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This work presents a new two‐level representative volume element model for generating random fiber distributions in continuous fiber composite materials. A representative volume element (RVE) model with random geometric boundaries is generated, and the adaptive connections between neighboring RVEs are realized to eliminate unreasonable connections that may occur at the boundaries of RVEs. Subsequently, a novel adaptive generation and construction algorithm for larger RVE (LRVE) is proposed to consider more micro‐scale geometric and material uncertainties. A computational framework is established to implement the adaptive construction of LRVE and determine the statistical uncertainties of continuous fiber composite materials. The uncertain statistical results of the proposed algorithm are compared with those of the random sequential expansion algorithm and the complete spatial random pattern, showing good agreements among them. Finally, the uncertainty of macro‐scale linear elastic anisotropic material parameters is evaluated by using the integrated software framework. The maximum relative error of the predicted macro‐scale elastic properties is only 8.70%, which outperforms other numerical analysis results in literatures. The proposed algorithm is helpful for further research on multi‐scale linear elastic uncertainty analysis and reliability design of continuous fiber composite materials. [ABSTRACT FROM AUTHOR]

Highlights This paper investigates how combining natural and synthetic fibers within yarns, altering the degree of hybridisation, and varying weave architectures affect the homogenized elastic properties and stress distributions in 2D woven composite laminae using a two‐scale homogenization scheme. The novelty lies in integrating a micro‐scale representative volume element model with a meso‐scale repeating unit cell model to capture intra‐yarn natural/synthetic fiber hybridisation. The study focuses on 2/2 twill and 5‐harness satin woven laminae with flax/E‐glass, hemp/E‐glass and basalt/E‐glass hybrid yarns, all with a total fiber volume fraction of 0.6. Fiber distributions are created through a random sequential expansion algorithm for hybrid RVEs, while periodic meso‐structures are used to define weave architectures for RUCs. Results show that yarn‐level fiber hybridisation significantly influences matrix stress distributions, with variations of up to 22%. In contrast, weave architecture has a minimal effect, with variations in homogenized properties below 2%. Varying fiber types, degrees of hybridisation and weave architectures allow for the tailoring of yarn and lamina properties and altering the stress distributions at micro‐ and meso‐scales and potentially influencing damage mechanisms. The modeling approach for analyzing the mechanical behavior of intra‐yarn hybrid natural/synthetic woven laminae could potentially be used to tailor their tolerance to damage. Two‐scale homogenization integrates RVE and RUC for 2D woven hybrid composites. Analyzed flax/E‐glass, hemp/E‐glass, basalt/E‐glass in twill and satin weaves. Intra‐yarn hybridisation significantly affects properties and stress fields. Hybridizing fibers offers tailored properties and may improve damage tolerance. [ABSTRACT FROM AUTHOR]

This study investigated the internal stress distribution of unidirectional fiber-reinforced plastics (UD-FRP) at the micro level using principal component analysis (PCA). The composite material was simulated using a representative volume element model together with the embedded cell approach. Two fundamental quasi-static load cases, transverse and longitudinal tensile deformation, were considered. The experimental results show that mechanical failure occurred at 2.15 ± 0.06% transverse tensile strain and at 1.52 ± 0.07% longitudinal tensile strain. Furthermore, the undamaged state and a combination of matrix and interface damage, as well as fiber breakage, were simulated. From the simulations, the octahedral shear stress and octahedral normal stress were computed at the integration points of the matrix elements, constituting what is known as the octahedral stress field. A modification on the PCA to obtain mesh-independent eigenvalues is presented and was used to investigate the effects of damage events on the octahedral stress field. The results indicate that each damage mechanism had a distinct signature in the redistribution of the stress field, characterized by specific changes in the eigenvalues and orientation of the principal component (θ1). Furthermore, the PCA suggests that the accumulation of matrix damage began to be relevant at the 1% strain, while fiber breakage began at an average longitudinal strain of 0.98 ± 0.12%. Additionally, it is shown that the first principal component served as an indicator of the predominant stress state of the stress field. This investigation suggests that the PCA can provide valuable insights regarding the complex damage mechanisms of UD-FRP that may not be captured by conventional mechanical analysis. [ABSTRACT FROM AUTHOR]

As a key and weak point of continuous fiber-reinforced composites (CFRCs), the interface between the fiber and the matrix is vulnerable to failure under external loads, with its performance directly affecting the overall properties of CFRCs. Hence, a micro–macro coupling method that considered the microscopic properties of the interface was utilized to analyze and predict the mechanical properties of CFRCs more accurately. The microscopic mechanical parameters of the fiber–matrix interface, which were obtained using molecular dynamics, were transferred to the representative volume element (RVE). The stiffness matrix of the CFRC, required for the macroscopic finite element model, was then calculated using a unified periodic homogenization method based on the RVE and assigned to the finite element model for a macroscopic simulation. Nylon/continuous carbon fiber specimens were fabricated through additive manufacturing, with the tensile and bending strengths of the specimens obtained through tensile and three-point bending tests. The tensile strength of the experimental specimen was 200.1 MPa, while the result of the simulation containing the interface was 205.5 MPa, indicating a difference of less than 5% between the two. In contrast, the result of the simulation without an interface was 317.7 MPa, representing a high error of 58.7% compared with the experimental results. Moreover, the bending strength, Young's modulus, and flexural modulus results with and without an interface showed the same trend as that for the tensile strength. This illustrates the effectiveness of the proposed micro–macro coupling method for analyzing and predicting the mechanical properties of CFRCs. [ABSTRACT FROM AUTHOR]

A representative model for multilayer natural fibre composite (NFC) plates is introduced to investigate its homogenised strength criterion. A three-layer NFC plate model is used to analyse the local stress–strain characteristics in multi-layered NFC. Finite element analysis (FEA) is performed on the representative volume element (RVE) under various boundary conditions to investigate stress and strain at macroscopic and microscopic levels. The explicit assessment of homogenised strength requires calculating stress tensors and equivalent stresses to determine parameter values. The precise specification of homogenised strength requirements assists in comprehending the material's behaviour under various loading conditions, which affects composite application design and optimisation techniques. The study examined the effect of fibre orientation angles on NFC's mechanical behaviour. The results demonstrate that flax fibres have comparatively higher stress levels than coir fibres. This study improves the understanding of natural fibre laminate composites' macroscopic and microscopic behaviours, that is, the material's response under different loadings. The definition of homogenised strength criterion on NFC improves their design evaluations. [ABSTRACT FROM AUTHOR]

In this contribution, we derive a consistent variational formulation for computational homogenization methods and show that traditional FE 2$$ {}^2 $$ and IGA 2$$ {}^2 $$ approaches are special discretization and solution techniques of this most general framework. This allows us to enhance dramatically the numerical analysis as well as the solution of the arising algebraic system. In particular, we expand the dimension of the continuous system, discretize the higher dimensional problem consistently and apply afterwards a discrete null‐space matrix to remove the additional dimensions. A benchmark problem, for which we can obtain an analytical solution, demonstrates the superiority of the chosen approach aiming to reduce the immense computational costs of traditional FE 2$$ {}^2 $$ and IGA 2$$ {}^2 $$ formulations to a fraction of the original requirements. Finally, we demonstrate a further reduction of the computational costs for the solution of general nonlinear problems. [ABSTRACT FROM AUTHOR]

The custom design of a composite material requires the knowledge of its effective behavior which depends on several parameters such as the properties of the constituents, their distributions, shapes and sizes. In thermal conductivity, all these parameters have a direct and significant influence on the effective thermal conductivity (ETC) of composites. These parameters act differently on the behavior of the composite according to its use as much as a good conductor by improving its ETC or by reducing it by considering it as an insulator. The main goal of this work is an extensive study of all possible situations of ETC by a numerical homogenization technique based on the Finite Elements Method. For this purpose, the two main categories of composites, namely the periodic composites represented by the unit cell and the random RVE, are considered. For each category of composite, different contrasts, different particles' volume fractions, aspect ratios, positions, and orientations are studied. In order to ensure the simulation results are effective and representative, two boundary conditions, namely Uniform Temperature Gradient Boundary Conditions (UGT) and Periodic Thermal Boundary Conditions (PBC), were imposed on all considered microstructures. The results of this study constitute a synthesis of the effective thermal conductivities of all the possible situations which can be summarized as follows: On the one hand, the reinforcements shape effect is very important irrespective of the nature of the periodic and random composites and on the other hand, the two types of composites do not have the same behavior as that for the reinforcements with a circular or almost circular shape. This study also emphasizes the situations where the ETC can be estimated analytically and when homogenization is necessary. From a practical point of view, and on the basis of the obtained results, this study made it possible to show clearly in which situation the composite becomes more conducting and in the opposite case when it becomes more insulating. [ABSTRACT FROM AUTHOR]

This study employs a microstructure-based finite element modeling approach to understand the mechanical behavior of asphalt mixtures across different length scales. Specifically, this work aims to develop a multi-scale modeling approach employing representative volume elements (RVEs) of optimal size; this is a key issue in asphalt modeling for high-fidelity fracture modeling of heterogeneous asphalt mixtures. To determine the optimal RVE size, a convergence analysis of homogenized elastic properties is conducted using two types of RVEs, one made with polydisperse spherical inclusions, and another made with polydisperse truncated cylindrical inclusions, each aligned with the American Association of State Highway and Transportation Official's maximum density gradation curve for a 12.5 mm Nominal Maximum Aggregate Size (NMAS). The minimum RVE lengths for this NMAS were found to be in the range of 32–34 mm. After the optimal RVE size for each inclusion shape is obtained, computational models of heterogeneous Indirect Tensile Asphalt Cracking Test samples are then generated. These models include the components of viscoelastic mastic, linear elastic aggregates, and cohesive zone modeling to simulate the rate-dependent failure evolution from micro- to macro-cracking. Examination of load-displacement responses at multiple loading rates shows that both heterogeneous models replicate experimentally measured data satisfactorily. Through micro- and macro-level analyses, this study enhances our understanding of the composition-performance relationships in asphalt pavement materials. The procedure proposed in this study allows us to identify the optimal RVE sizes that preserve computational efficiency without significantly compromising their ability to capture the asphalt material behavior under specific operational conditions. [ABSTRACT FROM AUTHOR]

Carbon nanotubes (CNTs) are extensively utilized in the fabrication of high-performance composites due to their exceptional mechanical, electrical, and thermal characteristics. To investigate the mechanical properties of CNTs filled polymers accurately and effectively, a 3D modeling approach that incorporates the microstructural attributes of CNTs was introduced. Initially, a representative volume element model was constructed utilizing the modified nearest neighbor algorithm. During the modeling phase, a corresponding interference judgment method was suggested, taking into account the potential positional relationships among the CNTs. Subsequently, stress–strain curves of the model under various loading conditions were derived through finite element analysis employing the volume averaging technique. To validate the efficacy of the modeling approach, the stress within a CNT/epoxy resin composite with varying volume fractions under different axial strains was computed. The resulting stress–strain curves were in good agreement with experimental data from the existing literature. Hence, the modeling method proposed in this study provides a more precise representation of the random distribution of CNTs in the matrix. Furthermore, it is applicable to a broader range of aspect ratios, thereby enabling the CNT simulation model to more closely align with real-world models. [ABSTRACT FROM AUTHOR]

We present an efficient approach to evaluate the size dependency of elastic and plastic properties of metallic polycrystalline materials. Specifically, we consider different volume fractions of ferrite and martensite phases for the construction of three macroscopic domains. Statistical Volume Elements (SVEs) of different sizes are extracted from these domains using the moving window method. Linear and Crystal Plasticity (CP) simulations provide elastic and plastic properties of the SVEs such as the bulk and shear moduli, yield strength, and hardening modulus. We use a variation-based criterion to determine the Representative Volume Element (RVE) size of these properties. This RVE size corresponds to a size beyond which the given property can be idealized as homogeneous. We also use anisotropy indices and an additional RVE size criterion to determine the size limits beyond which these properties can be idealized as isotropic. Numerical results show that the plastic properties often reach their homogeneity and isotropy limits at larger sizes compared to elastic properties. This effect is more pronounced for the hardening modulus compared to the yield strength. [ABSTRACT FROM AUTHOR]

We describe an algorithm for generating fiber-filled volume elements for use in computational homogenization schemes which accounts for a coupling of the fiber-length and the fiber-orientation. For prescribed fiber-length distribution and fiber-orientation tensor of second order, a maximum-entropy estimate is used to produce a fiber-length-orientation distribution which mimics real injection molded specimens, where longer fibers show a stronger alignment than shorter fibers. We derive the length-orientation closure from scratch, discuss its integration into the sequential addition and migration algorithm for generating fiber-filled microstructures for industrial volume fractions and investigate the resulting effective elastic properties. We demonstrate that accounting for the length-orientation coupling permits to match the measured Young's moduli in principal fiber direction and transverse to it more accurately than for closure approximations ignoring the length-orientation coupling. [ABSTRACT FROM AUTHOR]

The Direct FE2 method is a recently developed concurrent multi-scale simulation approach with a monolithic solution scheme, where the macroscopic and microscopic models are solved in a unit iteration process. The conventional Direct FE2 using quadrilateral element has some limitations in determining the failure state of a macro-element. In this work, we develop a new Direct FE2 method based on the Single-integration Point triangle element (Direct SP-FE2) and apply it to simulate the micro-crack-induced fracture problems for the first time. The cohesive element is inserted into a representative volume element (RVE), so that the failure process of a macro-element can be determined by the micro-crack propagation on RVE. Accordingly, the relationship between macro-deformations and microstructures can be established directly, thus avoiding complex derivation and utilization of a multi-scale damage constitutive model. In Direct SP-FE2, the failure state of a macro-element can be directly predicted by the RVE at the single-integration point inside, avoiding the uncertainty associated with predictions by multiple RVEs. As a result, compared to the conventional Direct FE2 with a quadrilateral element, the Direct SP-FE2 shows advantages in capturing complex geometric boundaries and predicting the damage evolution process and failure state more accurately. Various numerical examples are conducted to comprehensively validate the effectiveness of the present method in describing the influence of micro-cracks on macro-structure deformations. For the macro-damage behaviors, the simulation results by the Direct SP-FE2 show good agreement with the direct numerical simulation (DNS) results of the full FE model at a significantly lower computational time. With the developed Direct SP-FE2, a variety of complex micro-crack fracture problems in composite materials can be successfully modeled by manipulating the interior RVE structure. [ABSTRACT FROM AUTHOR]

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]

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]

This work presents results of numerical simulations to investigate the effect of different void percentages on composite materials' Coefficient of Thermal Expansion (CTE) and local stress fields. A random distribution of voids is considered within the Representative Volume Element (RVE) matrix, and different types of microstructures are considered, including square-packed and randomly distributed fibers. The use of a higher-order beam model within the framework of Carrera Unified Formulation (CUF) leads to a Component-Wise (CW) approach, resulting in an accurate, 3D description of the cross-section although using a 1D formulation. Numerical results for different fiber volume fractions and void concentration percentages demonstrate the agreement of the computed effective coefficients of thermal expansion of the present micromechanical thermoelastic model with references from the literature. The local stress fields are affected by voids, with higher effects over the matrix. Furthermore, higher void fractions lead to higher variability of stress peaks. [ABSTRACT FROM AUTHOR]

A combined experiment and multiscale modeling approach was presented to correlate the mechanical properties of a roll-bonded AA1050/AA3004 bimetal clad sheet and constituents. The mechanical responses of the 2-ply AA1050/AA3004 and constituents were measured under various loading conditions. For the measurements, each constituent was separated from the clad sheet using electrical discharge machining and uniaxial tensile tests. Continuum-scale yield functions such as isotropic von Mises and anisotropic/non-quadratic Yld2000-2d were developed for the two constituents and the bimetal clad sheet. A grain-scale crystal plasticity finite element (CPFE) simulations were also performed incorporated with newly developed representative volume element considering measured microstructural attributes. These CPFE predictions were used to identify the anisotropy coefficients for Yld2000-2d. Using the identified yield functions, finite element modeling was followed in which the mechanical properties of each constituent sheet were addressed separately. This is a new approach developed in the current work and it enables a fundamental correlation between multilayered material and its constituents. The mechanical properties of the bimetal clad sheet under the uniaxial tensions were predicted using those of the constituents and compared with calculations based on known rule of mixture (ROM) approach. The two approaches well reproduced stress–strain curves and r–value evolutions. The two FE modeling approaches were also applied to an independent test (i.e., the limiting dome height). The predictions were in good agreement with the experimental data. Finally, the mechanical properties of the bimetal clad sheet and constituents were correlated, and proper modeling scheme for multilayered materials is proposed.

This study presents experimental and numerical investigations on the quasi-static compressive responses of various subscale Miura-foldcore composites. A series of quasi-static compression tests were conducted on standard Miura foldcore specimens fabricated using carbon/epoxy woven fabric prepregs. Representative volume element (RVE) models, incorporating periodic boundary conditions (PBCs), were developed to predict the size-dependent compressive response of subscale Miura foldcores. The effective properties of the carbon/epoxy woven fabric composite used in this study were calculated using the NASA multiscale analysis tool (NASMAT) via two-step homogenization process. The FE model exhibited comparable agreement with experimental results, showcasing variations of less than 7% and 12% in maximum compressive load and compressive stiffness, respectively. The implementation of PBC in the foldcore RVE models improved modeling accuracy by <4%, but drastically increased total computational time (>50%). The periodic pattern of foldcore unit-cells, where two single foldcore unit-cells were placed in parallel or perpendicular, imposed geometric constraints, resulting in small variations in predicted stress and strain distribution contours. The key findings highlighted in this study suggest that a 1 × 1 foldcore unit-cell model without PBC is sufficient to predict accurate quasi-static compressive responses of foldcore composites. This study advances the understanding of subscale Miura-foldcore composites and provides valuable insights into the limitations associated with the use of PBC in foldcore RVE models. The findings also offer a practical guide for fabricating and analyzing traditional Miura folding patterns, promoting a more efficient and accurate approach for optimizing foldcore composite designs considering both structural performance and manufacturability. [ABSTRACT FROM AUTHOR]

The properties of unidirectional (UD) composites has been investigated by analyzing their elastic and strength characteristics under shear loading. The UD fiber‐reinforced polymer (FRP) composites usually consist of fibers randomly dispersed throughout the cross‐section in the transverse direction which is generally not accounted for. A micromechanical model based on finite element analysis (FEA) approach is utilized here to examine these properties. The study begins by identifying micro scale unit cells or repetitive unit cells (RUCs) at the micro scale, as well as representative volume elements (RVEs). The distribution of fiber volume fraction (Vf) varies among various micro scale unit cells positioned in the transverse cross‐section. The elastic properties and strength are estimated by considering the properties of the matrix and fibers, and the configuration of micro scale unit cells, which feature a fiber arrangement which is categorized as hexagonal and varying Vf at different locations (from 0.35 to 0.75). However, the overall Vf for the UD composite remains constant at 0.65. Studies are also carried out with the random distribution of fibers at micro scale unit cells. The findings reveal that the random distribution of fibers significantly impacts the shear behavior of the composite. This investigation provides valuable insights into how the mechanical properties of the UD composite are subjective by the distribution of fiber, thereby contributing to the design and development of this light weight high‐performance material. Highlights: Elastic and strength analysis of UD composites is presented.Emphasis is on fiber dispersion in transverse plane.Microscale unit cells, RUCs and RVE are identified.Studies are carried out based on micromechanical model.Influence of fiber distribution on shear behavior is investigated. [ABSTRACT FROM AUTHOR]

Estimating the elastic characteristics of natural fiber‐reinforced polymer composites such as luffa fiber reinforced with epoxy is challenging. The structure of luffa cylindrica is complex, like a three‐dimensional natural fibrous mat, netting‐like structure. The multiscale modeling of such structures is the challenge to be addressed. The prime objective of this work is to determine the specific elastic properties of luffa–cenosphere‐reinforced epoxy (LCE) composite, considering the effect of filler volume fractions. Furthermore, multiscale modeling techniques, such as representative volume elements (RVEs) of finite element techniques with chopped, unidirectional, plain, and twill weaving fiber arrangements, were employed. The longitudinal modulus, transverse modulus, shear modulus, and Poisson's ratio were predicted through these modeling approaches. However, experimental and analytical methodologies, including the rule of mixture and Halpin–Tsai, were considered to validate the finite element analysis results. The elastic characteristics of LCE composite were therefore shown to be enhanced by increasing filler volume fraction. However, the cenosphere's 20% volume fraction has the highest elastic properties as determined by analytical, experimental, and computational models. Analytical and finite element simulation results were compared with the experimental results, and based on the findings, the most suitable (unidirectional, chopped, plain, and twill weaving) RVE was identified for finite element modeling of LCE composite for the evaluation of elastic properties. Results from practical approaches and the RVE twill weaving model showed good agreement, with less than 1% error, compared to the other analytical and finite element methods. Highlights: NFCs are gaining ground in polymer composites.Overcoming challenges in modeling of luffa fiber inside epoxy matrix.The study uses multiscale modeling with diverse fiber arrangements.Experimental and analytical methods used to confirm FEA results.Increased cenosphere volume fraction boosts LCE composite properties. [ABSTRACT FROM AUTHOR]

Purpose: During the forming process, aluminum alloy sheets develop various types of textures and are subjected to cyclic loading as structural components, resulting in fatigue damage. This study aims to develop polycrystalline models with different orientation distributions and incorporate suitable fatigue indicator parameters to investigate the effect of orientation distribution on the mechanical properties of Al-7.02Mg-1.78Zn alloys under cyclic loading. Design/methodology/approach: In this study, a two-dimensional polycrystalline model with 150 equiaxed grains was constructed based on optical microscope images. Subsequently, six different orientation distributions were assigned to this model. The fatigue indicator parameter of strain energy dissipation is utilized to analyze the stress response and fatigue crack driving force in polycrystalline models with different orientation distributions subjected to cyclic loading. Findings: The study found that orientation distribution significantly influences fatigue crack initiation. Orientation distributions with a larger average Schmid factor exhibit reduced stress response and lower fatigue indicator parameters. Locations with a larger average Schmid factor experience greater plastic deformation and present a higher risk for fatigue crack initiation. RVE with a single orientation undergoes more rotation to reach cyclic steady state under cyclic loading due to the ease of deformation transfer. Originality/value: Currently, there are no reports in the literature on the calculation of fatigue crack initiation for Al-Mg-Zn alloys using the crystal plasticity finite element method. This study presents a novel strategy for simulating the response of Al-7.02Mg-1.78Zn materials with different orientation distributions under symmetric strain cyclic loading, providing valuable references for future research. [ABSTRACT FROM AUTHOR]

Copyright of Polymer Materials Science & Engineering is the property of Sichuan University, Polymer Research Institute and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Although the effects of additive manufacturing process parameters on the mechanical properties of 3D printed parts have been numerically investigated in the literature, less attention has been paid on the size effects of voids between deposited filaments. This study fills this gap by developing a methodology based on a combined finite element (FE) and design of experiment (DoE) technique. The development of FE methodology is based on micro-mechanical analysis of representative volume element (RVE) of 3D printed parts to predict the effective orthotropic properties. To account for the size effects of inter-bead voids, the RVE includes contribution of the multiple parameters of layer heights, layer widths and overlapping regions. To study the main and interaction effects of the above input parameters on the stiffness properties of 3D printed parts, a structured approach based on full factorial design is used. Although the size effects of voids on the constituents of elastic moduli of RVE were investigated, the main focus in the present work is to develop a regression model to predict the stiffness properties. The FE stress analysis of the RVE conducted in this study provides an insight about the potential failure modes such as delamination and filament debonding that may occur in load bearing 3D printed parts. For a case study, the results of FE-based homogenization technique in terms of stiffness properties are validated against the experimental data via three-point bending and Iosipescu shear tests which were conducted in conjunction with digital image correlation technique. The combined numerical and statistical approach proposed in this study provides a swift iterative design of 3D printed parts prior to the time-consuming computation modelling, contributing to reduce the number of tests and manufacturing costs. [ABSTRACT FROM AUTHOR]

The mechanical behaviour of metamaterials typically depends on their microstructural configuration and composition, in addition to their relative density. The design of these materials requires extensive experiments or complex finite element models which tend to be numerically demanding. In order to understand, control and optimise the macroscopic mechanical behaviour, in this paper numerical homogenisation is applied to a simple square unit cell with a single inclusion using a combination of elastic and viscoelastic responses on the micro level. Through a systematic analysis of unit cell behaviour with increasingly complex microstructural configurations, it is shown how certain macroscale constitutive laws can be obtained in a controlled and controllable manner. [ABSTRACT FROM AUTHOR]

The influence of prior austenite grain (PAG) orientation on the deformation behavior of a low-carbon martensitic steel is investigated using crystal plasticity (CP) modeling with hierarchical representative volume elements (RVEs). The Kurdjumov-Sachs (K-S) relationship is refined for accurate PAG reconstruction in martensitic steel. A robust calibration strategy for CP parameters based on nanoindentation tests is developed by integrating analytical calculations with inverse methods. Virtual polycrystalline aggregates are subsequently generated by manipulating initial PAG orientations. The simulations reveal that assigning cube texture to PAGs enhances strain hardening of martensite under plane strain tension. Moreover, the RVEs with brass and copper orientated PAGs exhibit similar deformation behavior, and a more homogeneous strain distribution is realized in the RVE with PAG cube orientation. The influence of PAG orientation on stress and strain fields is correlated with lattice rotation behavior during deformation. Notably, different strain paths elicit distinct lattice rotation trajectories, wherein uniaxial tension and plane strain tension favor grains reorientation toward hard γ-fiber, whilst equi-biaxial tension drives the crystal matrix to concentrate on 〈001〉 and 〈011〉 directions. These findings provide insights into the intricate relationship between microstructural orientation and deformation behavior in martensitic steels, which is crucial for performance optimization.

This study is to investigate the effects of random interfacial debonded on the elastic constants of carbon fiber reinforced composites. The results reveal that the interfacial debonded fraction (IDF) significantly effects the elastic constants, and the randomness of interfacial debonded position significantly effects the stress distribution, but different interfacial debonded positions at the same IDF have a negligible effect on the elastic constants. The increase of IDF leads to a gradual increase in the disruption of tandem integrity between fibers and matrix, limiting the capability of the interface to transfer loads more significantly. [ABSTRACT FROM AUTHOR]

In the article, we propose a new method to generate representative volume element (RVE) of random spatial distributions with cylindrical fibers and spherical particles based on the Improved Artificial Bee Colony (IABC) algorithm. In this employed bee phase of IABC, the proposed algorithm adopts a new search strategy, which improves the computational efficiency. To analyze the differences between the fiber distribution generated by this algorithm and the actual fiber distribution, we conducted statistical analysis on the distribution of the generated RVE. The statistical analysis results of the nearest neighbor distance (NND), Second-order intensity function, and pair correlation function were in good agreement with the experiment and complete spatial randomness (CSR) patterns. In addition, the predicted elastic properties were compared with experimental measurements and theoretical prediction methods. The results demonstrate the accuracy and efficiency of the proposed algorithm. This algorithm can quickly generate the RVE of cylindrical fibers and spherical particles with volume fractions of 80% and 62%, and the calculation time for generating the RVE of cylindrical fibers is about 17s. [ABSTRACT FROM AUTHOR]

To investigate the enhancement mechanism and effect of laser treatment on the performance of an interface between a carbon-fiber-reinforced polymer and magnesium (CFRP/Mg), finite element simulations and experiments were conducted to demonstrate the macroscopic and microscopic failure processes of the laser-treated interface. Based on the high controllability of the groove parameters in laser machining, the quantitative relationship between the texture parameters and the shear properties of the CFRP/Mg interface was analyzed. In addition, shear tests and simulations of the laser-treated interfaces with different groove parameters were performed. Increasing the groove depth and decreasing the groove spacing effectively improved the shear strength of the CFRP/Mg interface. In addition, the reliability of the interface cohesion parameters obtained using the representative volume element model was verified by experiments and simulations, which is important for the application of laser technology to composite laminates. [ABSTRACT FROM AUTHOR]

We present an extension of a multiscale micromorphic theory to three-dimensional problems for porous materials, where a clear scale separation is not given. Following the multiscale micromorphic framework of Biswas and Poh (J Mech Phys Solids 102:187–208, 2017), macroscopic governing equations of a micromorphic continuum are derived from a classical continuum on the microscale by means of a kinematic field decomposition. The macro–microenergy equivalence is guaranteed via the Hill–Mandel condition. For linear elasticity problems, generalized elasticity tensors are determined via several RVE computations once and for all, avoiding concurrent RVE computations for an online structural analysis. A three-dimensional implementation is revealed in detail. A comparative study with direct numerical simulations and first-order multiscale computations shows that the computational multiscale micromorphic method has sufficient accuracy and computational efficiency, thus providing a powerful tool for design and practical engineering applications of porous materials. [ABSTRACT FROM AUTHOR]

The skin is the largest organ in the human body and serves various functions, including mechanical protection and mechanosensation. Yet, even though skin's biomechanics are attributed to two main layers—epidermis and dermis—computational models have often treated this tissue as a thin homogeneous material or, when considering multiple layers, have ignored the most prominent heterogeneities of skin seen at the mesoscale. Here, we create finite element models of representative volume elements (RVEs) of skin, including the three-dimensional variation of the interface between the epidermis and dermis as well as considering the presence of hair follicles. The sinusoidal interface, which approximates the anatomical features known as Rete ridges, does not affect the homogenized mechanical response of the RVE but contributes to stress concentration, particularly at the valleys of the Rete ridges. The stress profile is three-dimensional due to the skin's anisotropy, leading to high-stress bands connecting the valleys of the Rete ridges through one type of saddle point. The peaks of the Rete ridges and the other class of saddle points of the sinusoidal surface form a second set of low-stress bands under equi-biaxial loading. Another prominent feature of the heterogeneous stress pattern is a switch in the stress jump across the interface, which becomes lower with respect to the flat interface at increasing deformations. These features are seen in both tension and shear loading. The RVE with the hair follicle showed strains concentrating at the epidermis adjacent to the hair follicle, the epithelial tissue surrounding the hair right below the epidermis, and the bulb or base region of the hair follicle. The regions of strain concentration near the hair follicle in equi-biaxial and shear loading align with the presence of distinct mechanoreceptors in the skin, except for the bulb or base region. This study highlights the importance of skin heterogeneities, particularly its potential mechanophysiological role in the sense of touch and the prevention of skin delamination. [ABSTRACT FROM AUTHOR]

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In this paper, we present an enhanced version of the two-scale numerical homogenization with application to asphalt concrete modeling in the elastic range. We modified the method of effective material parameters tensor assessment for analysis based on the representative volume element (RVE). As the method was tested on asphalt concrete, we also present two possible approaches to geometrical modeling of its internal microstructure. Selected numerical tests were performed to verify the proposed approach. The main novelties of this study, i.e. higher order approximation at the macroscale and modification of boundary conditions at the level of RVE analysis, improved the efficiency of our methodology by error reduction. Practically, we obtained a reduction of NDOF up to 3 orders of magnitude (comparing to full-scale and homogenized analysis) that was accompanied with the introduced error of order of several percent (measured in L2 norm). [ABSTRACT FROM AUTHOR]

AbstractPiezoelectric bimorph cantilevered beams are frequently employed in energy harvesting applications. The use of macro-fiber composites, which combine piezoelectric fibers with rectangular cross-sections and interdigitated electrodes, has significantly enhanced their performance by enabling operation in the 33-mode of piezoelectricity, thereby increasing conversion efficiency. In this article, the Timoshenko beam theory is applied to overcome the limitations of the Euler-Bernoulli theory in modeling transverse vibrations of harvesters with low slenderness ratios (length to thickness ratios). The mixture rule formulation is applied to determine the equivalent properties of the macro-fiber composite (MFC) structure. The electromechanical properties of a representative volume element (RVE) bounded by two successive interdigitated electrodes are coupled to the overall electro-elastic dynamic model of the structure using the Timoshenko theory. Frequency response functions for the power and tip vibration displacement of the MFC bimorph beam are determined from the model. Experimental data from the literature are used to validate the improved results predicted by the model developed in this article. A comparative analysis between the electromechanical responses predicted using a model based on Timoshenko and a model based on Euler-Bernoulli theory is conducted showing agreement, for harvesters with large slenderness ratios and discrepancies of up to 30% for low slenderness ratios. It has also been shown that the model based on Euler-Bernoulli theory overestimates both the mechanical and the electrical responses for low slenderness ratios as the shear and rotary inertia effects are not negligible in this case. [ABSTRACT FROM AUTHOR]

Part II of the paper presents comprehensive investigations aimed at demonstrating the validation and effectiveness of the proposed integrated model for simulating Coble creep deformation and void nucleation/growth in polycrystalline solids for material design. Quantitative comparisons between the model’s predictions of void area fraction in a 2D cross-section and experimental results using Alloy 201, a commercially pure nickel, demonstrated a high degree of agreement. Furthermore, the numerical simulation results align with theoretical equations, affirming the model’s validity and its capacity to represent complex phenomena accurately. Although traditional laboratory testing for pure Coble creep is challenging due to constraints such as time and equipment limitations, the proposed model offers a distinct advantage, allowing numerical simulation of Coble creep in materials with arbitrary polycrystalline morphologies under various environmental conditions. Leveraging this capability, the study conducted comprehensive numerical simulations to quantitatively explore the effects of environmental and polycrystalline morphology factors on Coble creep deformation and void nucleation/growth in polycrystalline solids. These aspects, which have not been comprehensively addressed in existing studies, were thoroughly investigated. The findings presented here establish a novel foundation for designing heat-resistant materials applicable across diverse equipment scenarios.

This study proposes an integrated model for simulating Coble creep deformation and void nucleation/growth in a 3D polycrystalline solid. Part I of the paper provides a theoretical framework for the proposed model. A representative volume element approach is employed to predict the effects of 3D polycrystalline morphology. The model comprises two distinct but interconnected stages: deformation and void nucleation/growth. The deformation stage of the proposed model comprises two sub-models: grain boundary (GB) migration and GB diffusion. The void nucleation/growth stage is composed of three consecutive calculations: void nucleation, void growth, and postprocessing. The process simulated in the void nucleation/growth stage is driven by relative GB velocity of the respective GBFs and diffusional fluxes between adjacent GBFs, which are provided from the deformation stage. The void nucleation rate is quantified using the relative GB velocity, and the initial void size is determined based on the stability condition for void existence derived from Helmholtz free energy. The void growth rate is evaluated by the atomic diffusion on the GBF and the surface of each void.

The objective of this study is to improve the mechanical properties of self-healing carbon fiber reinforced polymer (CFRP) with microcapsules (MCs) incorporating healing agents, in order to achieve superior mechanical properties and healing efficiency. The approach to improve the mechanical properties is to hybridize spread carbon fiber (SCF) and woven carbon fiber (WCF) as reinforcements. The interlaminar shear strength and the healing efficiency of the self-healing SCF/WCF hybrid laminates were evaluated by short beam shear tests, and then compared with those of self-healing SCF/EP laminates and self-healing WCF/EP laminates. Moreover, the finite element analysis (FEA) using a representative volume element (RVE) model of the SCF/WCF hybrid laminates containing MCs was performed to evaluate the elastic properties and the internal stress and reveal the relation between them and microstructure. Furthermore, we performed the FEA of short beam shear test using the elastic properties predicted from the RVE models and verified the validation of the RVE model by comparing the analytical results with the experimental results. The experimental results showed that the hybridization of SCF and WCF can be effective for improving mechanical properties of self-healing CFRP laminates compared to those of self-healing SCF/EP laminates. However, the self-healing SCF/WCF hybrid laminates did not present sufficient healing efficiency due to the large transverse cracks in the WCF layers. Therefore, in order to improve healing efficiency, it is necessary to suppress the large crack propagation in the WCF layer. The analytical results indicated that the stress concentration occurred in the WCF layer and could be mitigated by increasing the thickness of the SCF layer. The experimental results and analytical results were in good agreement. Therefore, the RVE model used in this study effectively predicted the properties of the self-healing CFRP laminates and provided microstructure design guidelines for achieving superior mechanical properties and healing efficiency.

Carbon fiber reinforced polymers are widely used to manufacture aerospace deployable structures. These structures are folded in launch configuration and then deployed in space for operational activities. Since the stowage of deployable structures in folded configuration occurs for long time, the understanding of the viscoelastic properties of the material is essential to predict the structural behavior during both the deployment phase and the operational life. In this work, numerical relaxation analysis is performed on the representative volume element (RVE) of a carbon fiber reinforced polymer using a homogenization approach at the microscale. This aims to predict the effects of matrix viscoelasticity on the structural performance of a deployable structure. [ABSTRACT FROM AUTHOR]

As a key and weak point of continuous fiber-reinforced composites (CFRCs), the interface between the fiber and the matrix is vulnerable to failure under external loads, with its performance directly affecting the overall properties of CFRCs. Hence, a micro–macro coupling method that considered the microscopic properties of the interface was utilized to analyze and predict the mechanical properties of CFRCs more accurately. The microscopic mechanical parameters of the fiber–matrix interface, which were obtained using molecular dynamics, were transferred to the representative volume element (RVE). The stiffness matrix of the CFRC, required for the macroscopic finite element model, was then calculated using a unified periodic homogenization method based on the RVE and assigned to the finite element model for a macroscopic simulation. Nylon/continuous carbon fiber specimens were fabricated through additive manufacturing, with the tensile and bending strengths of the specimens obtained through tensile and three-point bending tests. The tensile strength of the experimental specimen was 200.1 MPa, while the result of the simulation containing the interface was 205.5 MPa, indicating a difference of less than 5% between the two. In contrast, the result of the simulation without an interface was 317.7 MPa, representing a high error of 58.7% compared with the experimental results. Moreover, the bending strength, Young’s modulus, and flexural modulus results with and without an interface showed the same trend as that for the tensile strength. This illustrates the effectiveness of the proposed micro–macro coupling method for analyzing and predicting the mechanical properties of CFRCs.

This study investigated the internal stress distribution of unidirectional fiber-reinforced plastics (UD-FRP) at the micro level using principal component analysis (PCA). The composite material was simulated using a representative volume element model together with the embedded cell approach. Two fundamental quasi-static load cases, transverse and longitudinal tensile deformation, were considered. The experimental results show that mechanical failure occurred at 2.15 ± 0.06% transverse tensile strain and at 1.52 ± 0.07% longitudinal tensile strain. Furthermore, the undamaged state and a combination of matrix and interface damage, as well as fiber breakage, were simulated. From the simulations, the octahedral shear stress and octahedral normal stress were computed at the integration points of the matrix elements, constituting what is known as the octahedral stress field. A modification on the PCA to obtain mesh-independent eigenvalues is presented and was used to investigate the effects of damage events on the octahedral stress field. The results indicate that each damage mechanism had a distinct signature in the redistribution of the stress field, characterized by specific changes in the eigenvalues and orientation of the principal component (θ1). Furthermore, the PCA suggests that the accumulation of matrix damage began to be relevant at the 1% strain, while fiber breakage began at an average longitudinal strain of 0.98 ± 0.12%. Additionally, it is shown that the first principal component served as an indicator of the predominant stress state of the stress field. This investigation suggests that the PCA can provide valuable insights regarding the complex damage mechanisms of UD-FRP that may not be captured by conventional mechanical analysis.

This study employs a microstructure-based finite element modeling approach to understand the mechanical behavior of asphalt mixtures across different length scales. Specifically, this work aims to develop a multi-scale modeling approach employing representative volume elements (RVEs) of optimal size; this is a key issue in asphalt modeling for high-fidelity fracture modeling of heterogeneous asphalt mixtures. To determine the optimal RVE size, a convergence analysis of homogenized elastic properties is conducted using two types of RVEs, one made with polydisperse spherical inclusions, and another made with polydisperse truncated cylindrical inclusions, each aligned with the American Association of State Highway and Transportation Official’s maximum density gradation curve for a 12.5 mm Nominal Maximum Aggregate Size (NMAS). The minimum RVE lengths for this NMAS were found to be in the range of 32–34 mm. After the optimal RVE size for each inclusion shape is obtained, computational models of heterogeneous Indirect Tensile Asphalt Cracking Test samples are then generated. These models include the components of viscoelastic mastic, linear elastic aggregates, and cohesive zone modeling to simulate the rate-dependent failure evolution from micro- to macro-cracking. Examination of load-displacement responses at multiple loading rates shows that both heterogeneous models replicate experimentally measured data satisfactorily. Through micro- and macro-level analyses, this study enhances our understanding of the composition-performance relationships in asphalt pavement materials. The procedure proposed in this study allows us to identify the optimal RVE sizes that preserve computational efficiency without significantly compromising their ability to capture the asphalt material behavior under specific operational conditions.

Carbon nanotubes (CNTs) are extensively utilized in the fabrication of high-performance composites due to their exceptional mechanical, electrical, and thermal characteristics. To investigate the mechanical properties of CNTs filled polymers accurately and effectively, a 3D modeling approach that incorporates the microstructural attributes of CNTs was introduced. Initially, a representative volume element model was constructed utilizing the modified nearest neighbor algorithm. During the modeling phase, a corresponding interference judgment method was suggested, taking into account the potential positional relationships among the CNTs. Subsequently, stress–strain curves of the model under various loading conditions were derived through finite element analysis employing the volume averaging technique. To validate the efficacy of the modeling approach, the stress within a CNT/epoxy resin composite with varying volume fractions under different axial strains was computed. The resulting stress–strain curves were in good agreement with experimental data from the existing literature. Hence, the modeling method proposed in this study provides a more precise representation of the random distribution of CNTs in the matrix. Furthermore, it is applicable to a broader range of aspect ratios, thereby enabling the CNT simulation model to more closely align with real-world models.

We present an efficient approach to evaluate the size dependency of elastic and plastic properties of metallic polycrystalline materials. Specifically, we consider different volume fractions of ferrite and martensite phases for the construction of three macroscopic domains. Statistical Volume Elements (SVEs) of different sizes are extracted from these domains using the moving window method. Linear and Crystal Plasticity (CP) simulations provide elastic and plastic properties of the SVEs such as the bulk and shear moduli, yield strength, and hardening modulus. We use a variation-based criterion to determine the Representative Volume Element (RVE) size of these properties. This RVE size corresponds to a size beyond which the given property can be idealized as homogeneous. We also use anisotropy indices and an additional RVE size criterion to determine the size limits beyond which these properties can be idealized as isotropic. Numerical results show that the plastic properties often reach their homogeneity and isotropy limits at larger sizes compared to elastic properties. This effect is more pronounced for the hardening modulus compared to the yield strength.

The present article investigates the failure mechanism of the composite laminates with respect to a coupled thermo-mechanical effect. To this end, a novel coupled thermo-mechanical modeling scheme is presented. To accurately capture the nonlinear deformation at macro- and micro-scale affected by the temperature field, the finite volume method is employed to compute the thermal stress, which is introduced into the representative volume element to evaluate the whole microscopic stress field and the macroscopic mechanical behaviors on basis of the finite volume direct averaging micromechanics. In addition, a visco-plastic constitutive model with full consideration of the temperature effect is implanted into the presented multi-scale model to investigate their nonlinear responses. The thermo-mechanical coupling test scheme is subtly designed, and the experimental data shows a high consistency with the theoretical results. On this basis, the microscopic morphology of the fracture surface is further characterized. It is revealed that an elevate temperature improve the matrix toughness to some extent. [ABSTRACT FROM AUTHOR]

Hydrogen grain boundary (GB) trapping is widely accepted as the main cause for hydrogen induced intergranular failure. Several studies were conducted to unveil the role of GBs on hydrogen transport; however, a clear understanding is yet to be attained. This is due to the limitations of the state-of-the-art experimental procedures for such highly kinetic processes. In this study, we aim at providing a deeper understanding of hydrogen-GB interactions using full-field representative volume element (RVE). The phase-field method is chosen for generating RVEs, since it is an appropriate numerical tool to represent GBs. A novel fully-kinetic formulation for hydrogen diffusion and GB trapping is presented, which is compatible with the phase-field based RVEs. GB diffusivity (D gb) and trap-binding energy (E gb) were used as parameters to understand the interactions between diffusion and GB trapping. Uptake and permeation simulations were performed with constant and gradient occupancy boundary conditions respectively. In both cases, increasing E gb , increased the hydrogen GB occupancy. The permeation simulations showed that the hydrogen flux along the GBs increased with increasing both, D gb and, surprisingly, E gb. Since trapping increases the hydrogen occupancy along GBs, it also increases the occupancy gradients, resulting in a higher flux. This led to the conclusion that, in the case of an external occupancy gradient, GB trapping and diffusion cooperate, rather than compete, to increase the hydrogen flux. On the other hand, the decisive factor for the retention of hydrogen at the GBs in permeation simulations was D gb rather than E gb. [Display omitted] • A new full-field model for H diffusion and GB trapping is presented. • The model shows the kinetic interactions of GB diffusivity and trapping. • The build-up of H due to trapping increases the permeation flux. • GB diffusion and trapping constructively interact, increasing H flux. [ABSTRACT FROM AUTHOR]

Summary: A multiscale model for saturated porous media is proposed, based on the concept of representative volume element (RVE). The physics between macro and micro‐scales is linked in terms of virtual power measures given by the general theory of poromechanics. Then, applying the so‐called Principle of Multiscale Virtual Power, together with suitable admissible constraints on micro‐scale displacement and pore pressure fields, a well‐established variational framework is obtained. This setting allows deriving the weak form of micro‐scale balance equations as well as the homogenization rules for the macro‐scale stress‐like variables and body forces. Whenever the micro‐scale mechanical constitutive functionals admit, as input arguments, the full‐order expansion of the micro‐scale pore pressure field, a size effect is inherited on the macro‐scale material response. The current literature attributes this issue to the so‐called "dynamical" or "second‐order" term of the homogenized flux velocity. It has been commonly suggested that the influence of this term is negligible by assuming infinitely small micro‐scale dimensions. However, such an idea compromises the fundamental notion of the existence of RVE for highly heterogeneous media. In this work, we show that the micro‐scale size dependence can be consistently eliminated by a simple constitutive‐like assumption. Accordingly, slight and selective redefinitions in the input arguments of micro‐scale material laws are proposed, leading to a constitutive formulation that allows the combination of micro‐scale variables with different orders of expansion. Just at this specific (constitutive) level, a reduced‐order expansion is selectively adopted for the micro‐scale pore pressure field. Thus, the RVE notion is restored while still retaining the major effects of the "dynamical" component of the homogenized flux velocity. The proposed formulation is implemented within a finite element squared (FE2$$ {}^2 $$) environment. Some numerical experiments are presented showing the viability of the methodology, including comparisons against analytical, mono‐scale and DNS solutions. [ABSTRACT FROM AUTHOR]