective thermal expansion coefficient (CTE) of carbon nanotube reinforced aluminum (CNT/Al) composites. The influences of geometric configuration, orientation and volume fraction of CNTs on CTE of the CNT/Al composites were investigated. The results show that the orientation of CNTs significantly influences the stress and strain distributions around CNTs, and when CNTs are parallel to the load direction, the constraint effect of CNTs on the matrix is the largest. Furthermore, the configuration of CNTs also plays an important role in reducing thermal expansion behavior of CNT/Al composites, and the bundled configuration exhibit the lowest CTE. In particular, with the increase of the number of CNTs in each bundle, the CTE decreases and then tends to be unchanged. When the volume fraction of CNTs is 5%, and the number of CNTs in each bundle is 25, the CTE of the composite reaches 5.12 × 10−6/°C, which is 76% lower than the CTE of the matrix. A linear decrease of the CTE of CNT/Al composites is observed as the CNT volume fraction increases. Overall, this work establishes a comprehensive understanding of factors affecting the CTE, and the obtained findings could provide a good theoretical basis for designing low CTE CNT/Al composites.

The simulation model represents the microstructure that can accurately analyze and predict composites’ micro-stresses and mechanical properties. The conventional representative volume element (RVE) model can only contain one single-particle form. It makes that all the particles in the simulation model have the same shape, which is significantly different from actual particles. In the present study, four typical particle-modeling methods were adopted to establish geometric models to analyze the particle morphology and RVE size selection rules. Particles with the same granularity and similar volume were selected to generate RVE models with randomly distributed particles to predict the mechanical properties and analyze the micro-stress. The micro-stress distribution of the matrix and particles conformed to the rule of normal distribution, while the stress of the interphase does not conform to this law. The particle morphology has a negligible effect on the stress distribution of the matrix; however, it has a significant influence on the stress distribution of particles and interphases, especially during plastic deformation. Furthermore, the micro-stress of composites containing nanoparticles also conforms to the above law, but the stress of the interphase is more minor, and the stress of particles is more dispersed than composites with micron particles.

To evaluate creep in materials under actual-use conditions, it is necessary to consider the polycrystalline morphology. Herein, we propose the first model for quantitatively predicting the influence of 3D polycrystalline morphology on Coble creep deformation. This model was developed using a representative volume element (RVE). Two grain growth mechanisms, namely, grain boundary migration and grain boundary diffusion, were formulated considering the 3D data structure of a polycrystal and then superposed to simulate RVE deformation. The model was validated by comparison with the theoretical solution for Coble creep deformation under uniaxial loading conditions. The proposed model accurately reproduced the influences of grain size, applied stress, and temperature, thus demonstrating its validity. In addition, the influence of polycrystalline morphology was investigated by performing systematic numerical simulations. The model directly provided quantitative predictions of the performance of materials with arbitrary polycrystalline morphologies under any loading or temperature condition. Consequently, the proposed RVE model has the potential to serve as a basis for designing novel materials with resistance against high-temperature creep.

The present work is undertaken to determine the ability of the small punch test to determine mechanical properties of CoNiCrAlY, a two phase bond-coat material found in thermal barrier coatings. It utilises a multi-scale modelling methodology in which 2-dimensional representative volume elements of CoNiCrAlY and finite element models of the small punch test are developed. Effective Young’s moduli and Poisson’s ratios are obtained from the representative volume elements and are compared with those obtained from analytical homogenization through the Voigt, Reuss and Voigt-Reuss-Hill schemes. The volume fraction of the β-Nial phase in CoNiCrAlY is varied and the force–displacement responses of representative volume elements are contrasted with those from small punch test finite element models, through comparison of ratios of discrete fréchet distances. The results of the study estimated Young’s modulus and Poisson’s ratio to be 178.56 ± 7.65GPa and 0.249 ± 0.037 respectively, and for an increasing β-Nial phase volume fraction, the Young’s modulus and Poisson’s ratio decrease. Lastly, the results suggest that the small punch test is insensitive to variations in material elastic behaviour because its results are more influenced by the yield properties of a material.

We describe a sequential addition and migration (SAM) algorithm for generating microstructures of fiber‐reinforced composites with a direct control of the magnitude of curvature of the fibers. The algorithm permits to generate microstructures with fibers that are significantly longer than the edge lengths of the underlying cell. Industrially processed short and long‐fiber composites naturally feature a high volume fraction, which needs to be reflected by state‐of‐the‐art microstructure generation tools. Nowadays, it is well understood that digital twins of the microstructure of composites are essential for reliable computational multiscale methods. The original SAM algorithm was shown to reliably generate microstructures for short and straight cylindrical fibers. Digital volume images reveal, however, that the fibers in such fiber‐reinforced composites may show significant curvature, in particular for long fibers. The work at hand introduces an extension of the original SAM approach to curved fibers. More precisely, curved fibers are considered as sequences of straight fibers which are joined at their respective ends and whose level of bending is controlled by the angle between adjacent fiber segments. We discuss how to efficiently implement the novel method and how to select the crucial numerical parameters. We compare the introduced methodology to the original SAM algorithm for short fibers and demonstrate the superiority of the novel strategy for long fibers. [ABSTRACT FROM AUTHOR]

In this study, we developed hot working process maps for incompressible TRIP steel composites with 0%, 5%, 10%, and 20% zirconia particles using crystal plasticity-based numerical simulations. Experimentally recorded material flow curves were used to calibrate material model parameters for TRIP steel and zirconia. The fitted material models were used for running the composite simulations. Representative volume elements (RVEs) for composites were generated using the open-source DREAM.3D program. After post-processing, the simulation results were used to calculate global and local stress–strain values at temperatures ranging from 700 to 1200 °C and strain rates ranging from 0.001 to 100 s−1. Local stress–strain maps allow researchers to investigate the effect of zirconia particles on composites, which is difficult to measure experimentally at these high temperatures. On the dynamic material model (DMM), the global results were then used to construct process maps. Because the ability of the simulation model to depict dynamic softening was constrained, the processing maps derived from the simulation data did not depict regions of instability. By running crystal plasticity-based numerical simulations, we reported important findings that might help in building hot working process maps for dual-phase materials. [ABSTRACT FROM AUTHOR]