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Статті в журналах з теми "Multi-Scale finite element method"

Автор: Grafiati

Опубліковано: 7 грудня 2024

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1

Li, Cui Yu, and Xiao Tao Zhang. "Multi-Scale Finite Element Method and its Application." Advanced Materials Research 146-147 (October 2010): 1583–86. http://dx.doi.org/10.4028/www.scientific.net/amr.146-147.1583.

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In order to improve the computing precision and computing efficiency of strength of woven composite material, the strength of woven composite material based on multi-scale finite element method (MsFEM) is simulated. The periodical boundary conditions are applied to the finite element method analyses to ensure stress continuous and strain continuous on boundary surfaces. The method can efficiently capture the large scale behavior of the solution without resolving all the small scale features by constructing the multi-scale finite element base functions that are adaptive to the local property of the differential operator. The characteristic difference between MsFEM and the conventional finite element method is attributed to base function. The applications demonstrate that the advantages of the multi-scale finite element method for numerical simulation of strength problem of woven composite material, i.e. significantly reducing computational efforts, and improving the accuracy of the solutions.

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2

Hiu, Haifeng, Changzhi Wang, and Xiaoguang Hu. "Multi-scale Finite Element Method for Members for Pipe Frames." IOP Conference Series: Earth and Environmental Science 446 (March 21, 2020): 052045. http://dx.doi.org/10.1088/1755-1315/446/5/052045.

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3

Chen, Ning, Jiaojiao Chen, Jian Liu, Dejie Yu, and Hui Yin. "A homogenization-based Chebyshev interval finite element method for periodical composite structural-acoustic systems with multi-scale interval parameters." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 233, no. 10 (December 12, 2018): 3444–58. http://dx.doi.org/10.1177/0954406218819030.

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For the periodical composite structural-acoustic system with multi-scale interval uncertainties, a new interval analysis approach is presented in this study. In periodical composites structural-acoustic systems with multi-scale interval parameters, the variation ranges of the sound pressure response can be calculated using the homogenization-based interval finite element method. However, the homogenization-based interval finite element method that is based on Taylor series can only suit periodical composites structural-acoustic problems with small uncertainty degree. To consider larger uncertainty degree, by combining the Chebyshev polynomial series and the homogenization-based finite element, a homogenization-based Chebyshev interval finite element method is presented to predict the sound pressure responses of the structural-acoustic system involving periodical composite and multi-scale interval parameters. Compared with homogenization-based interval finite element method, homogenization-based Chebyshev interval finite element method can obtain higher accurate numerical solutions in the approximate process. Besides, homogenization-based Chebyshev interval finite element method can be implemented without conducting the complex derivation process. Numerical results verify the validity and practicability of the presented homogenization-based Chebyshev interval finite element method for the periodical composite structural-acoustic problem.

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4

Xiang, Jia Wei, Zhan Si Jiang, and Jin Yong Xu. "A Wavelet-Based Finite Element Method for Modal Analysis of Beams." Advanced Materials Research 97-101 (March 2010): 2728–31. http://dx.doi.org/10.4028/www.scientific.net/amr.97-101.2728.

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A new wavelet-based finite element method was proposed for analyzing modal parameters of beams. The Hermite cubic splines wavelet on the interval (HCSWI) was employed as the multi-scale interpolating basis for construct beam element. For the orthogonal characteristic of the wavelet basis with respect to given inner product, the corresponding multi-scale finite element equation will decoupled across scales totally or partially and suit for nesting approximation. Some numerical examples indicate that the proposed method have higher efficiency and precision.

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5

Peng, Mengyao, Min Liu, Shuitao Gu, and Shidong Nie. "Multiaxial Fatigue Analysis of Jacket-Type Offshore Wind Turbine Based on Multi-Scale Finite Element Model." Materials 16, no. 12 (June 14, 2023): 4383. http://dx.doi.org/10.3390/ma16124383.

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The fatigue damage of a local joint is the key factor accounting for the structural failure of a jacket-type offshore wind turbine. Meanwhile, the structure experiences a complex multiaxial stress state under wind and wave random loading. This paper aims to develop a multi-scale modeling method for a jacket-type offshore wind turbine, in which local joints of the jacket are modeled in a detail by using solid elements, and other components are modeled via the common beam element. Considering the multiaxial stress state of the local joint, multi-axial fatigue damage analysis based on the multiaxial S–N curve is performed using equivalent Mises and Lemaitre methods. The uniaxial fatigue damage data of the jacket model calculated using the multi-scale finite element model are compared with those of the conventional beam model. The results show that the tubular joint of jacket leg and brace connections can be modeled using the multi-scale method, since the uniaxial fatigue damage degree can reach a 15% difference. The comparison of uniaxial and multiaxial fatigue results obtained using the multi-scale finite element model shows that the difference can be about 15% larger. It is suggested that the multi-scale finite element model should be used for better accuracy in the multiaxial fatigue analysis of the jacket-type offshore wind turbine under wind and wave random loading.

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6

KIM, HYOUNG SEOP. "MULTI-SCALE FINITE ELEMENT SIMULATION OF SEVERE PLASTIC DEFORMATION." International Journal of Modern Physics B 23, no. 06n07 (March 20, 2009): 1621–26. http://dx.doi.org/10.1142/s0217979209061366.

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The technique of severe plastic deformation (SPD) enables one to produce metals and alloys with an ultrafine grain size of about 100 nm and less. As the mechanical properties of such ultrafine grained materials are governed by the plastic deformation during the SPD process, the understanding of the stress and strain development in a workpiece is very important for optimizing the SPD process design and for microstructural control. The objectives of this work is to present a constitutive model based on the dislocation density and dislocation cell evolution for large plastic strains as applied to equal channel angular pressing (ECAP). This paper briefly introduces the constitutive model and presents the results obtained with this model for ECAP by the finite element method.

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7

Jia, Hongxing, Shizhu Tian, Shuangjiang Li, Weiyi Wu, and Xinjiang Cai. "Seismic application of multi-scale finite element model for hybrid simulation." International Journal of Structural Integrity 9, no. 4 (August 13, 2018): 548–59. http://dx.doi.org/10.1108/ijsi-04-2017-0027.

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Purpose Hybrid simulation, which is a general technique for obtaining the seismic response of an entire structure, is an improvement of the traditional seismic test technique. In order to improve the analysis accuracy of the numerical substructure in hybrid simulation, the purpose of this paper is to propose an innovative hybrid simulation technique. The technique combines the multi-scale finite element (MFE) analysis method and hybrid simulation method with the objective of achieving the balance between the accuracy and efficiency for the numerical substructure simulation. Design/methodology/approach To achieve this goal, a hybrid simulation system is established based on the MTS servo control system to develop a hybrid analysis model using an MFE model. Moreover, in order to verify the efficiency of the technique, the hybrid simulation of a three-storey benchmark structure is conducted. In this simulation, a ductile column—represented by a half-scale scale specimen—is selected as the experimental element, meanwhile the rest of the frame is modelled as microscopic and macroscopic elements in the Abaqus software simultaneously. Finally, to demonstrate the stability and accuracy of the proposed technique, the seismic response of the target structure obtained via hybrid simulation using the MFE model is compared with that of the numerical simulation. Findings First, the use of the hybrid simulation with the MFE model yields results similar to those obtained by the fine finite element (FE) model using solid elements without adding excessive computing burden, thus advancing the application of the hybrid simulation in large complex structures. Moreover, the proposed hybrid simulation is found to be more versatile in structural seismic analysis than other techniques. Second, the hybrid simulation system developed in this paper can perform hybrid simulation with the MFE model as well as handle the integration and coupling of the experimental elements with the numerical substructure, which consists of the macro- and micro-level elements. Third, conducting the hybrid simulation by applying earthquake motion to simulate seismic structural behaviour is feasible by using Abaqus to model the numerical substructure and harmonise the boundary connections between three different scale elements. Research limitations/implications In terms of the implementation of the hybrid simulation with the MFE model, this work is helpful to advance the hybrid simulation method in the structural experiment field. Nevertheless, there is still a need to refine and enhance the current technique, especially when the hybrid simulation is used in real complex engineering structures, having numerous micro-level elements. A large number of these elements may render the relevant hybrid simulations unattainable because the time consumed in the numeral calculations can become excessive, making the testing of the loading system almost difficult to run smoothly. Practical implications The MFE model is implemented in hybrid simulation, enabling to overcome the problems related to the testing accuracy caused by the numerical substructure simplifications using only macro-level elements. Originality/value This paper is the first to recognise the advantage of the MFE analysis method in hybrid simulation and propose an innovative hybrid simulation technique, combining the MFE analysis method with hybrid simulation method to strike a delicate balance between the accuracy and efficiency of the numerical substructure simulation in hybrid simulation. With the help of the coordinated analysis of FEs at different scales, not only the accuracy and reliability of the overall seismic analysis of the structure is improved, but the computational cost can be restrained to ensure the efficiency of hybrid simulation.

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8

Bardi, Istvan, Kezhong Zhao, Rickard Petersson, John Silvestro, and Nancy Lambert. "Multi-domain multi-scale problems in high frequency finite element methods." COMPEL - The international journal for computation and mathematics in electrical and electronic engineering 32, no. 5 (September 9, 2013): 1471–83. http://dx.doi.org/10.1108/compel-04-2013-0123.

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9

Gai, Wen Hai, R. Guo, and Jun Guo. "Molecular Dynamics Approach and its Application in the Analysis of Multi-Scale." Applied Mechanics and Materials 444-445 (October 2013): 1364–69. http://dx.doi.org/10.4028/www.scientific.net/amm.444-445.1364.

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Numerical simulation of the behavior of materials can be used as a versatile, efficient and low cost tool for developing an understanding of material behavior [. The numerical simulation methods include quantum mechanics, molecular dynamics, Voronoi cell finite element method and finite element method et al. These methods themselves are not sufficient for many fundamental problems in computational mechanics, and the deficiencies lead to the thrust of multiple-scale methods. The multi-scale method to model micro-scale systems by coupled continuum mechanics and molecular dynamics was introduced. This paper describes the basic methods of multi-scale and general simulation process of molecular dynamics was reviewed.

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10

HE, WEN-YU, and WEI-XIN REN. "ADAPTIVE TRIGONOMETRIC HERMITE WAVELET FINITE ELEMENT METHOD FOR STRUCTURAL ANALYSIS." International Journal of Structural Stability and Dynamics 13, no. 01 (February 2013): 1350007. http://dx.doi.org/10.1142/s0219455413500077.

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Owing to its good approximation characteristics of trigonometric functions and the multi-resolution local characteristics of wavelet, the trigonometric Hermite wavelet function is used as the element interpolation function. The corresponding trigonometric wavelet beam element is formulated based on the principle of minimum potential energy. As the order of wavelet can be enhanced easily and the multi-resolution can be achieved by the multi-scale of wavelet, the hierarchical and multi-resolution trigonometric wavelet beam element methods are proposed for the adaptive analysis. Numerical examples have demonstrated that the aforementioned two methods are effective in improving the computational accuracy. The trigonometric wavelet finite element method (WFEM) proposed herein provides an alternative approach for improving the computational accuracy, which can be tailored for the problem considered.

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11

Liu, B., Y. Huang, H. Jiang, S. Qu, and K. C. Hwang. "The atomic-scale finite element method." Computer Methods in Applied Mechanics and Engineering 193, no. 17-20 (May 2004): 1849–64. http://dx.doi.org/10.1016/j.cma.2003.12.037.

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12

Hoppe, R. H. W., and S. I. Petrova. "Multi-scale Method for the Crack Problem in Microstructural Materials." Computational Methods in Applied Mathematics 10, no. 1 (2010): 69–86. http://dx.doi.org/10.2478/cmam-2010-0003.

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AbstractThe paper deals with the numerical computation of a crack problem posed on microstructural heterogeneous materials containing multiple phases in the microstructure. The failure of such materials is a natural multi-scale effect since cracks typically nucleate in regions of defects on the microscopic scale. The modeling strategy for solving the crack problem concerns simultaneously the macroscopic and microscopic models. Our approach is based on an efficient combination of the homogenization technique and the mesh superposition method (s-version of the finite element method). The homogenized model relies on a double-scale asymptotic expansion of the displacement field. The mesh superposition method uses two independent (global and local) finite element meshes and the concept of superposing the local mesh arbitrarily on the global continuous mesh. The crack is treated by the local mesh and the homogenized material model is considered on the global mesh. Numerical experiments for problems on biomorphic microcellular ceramic templates with porous microstructures of different materials constituents are presented.

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13

Li, L. X., Y. L. Chen, and Z. C. Lu. "Generalization of the multi-scale finite element method to plane elasticity problems." Applied Mathematical Modelling 39, no. 2 (January 2015): 642–53. http://dx.doi.org/10.1016/j.apm.2014.06.012.

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14

ZHU, SONGYE, WEN-YU HE, and WEI-XIN REN. "ADAPTIVE-SCALE DAMAGE DETECTION FOR FRAME STRUCTURES USING BEAM-TYPE WAVELET FINITE ELEMENT: EXPERIMENTAL VALIDATION." Journal of Earthquake and Tsunami 07, no. 03 (September 2013): 1350024. http://dx.doi.org/10.1142/s1793431113500243.

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The superior human vision system provides ingenious insight into an ideal damage detection strategy in which structural modeling scales are not only spatially varying but also dynamically changed according to actual needs. This paper experimentally examines the efficacy of a multi-scale damage detection method based on wavelet finite element model (WFEM). The beam-type wavelet finite element in this study utilizes the second-generation cubic Hermite multi-wavelets as interpolation functions. The dynamic testing results of a one-bay steel portal frame with multiple damages are employed in the experimental validation. Through a multi-stage updating of the WFEM, the multiple damages in the steel portal frame are detected in a progressive manner: the suspected region is first identified using a low-scale structural model, and the more accurate location and severity of the damage can be identified using a multi-scale model with local refinement. As the multi-scale WFEM considerably facilitates the adaptive change of modeling scales, the proposed multi-scale damage detection method can efficiently locate and quantify damage with minimal computation effort and a limited number of updating parameters and sensors, compared with conventional finite element methods.

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15

Zhai, Jun-Jun, Xiang-Xia Kong, and Lu-Chen Wang. "Thermo-Viscoelastic Response of 3D Braided Composites Based on a Novel FsMsFE Method." Materials 14, no. 2 (January 7, 2021): 271. http://dx.doi.org/10.3390/ma14020271.

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A homogenization-based five-step multi-scale finite element (FsMsFE) simulation framework is developed to describe the time-temperature-dependent viscoelastic behavior of 3D braided four-directional composites. The current analysis was performed via three-scale finite element models, the fiber/matrix (microscopic) representative unit cell (RUC) model, the yarn/matrix (mesoscopic) representative unit cell model, and the macroscopic solid model with homogeneous property. Coupling the time-temperature equivalence principle, multi-phase finite element approach, Laplace transformation and Prony series fitting technology, the character of the stress relaxation behaviors at three scales subject to variation in temperature is investigated, and the equivalent time-dependent thermal expansion coefficients (TTEC), the equivalent time-dependent thermal relaxation modulus (TTRM) under micro-scale and meso-scale were predicted. Furthermore, the impacts of temperature, structural parameters and relaxation time on the time-dependent thermo-viscoelastic properties of 3D braided four-directional composites were studied.

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16

Zhai, Jun-Jun, Xiang-Xia Kong, and Lu-Chen Wang. "Thermo-Viscoelastic Response of 3D Braided Composites Based on a Novel FsMsFE Method." Materials 14, no. 2 (January 7, 2021): 271. http://dx.doi.org/10.3390/ma14020271.

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Анотація:

A homogenization-based five-step multi-scale finite element (FsMsFE) simulation framework is developed to describe the time-temperature-dependent viscoelastic behavior of 3D braided four-directional composites. The current analysis was performed via three-scale finite element models, the fiber/matrix (microscopic) representative unit cell (RUC) model, the yarn/matrix (mesoscopic) representative unit cell model, and the macroscopic solid model with homogeneous property. Coupling the time-temperature equivalence principle, multi-phase finite element approach, Laplace transformation and Prony series fitting technology, the character of the stress relaxation behaviors at three scales subject to variation in temperature is investigated, and the equivalent time-dependent thermal expansion coefficients (TTEC), the equivalent time-dependent thermal relaxation modulus (TTRM) under micro-scale and meso-scale were predicted. Furthermore, the impacts of temperature, structural parameters and relaxation time on the time-dependent thermo-viscoelastic properties of 3D braided four-directional composites were studied.

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17

He, Wen-Yu, Songye Zhu, and Zhi-Wei Chen. "Wavelet-based multi-scale finite element modeling and modal identification for structural damage detection." Advances in Structural Engineering 20, no. 8 (January 18, 2017): 1185–95. http://dx.doi.org/10.1177/1369433216687566.

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Wavelet techniques enable multi-resolution analysis that can represent a function (either field or signal function) in a multi-scale manner. This article presents a damage detection method with dynamically changed scales in both temporal and spatial domains, by taking advantage of the wavelet-based multi-resolution analysis. This method combines a wavelet-based finite element model (WFEM) that employs B-spline wavelet as shape functions and wavelet-based modal identification method to detect structural damage progressively. High-fidelity modal information can be computed or identified with minimized computation cost by lifting the wavelet scales in the wavelet-based finite element model and in signal processing individually according to the actual requirements. Numerical examples demonstrate that the accuracy of damage detection is improved considerably by this lifting strategy during the damage detection process. Besides, fewer degrees of freedom are involved in the wavelet-based finite element model than those of traditional finite element method. The computational efficiency can be improved to large extent and computation resources can be utilized more rationally using the proposed multi-scale approach.

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18

Tang, Shao Fan, Fu Hua Huang, Jun Liang, and Shan Yi Du. "Multi-Scale Analysis for Thermo-Elasticity Properties of Composite Materials with Small Periodic Configuration." Key Engineering Materials 334-335 (March 2007): 25–28. http://dx.doi.org/10.4028/www.scientific.net/kem.334-335.25.

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In this paper, based on the equations of coupled thermo-elasticity, two-scale asymptotic expressions of the temperature and displacement of composite materials under coupled thermo-elasticity condition are set up with the perturbation method. By the multi-scale finite element method, the temperature and 2-order displacement, strain and stress of composite materials with small periodic configuration under coupled thermo-elasticity condition are calculated. Comparing with the results calculated by finite element method with refined meshes, it’s shown that multi-scale method is an efficient method, and the calculation precision is satisfied.

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19

R. C. Reis, Renata, Marcio L. M. Kimpara, João Onofre Pereira Pinto, and Babak Fahimi. "MULTI-PHYSICS SIMULATION OF 6/4 SWITCHED RELUCTANCE MOTOR BY FINITE ELEMENT METHOD." Eletrônica de Potência 26, no. 1 (March 31, 2021): 8–18. http://dx.doi.org/10.18618/rep.2021.1.0004.

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20

He, Wen-Yu, Songye Zhu, and Zhi-Wei Chen. "A Multi-Scale Wavelet Finite Element Model for Damage Detection of Beams Under a Moving Load." International Journal of Structural Stability and Dynamics 18, no. 06 (June 2018): 1850078. http://dx.doi.org/10.1142/s0219455418500785.

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The resolution of structural finite element model (FEM) determines the computation cost and accuracy in dynamic analysis. This study proposes a novel wavelet finite element model (WFEM), which facilitates adaptive mesh refinement, for the dynamic analysis and damage detection of beam structures subjected to a moving load (ML). The multi-scale equations of motion for the beam under the ML are derived using the second-generation cubic Hermite multi-wavelets as the shape functions. Then an adaptive-scale analysis strategy is established, in which the scales of the wavelet beam elements are dynamically changed according to the ML position. The performance of the multi-scale WFEM is examined in both dynamic analysis and damage detection problems. It is demonstrated that the multi-scale WFEM with a similar number of degrees of freedom can achieve much higher accuracy than the traditional FEM. In particular, the multi-scale WFEM enables the detection of sub-element damage with a progressive model updating process. The advantage in computation efficiency and accuracy makes the proposed method a promising tool for multi-scale dynamic analysis or damage detection of structures.

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21

Wu, Yuching, and Jianzhuang Xiao. "Implementation of the Multiscale Stochastic Finite Element Method on Elliptic PDE Problems." International Journal of Computational Methods 14, no. 01 (January 11, 2017): 1750003. http://dx.doi.org/10.1142/s0219876217500037.

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In this study, a multi-scale finite element method was proposed to solve two linear scale-coupling stochastic elliptic PDE problems, a tightly stretched wire and flow through porous media. At microscopic level, the main idea was to form coarse-scale equations with a prescribed analytic form that may differ from the underlying fine-scale equations. The relevant stochastic homogenization theory was proposed to model the effective global material coefficient matrix. At the macroscopic level, the Karhunen–Loeve decomposition was coupled with a Polynomial Chaos expansion in conjunction with a Galerkin projection to achieve an efficient implementation of the randomness into the solution procedure. Various stochastic methods were used to plug the microscopic cell to the global system. Strategy and relevant algorithms were developed to boost computational efficiency and to break the curse of dimension. The results of numerical examples were shown consistent with ones from literature. It indicates that the proposed numerical method can act as a paradigm for general stochastic partial differential equations involving multi-scale stochastic data. After some modification, the proposed numerical method could be extended to diverse scientific disciplines such as geophysics, material science, biological systems, chemical physics, oceanography, and astrophysics, etc.

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22

Mohammadpour, Ehsan, and Mokhtar Awang. "Nonlinear Multi-Scale Finite Element Method to Predict Tensile Behavior of Carbon Nanotube-Reinforced Polymer Composites." Journal of Nano Research 26 (December 2013): 169–76. http://dx.doi.org/10.4028/www.scientific.net/jnanor.26.169.

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The ability of carbon nanotubes (CNTs) to consider as the strongest and stiffest elements in nanoscale composites remains a powerful motivation for the research in this area. This paper describes a finite element (FE) approach for prediction of the mechanical behavior of polypropylene (PP) matrix reinforced with single walled carbon nanotubes (SWCNTs). A representative volume element is proposed for modeling the tensile behavior of aligned CNTs/PP composites. The CNT is modeled with solid elements. Modified Morse potential is used for simulating the mechanical properties of an isolated carbon nanotube. The matrix is modeled as a continuum medium by utilizing an appropriate nonlinear material model. A cohesive zone model is assumed between the nanotube and the matrix with perfect bonding until the interfacial shear stress exceeds the bonding strength. Using the representative volume element, a unidirectional CNT/PP composite was modeled and the results were compared with corresponding rule-of-mixtures predictions. The effect of interfacial shear strength on the tensile behavior of the nanocomposite was also studied. The influence of the SWCNT within the polymer is clearly illustrated and discussed. The results showed that polymer's Young's modulus and tensile strength increase significantly in the presence of carbon nanotubes.

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23

Fang, Xiwu, Zhenyu Liu, Jianrong Tan, Chan Qiu, and Fengbei Chen. "Multi-scale simulation method with coupled finite/discrete element model and its application." Chinese Journal of Mechanical Engineering 26, no. 4 (July 2013): 659–67. http://dx.doi.org/10.3901/cjme.2013.04.659.

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24

NAKAMACHI, Eiji, Shinji IIHOSHI, Yiping CHEN, Sei UEDA, Yasutomo UETSUJI, and Kouhei FUJITA. "Multi-Scale Plastic Deformation Analyses By Using A Crystallographic Homogenization Finite Element Method." Transactions of the Japan Society of Mechanical Engineers Series A 70, no. 690 (2004): 191–97. http://dx.doi.org/10.1299/kikaia.70.191.

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25

UETSUJI, Yasutomo, Yukihiro NAKAMURA, Sei UEDA, and Eiji NAKAMACHI. "Multi-scale Finite Element Analysis of Piezoelectric Ceramics Based on Crystallographic Homogenization Method." Proceedings of The Computational Mechanics Conference 2002.15 (2002): 293–94. http://dx.doi.org/10.1299/jsmecmd.2002.15.293.

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26

KURAMAE, Hiroyuki, and Eiji NAKAMACHI. "Parallel Computing for Multi-scale Finite Element Analysis based on Crystalline Homogenization Method." Proceedings of The Computational Mechanics Conference 2004.17 (2004): 715–16. http://dx.doi.org/10.1299/jsmecmd.2004.17.715.

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27

Li, Hao, and Yidu Yang. "The adaptive finite element method based on multi-scale discretizations for eigenvalue problems." Computers & Mathematics with Applications 65, no. 7 (April 2013): 1086–102. http://dx.doi.org/10.1016/j.camwa.2013.01.043.

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28

Xu, Qiang, Jian-Yun Chen, Jing Li, Gang Xu, and Hong-Yuan Yue. "Study on spline wavelet finite-element method in multi-scale analysis for foundation." Acta Mechanica Sinica 29, no. 5 (October 2013): 699–708. http://dx.doi.org/10.1007/s10409-013-0075-5.

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29

Kieda, Shigekazu, Noriyuki Ashiwake, Takahiro Daikoku, and Shizuo Zushi. "Application of Stochastic Finite Element Method to Thermal Analysis for Computer Cooling." Journal of Electronic Packaging 115, no. 3 (September 1, 1993): 270–75. http://dx.doi.org/10.1115/1.2909328.

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Анотація:

A stochastic finite element method is applied to thermal analysis of cooling in large-scale computers using a multi-fin flexible thermal contactor. The stochastic finite element method is a general technique to incorporate the effect of stochastic or statistical features of parameters into a finite element method by means of sensitivity analysis. Using this method, the temperature distribution of the chip is calculated, and also temperature variations associated with variations of thermal properties, heat generation rates, and uncertainties involved in real systems are estimated. Following presentation of the results obtained, the thermal performance of this system and applicability of the stochastic finite element method to computer cooling problems are discussed.

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30

Lu, Yaohui, Heyan Zheng, Chuan Lu, Tianli Chen, Jing Zeng, and Pingsha Dong. "Analysis methods of the dynamic structural stress in a full-scale welded carbody for high-speed trains." Advances in Mechanical Engineering 10, no. 10 (October 2018): 168781401880591. http://dx.doi.org/10.1177/1687814018805917.

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The calculation of the dynamic stress of a large and complex welded carbody is the key to the fatigue design and the durability evaluation of the carbody. Adopting the advanced structural stress based on the finite element method, a new finite element transformation method between random loads and dynamic stresses is proposed to be applied in carbody for high-speed trains. The multi-axial random dynamic load spectrums of full-scale carbody are obtained by the vehicle system dynamics method, and the shell finite element model of a full-scale carbody is established. Adopting the concept of a surrogate model, the finite element transformation relationship between the random load and the dynamic structural stress at concerned points is constructed by using multidisciplinary methods to compute the dynamic stress spectrums of concerned points at the welding seam, and dynamic structural stresses are compared and validated through carbody rig-test. The analysis methods of dynamic structural stress are performed systematically for a full-scale welded structure, which provides reference methods for the fatigue durability evaluation of large-scale welded structures.

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31

Liu, Miao, Yan Cao, Zhijie Wang, and Chaorui Nie. "Multi-scale Numerical Simulation of Powder Metallurgy Densification Process." Journal of Physics: Conference Series 2501, no. 1 (May 1, 2023): 012022. http://dx.doi.org/10.1088/1742-6596/2501/1/012022.

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Анотація:

Abstract In order to reduce defects such as pores, gold phases and cracks in powder metallurgy, scholars have studied the densification process of powder metallurgy. Based on the study of the powder metallurgy deformation mechanism, this paper classifies and summarizes the numerical simulation theory and the methods. At present, the numerical simulation of the densification process of powder metallurgy is carried out mainly in macroscopic, mesoscopic and microscopic directions. Macro scale is an application of finite element method based on continuum theory. The meso-scale is an application of the discrete element method based on the discontinuous media theory. Cellular automata simulation is the main numerical simulation method in the microscale. Different modeling theories and methods have their own adaptability and limitations. By combining the numerical simulation theory and the method of various scales, the process of densification of the material can be realized more accurately and accurately.

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32

Zheng, Jincheng, Peiwei Zhang, Dahai Zhang, and Dong Jiang. "A Multi-Scale Submodel Method for Fatigue Analysis of Braided Composite Structures." Materials 14, no. 15 (July 27, 2021): 4190. http://dx.doi.org/10.3390/ma14154190.

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Анотація:

A multi-scale fatigue analysis method for braided ceramic matrix composites (CMCs) based on sub-models is developed in this paper. The finite element shape function is used as the interpolation function for transferring the displacement information between the macro-scale and meso-scale models. The fatigue failure criterion based on the shear lag theory is used to implement the coupling calculation of the meso-scale and micro-scale. Combining the meso-scale cell model and the fatigue failure criterion based on the shear lag theory, the fatigue life of 2D SiC/SiC is analyzed. The analysis results are in good agreement with the experimental results, which proves the accuracy of the meso-scale cell model and the fatigue life calculation method. A multi-scale sub-model fatigue analysis method is used to study the fatigue damage of 2D SiC/SiC stiffened plates under random tension–tension loads. The influence of the sub-models at different positions in the macro-model element on the analysis results was analyzed. The results shows that the fatigue analysis method proposed in this paper takes into account the damage condition of the meso-structured of composite material, and at the same time has high calculation efficiency, and has low requirements for modeling of the macro finite element model, which can be better applied to the fatigue analysis of CMCs structure.

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33

NITTA, Naoya, Hiroyuki KURAMAE, Yusuke MORITA, and Eiji NAKAMACHI. "2412 Development of multi-scale and multi-physics finite element method of articular cartilage and chondrocyte." Proceedings of The Computational Mechanics Conference 2012.25 (2012): 535–37. http://dx.doi.org/10.1299/jsmecmd.2012.25.535.

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34

Zhang, Li Qiang, Ping Yang, Fang Wei Xie, Tao Xi, Xin Gang Yu, and Xi Fu Song. "MD-ISE-FE Multiscale Modeling and Numerical Simulation of Thermal Conductivity of Cu Film Interface Structure." Advanced Materials Research 382 (November 2011): 242–46. http://dx.doi.org/10.4028/www.scientific.net/amr.382.242.

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Анотація:

With the devices miniaturization, the properties of materials at the micro/nano scale were much different from what at Macro-scale because of the scale effect. The Interface Stress Element (ISE) was introduced into the multi-scale model. These three methods, Molecular Dynamics (MD), ISE and Finite Element (FE) were effectively combined by designing a handshake region and using the transition interface element method. The multi-scale model of film was built based on MD-ISE-FE. The sequential coupling method was used to calculate, and then, the results of the FE and ISE region were applied to the MD region. The EAM potential was used to simulate. The results were the basically same with the other experimental and simulation results in the reference. It indicated that the multi-scale analysis method could be applied to calculate the thermodynamics properties of the interface structure at the Micro/nano scale.

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35

Bayona Roa, Camilo Andrés, Joan Baiges, and R. Codina. "Variational multi-scale finite element approximation of the compressible Navier-Stokes equations." International Journal of Numerical Methods for Heat & Fluid Flow 26, no. 3/4 (May 3, 2016): 1240–71. http://dx.doi.org/10.1108/hff-11-2015-0483.

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Анотація:

Purpose – The purpose of this paper is to apply the variational multi-scale framework to the finite element approximation of the compressible Navier-Stokes equations written in conservation form. Even though this formulation is relatively well known, some particular features that have been applied with great success in other flow problems are incorporated. Design/methodology/approach – The orthogonal subgrid scales, the non-linear tracking of these subscales, and their time evolution are applied. Moreover, a systematic way to design the matrix of algorithmic parameters from the perspective of a Fourier analysis is given, and the adjoint of the non-linear operator including the volumetric part of the convective term is defined. Because the subgrid stabilization method works in the streamline direction, an anisotropic shock capturing method that keeps the diffusion unaltered in the direction of the streamlines, but modifies the crosswind diffusion is implemented. The artificial shock capturing diffusivity is calculated by using the orthogonal projection onto the finite element space of the gradient of the solution, instead of the common residual definition. Temporal derivatives are integrated in an explicit fashion. Findings – Subsonic and supersonic numerical experiments show that including the orthogonal, dynamic, and the non-linear subscales improve the accuracy of the compressible formulation. The non-linearity introduced by the anisotropic shock capturing method has less effect in the convergence behavior to the steady state. Originality/value – A complete investigation of the stabilized formulation of the compressible problem is addressed.

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36

Qian, Denghui, and Guoqing Liu. "FE/PDE: a novel approach applied to PC plate structure with multi-scale and multi-physics field coupling." Physica Scripta 99, no. 6 (May 22, 2024): 065252. http://dx.doi.org/10.1088/1402-4896/ad49ea.

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Abstract For the more straightforward and more efficient solution of phononic crystal (PC) plate frequency band structure, transmission curve, and vibration mode, in this paper, related theories based on spatial Fourier series expansions, combined with Bloch’s theorem, a novel approach to solve the structural governing equations of PC plate is proposed by using the partial differential equations (PDE) module in the finite element software COMSOL. It is named the FE/PDE (Finite element and partial differential equations) method. The method’s accuracy is verified by comparing the results with those obtained from the traditional method. Systematic elucidation of the application of the method to probe the properties of multi-scale, multi-physics field coupled PC plate. In order to demonstrate the flexibility and scientific validity of the method, a novel nano-piezoelectric PC plate structure is proposed and solved. The method is simple, computationally efficient, and applicable, and provides a new method for investigating the properties of PC plates.

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37

Trahan, Corey Jason, Mark Loveland, Noah Davis, and Elizabeth Ellison. "A Variational Quantum Linear Solver Application to Discrete Finite-Element Methods." Entropy 25, no. 4 (March 28, 2023): 580. http://dx.doi.org/10.3390/e25040580.

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Анотація:

Finite-element methods are industry standards for finding numerical solutions to partial differential equations. However, the application scale remains pivotal to the practical use of these methods, even for modern-day supercomputers. Large, multi-scale applications, for example, can be limited by their requirement of prohibitively large linear system solutions. It is therefore worthwhile to investigate whether near-term quantum algorithms have the potential for offering any kind of advantage over classical linear solvers. In this study, we investigate the recently proposed variational quantum linear solver (VQLS) for discrete solutions to partial differential equations. This method was found to scale polylogarithmically with the linear system size, and the method can be implemented using shallow quantum circuits on noisy intermediate-scale quantum (NISQ) computers. Herein, we utilize the hybrid VQLS to solve both the steady Poisson equation and the time-dependent heat and wave equations.

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38

Guo, Ling Ling, Yan Bo Liu, and Yu Zheng. "Simulation about Multi-Needle Electrospinning Based on Finite Element Method." Advanced Materials Research 332-334 (September 2011): 2157–60. http://dx.doi.org/10.4028/www.scientific.net/amr.332-334.2157.

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Анотація:

In the current study, the finite element analysis was used to simulate the change in electric field intensity due to the change of needle diameter and length, receiving distance，voltage and the spacing between needles located in a row. The resulting conclusion could be used to guide the design and manufacture of electrospinning machines at industrial scale.

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39

Ozgun, Ozlem, Raj Mittra, and Mustafa Kuzuoglu. "General-Purpose Characteristic Basis Finite Element Method for Multi-Scale Electrostatic and Electromagnetic Problems." Electromagnetics 30, no. 1-2 (March 9, 2010): 205–21. http://dx.doi.org/10.1080/02726340903485505.

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40

IIHOSHI, Shinji, Y. P. CHEN, Sei UEDA, Yasutomo UETSUJI, and Eiji NAKAMACHI. "Development of Multi-scale Plastic Analysis Code Based on Crystalline Homogenization Finite Element Method." Proceedings of The Computational Mechanics Conference 2002.15 (2002): 127–28. http://dx.doi.org/10.1299/jsmecmd.2002.15.127.

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41

KURAMAE, Hiroyuki, and Eiji NAKAMACHI. "Parallel Multi-scale Finite Element Analysis Based on Crystalline Homogenization Method Using Computational Grid." Proceedings of The Computational Mechanics Conference 2003.16 (2003): 51–52. http://dx.doi.org/10.1299/jsmecmd.2003.16.51.

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42

Gao, David Yang, and Haofeng Yu. "Multi-scale modelling and canonical dual finite element method in phase transitions of solids." International Journal of Solids and Structures 45, no. 13 (June 2008): 3660–73. http://dx.doi.org/10.1016/j.ijsolstr.2007.08.027.

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43

Hou, Thomas Y., Feng-Nan Hwang, Pengfei Liu, and Chien-Chou Yao. "An iteratively adaptive multi-scale finite element method for elliptic PDEs with rough coefficients." Journal of Computational Physics 336 (May 2017): 375–400. http://dx.doi.org/10.1016/j.jcp.2017.02.002.

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44

Parvazinia, M., V. Nassehi, and R. J. Wakeman. "Multi-scale finite element modelling using bubble function method for a convection–diffusion problem." Chemical Engineering Science 61, no. 8 (April 2006): 2742–51. http://dx.doi.org/10.1016/j.ces.2005.11.031.

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45

Raman, A., and M. Annamalai. "Structural scale modelling by finite element method approach." Computers & Structures 23, no. 6 (January 1986): 775–78. http://dx.doi.org/10.1016/0045-7949(86)90245-2.

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46

Maaboudallah, Farouk, and Noureddine Atalla. "A Multi-Scale Investigation to Predict the Dynamic Instabilities Induced by Frictional Contact." Lubricants 11, no. 8 (August 11, 2023): 344. http://dx.doi.org/10.3390/lubricants11080344.

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Анотація:

We propose a new variational formulation to model and predict friction-induced vibrations. The multi-scale computational framework exploits the results of (i) the roughness measurements and (ii) the micro-scale contact simulations, using the boundary element method, to enrich the contact zone of the macroscopic finite element model of rubbing systems with nominally flat contact boundaries. The resulting finite elements at the contact interface of the macroscopic model include (i) a modified normal gap and (ii) a micro-scale description of the contact law (i.e., pressure gap) derived by solving the frictionless contact problem on a rough surface indenting a rigid half-plane. The method is applied to a disc brake system to show its robustness in comparison with classical deterministic formulations. With respect to the traditional complex eigenvalues analysis, the proposed multi-scale approach shows that the inclusion of roughness significantly improves the results at low frequencies. In this panorama, any improvement of dynamic instabilities predictions should be based on an uncertainty analysis incorporating roughness combined with other parameters such as friction coefficient and shear moduli of the pads, rather than on roughness itself.

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47

HISADA, Toshiaki, Seiryo SUGIURA, and Hiroshi WATANABE. "Development of Multi-Scale and Multi-Physics Heart Simulator based on Fluid-Structure Interaction Finite Element Method." Journal of the Society of Mechanical Engineers 107, no. 1026 (2004): 368–71. http://dx.doi.org/10.1299/jsmemag.107.1026_368.

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48

Sun, Xiangkun, Changwei Zhou, Mohamed Ichchou, Jean-Pierre Lainé, and Abdel-Malek Zine. "Multi-Scale Homogenization of Transversal Waves in Periodic Composite Beams." International Journal of Applied Mechanics 09, no. 03 (April 2017): 1750039. http://dx.doi.org/10.1142/s1758825117500399.

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Анотація:

This paper deals with the deduction of new homogenized models for the flexural wave in bi-periodic beams. According to the homogenization theory, the long-wave assumption is used and the valid frequency range of homogenized models is limited to the first Bragg band gap. However, the classical homogenization method, whose idea is taking the component’s mean values as effective material properties, has limitations in mimicking the dispersive behavior and the real valid frequency range is far less than the limit. Thus, enriched homogenized models, derived by the multi-scale asymptotic homogenization method, are proposed to provide more accurate homogenization models with larger real valid frequency range. The new homogenized models are validated by investigating the dispersion relation in the infinite case and the frequency response function in the finite case. Wave finite element method (WFEM) are used to provide associated references. A parametric study is carried out in the infinite case while two different boundary conditions are considered in the finite case.

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49

YAZDANI, A., and V. NASSEHI. "FINITE ELEMENT SOLUTION OF MULTI-SCALE TRANSPORT PROBLEMS USING THE LEAST SQUARES-BASED BUBBLE FUNCTION ENRICHMENT." International Journal of Modeling, Simulation, and Scientific Computing 03, no. 04 (November 18, 2012): 1250019. http://dx.doi.org/10.1142/s1793962312500195.

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Анотація:

This paper presents a technique for deriving least-squares-based polynomial bubble functions to enrich the standard linear finite elements, employed in the formulation of Galerkin weighted-residual statements. The element-level linear shape functions are enhanced using supplementary polynomial bubble functions with undetermined coefficients. The enhanced shape functions are inserted into the model equation and the residual functional is constructed and minimized by using the method of the least squares, resulting in an algebraic system of equations which can be solved to determine the unknown polynomial coefficients in terms of element-level nodal values. The stiffness matrices are subsequently formed with the standard finite elements assembly procedures followed by using these enriched elements which require no additional nodes to be introduced and no extra degree of freedom incurred. Furthermore, the proposed technique is tested on a number of benchmark linear transport equations where the quadratic and cubic bubble functions are derived and the numerical results are compared against the exact and standard linear element solutions. It is demonstrated that low order bubble enriched elements provide more accurate approximations for the exact analytical solutions than the standard linear elements at no extra computational cost in spite of using relatively crude meshes. On the other hand, it is observed that a satisfactory solution of the strongly convection-dominated transport problems may require element enrichment by using significantly higher order polynomial bubble functions in addition to the use of extremely fine computational meshes.

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50

Xiong, Xiaoshuang, Shirley Z. Shen, Lin Hua, Jefferson Z. Liu, Xiang Li, Xiaojin Wan, and Menghe Miao. "Finite element models of natural fibers and their composites: A review." Journal of Reinforced Plastics and Composites 37, no. 9 (February 6, 2018): 617–35. http://dx.doi.org/10.1177/0731684418755552.

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Анотація:

Finite element method has been widely applied in modeling natural fibers and natural fiber reinforced composites. This paper is a comprehensive review of finite element models of natural fibers and natural fiber reinforced composites, focusing on the micromechanical properties (strength, deformation, failure, and damage), thermal properties (thermal conductivity), and macro shape deformation (stress–strain and fracture). Representative volume element model is the most popular homogenization-based multi-scale constitutive method used in the finite element method to investigate the effect of microstructures on the mechanical and thermal properties of natural fibers and natural fiber reinforced composites. The representative volume element models of natural fibers and natural fiber reinforced composites at various length scales are discussed, including two types of geometrical modeling methods, the computer-based modeling method and the image-based modeling method. Their modeling efficiency and accuracy are also discussed.

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