Representative Volume Element Method Research Articles

Three-Dimensional Micromechanical Modeling of Martensite Particle Size Effects on the Deformation Behavior of Dual-Phase Steels.

The objective of this study was to examine the influence of martensite particle size on the formation of stress and strain in microstructures of dual-phase steels. In order to achieve this objective, the 3D representative volume element (RVE) method was utilized. Particle size distributions were obtained from the microstructures of DP600 and DP1000 dual-phase steels as they actually exist. Virtual dual-phase steel microstructures were generated according to the above distribution and subsequent validation analyses were performed. In the subsequent phase, microstructures of varying martensite particle sizes (1 µm, 1.98 µm, 3 µm for DP600 and 1.15 µm, 2 µm, 3 µm for DP1000) were formed, and the effects of particle size on deformation behavior under tensile loads were determined. The findings indicated that an increase in martensite particle size resulted in a reduction in tensile strength, accompanied by an increase in deformation amount.

Multi-objective topological design considering functionally graded materials and coated fiber reinforcement

This study presents a multi-objective topology optimization method tailored to structures fabricated from functionally graded materials (FGMs), coated FGMs, and coated fiber-reinforced composite materials (FRCMs) with fixed fiber thickness. The design objective is the simultaneous minimization of elastic and thermal compliance. The material properties of these composite materials were derived to generate datasets using the representative volume element method under periodic boundary conditions. Subsequently, machine learning modules were developed based on the datasets to combine with the design process. The multi-objective optimization problem was addressed using the weighted sum method ensuring the generation of the Pareto front. The adaptive weighting strategy is employed to avoid biased results toward a single objective function. To define the coated boundaries within the design domain, image post-processing techniques such as convolution filters, interpolation schemes, and erosion methods were employed on the material layout information of the optimized FGM structures. Through numerical examples, optimized material layouts for coated assemblies incorporating FGMs and FRCMs are presented, with the performance verified through objective function values.

Digital twin-based identification of crystal plastic material parameters for weld joints of orthotropic steel decks

The identification of crystal plasticity (CP) material parameters is indispensable for using CP models to simulate and understand the microcrack initiation and propagation of orthotropic steel decks (OSD). This study proposes a digital twin (DT)-based framework for identifying CP material parameters of weld joints of OSD by fusing multiscale CP finite element model (CPFEM) with macroscale stress–strain material tests. The material tests of the specimen (physical entity) cut from the weld joints of OSD and sliced to the centimeter scale are carried out using the standard dynamic test system. The CPFEM simulation is used to develop a multiscale virtual entity to map the physical entity. The particle swarm optimization algorithm is used to fuse the CPFEM simulation with the material test data to identify CP material parameters and produce a DT. The results demonstrate that the CP material parameters identified by the proposed framework are more accurate than those identified by a single representative volume element method. The results also show that the DT-based identification of CP material parameters has high applicability.

Plastic damage fracture characteristics and constitutive modeling of rocks under uniaxial compression considering crack geometry

AbstractThe study of damage and failure in fractured rock masses is crucial. This study employs the representative volume element (RVE) method to develop a microscale rock model. The model simulates the propagation and rupture of fractures by integrating factors including actual mineralogical composition, the Weibull distribution function, the Mohr–Coulomb damage criterion, and strain softening. Results indicate that fractures reduce the uniaxial compressive strength of the rock and that peak strength is significantly correlated with crack geometries. Plastic damage in rocks was categorized into three stages: elastic, rapid growth, and postpeak softening. A logistic growth model describes the plastic volume change curves for rocks with various fracture geometries, establishing the relationship between plastic damage volume and damage variables. Constitutive models for rocks with varying fracture geometries under uniaxial compression were formulated. The accuracy and applicability of these models were validated, providing a theoretical basis for rock engineering applications.

Mechanical behaviour of 3D printed carbon fibre reinforced composite metastructure with various filling rates

This paper evaluated the influence of filling rate and printing direction on the mechanical properties of composite metastructure via experimental and numerical approaches. A representative volume element (RVE) and finite element method were adopted to estimate the tensile and flexural properties and verify the applicability of these methods in the 3D printing of composite metastructure. Results showed that apparent tensile and flexural properties drop with decreasing filling rates. The tensile and flexural strength reached 70.7 MPa and 131.1 MPa for solid specimens. The bending test for samples with different printing directions showed that the printing direction of the core has no noticeable effect on flexural strength, but the +45°/-45° sample exhibited the highest modulus. The numerical estimation showed similar trend compared to experimental results for both tensile and flexural properties. Such an attempt indicates the feasibility of designing a composite metastructure with an optimum weight-strength relationship.

Meso-scale finite element modelling of biaxial non-crimp-fabric composites under compression

Non-crimp-fabric (NCF) reinforced composites have been receiving attention in the composite market due to their cost-effectiveness and excellent mechanical performance. However, compared to traditional unidirectional laminates (UD), NCF composites have different mechanical behaviours due to their heterogeneous internal structures. The influence of the internal structure of biaxial NCF composites on compressive behaviour was therefore investigated in this study. The representative volume element (RVE) method was adopted to establish finite element (FE) models for biaxial NCF composites at the micro- and meso‑scale. Micro-scale models developed at fibre/matrix level could provide homogenised compressive properties of 0° and 90° tows, while meso‑scale repeated unit cell (RUC) models developed at tow/resin-rich area level could predict homogenised compressive behaviours of biaxial NCF composites. Finally, the homogenised meso‑RUC results were employed in the macro-scale FE model to validate the test result. The novelty lies in developing RUC models to comprehensively investigate key parameters at the micro- and meso‑scale controlling the overall compressive strength, including matrix strength, layup sequence, tow waviness, tow placement, interfacial strength, and out-of-plane shear stress. Another novelty is to explain the differences in compressive strengths between the RUC model and the test result. These models form a multiscale framework for biaxial NCF composites, which could contribute to an analysis tool for NCF material design. The FE results by this multiscale framework indicated that the misaligned resin-rich areas could contribute to the higher compressive strength. Increasing tow waviness could change the failure mode from fibre crushing to fibre kinking failure, while matrix properties, interfacial strength, and fibre waviness were the key factors influencing compressive strength. The conclusion can further guide the development of NCF composites with optimal compressive strength.

Design Optimization of Flexural and Eigenvalue Characteristics of Perforated and Skewed Bio-Composite Functionally Graded Panels

The development of novel materials is of prime importance in the biomedical areas, especially for bone replacements and dental implants. This study uses finite element modeling of skewed functionally graded bio-composite structures with perforations to examine flexural and eigenfrequency responses. Here, the bio-composite structure comprises Titanium (Ti) and Hydroxyapatite (HAp). Voigt’s micromechanical material model via power-law distribution and Representative volume element (RVE) method is utilized to compute the in-homogenous material properties in the thickness direction. The strain field is based on the equivalent single-layer first-order shear deformation theory with five degrees of freedom, and the governing equations are obtained using principle of minimum potential energy. A computer algorithm is developed in a 2D finite element platform using eight-noded quadrilateral elements. The mesh stability of the skewed and perforated structure is confirmed through the smart mesh technique, and the present model’s accuracy is demonstrated by comparing it with the available reported results. Numerous examples reveal the significance of material gradation, skewness, aspect ratios, perforations, and support conditions on bio-composite functionally graded structures’ flexural and eigenfrequency responses. Furthermore, parametric optimization is conducted to minimize the flexural response and maximize the fundamental frequency by employing the response surface methodology (RSM), followed by determining optimal process parameters and valuable findings.

An insight into the influence of precipitation phase on the surface quality in diamond turning of an Aluminium alloy

Diamond turning is an effective technology for processing metal mirrors used in photoelectric communications, radar, and other fields. In diamond turning, the precipitated phase is an essential factor that influences the surface quality of the metal mirrors. However, in previous studies, the precipitation phase has typically been handled as a random variable in a surface morphology model to evaluate its influence on the surface roughness, instead of determining the formation mechanism and proposing suppression solutions. In this study, a new phenomenon is observed in the diamond turning of metal mirrors, that is, the micro diamond tool can reduce the protrusion of the precipitated phase under a small feed rate and improve the surface quality. Investigating the turning process using diamond tools with varying tool nose radii at small feed rates (<1 μm/r), the underlying transformation mechanism of the precipitation phase is determined with the advanced material characterization technologies. The growth of the precipitated phase with an increase in the tool nose radius is explained using the energy gradient theory. The results showed that the increased material strain on the machined surface decreased the activation energy of solute diffusion in the material, causing solute accumulation and precipitate phase growth. With a further increase of tool nose radius to around 1000 μm, the β'' phase breaks and rotates. The representative volume element method shows that when undergoing severe plastic deformation, dislocations and grain boundaries quickly aggregate and slide on the precipitated phase, which will lead to the fracture and rotation of β'' phase. These findings provide a theoretical basis for the development of highly smooth mirrors.

Dynamic bandgap responsiveness of modified re-entrant metamaterials in thermal-mechanical field

This paper introduces a nested sinusoidal re-entrant (NSR) metamaterial characterized by tunable complete bandgaps (CBGs) and dynamic responsiveness in thermal-mechanical dual fields. NSR comprises shape memory polymer and features a sinusoidal modification with nested re-entrant hexagonal and star-shape re-entrant structure. Dynamic response of NSR is studied using the representative volume element method, specifically focusing on the effective modulus and Poisson's ratio and CBGs under varying average strains. The findings indicate that both the mechanical properties and CBGs exhibit dynamic responses to mechanical field, demonstrating interrelation between mechanical adjustments and functional performance. Moreover, the study examines how temperature fluctuations influence the NSR's elastic modulus, thereby altering its CBGs. Hence, manipulating both compression and temperature variations presents a viable approach to control and adjust the CBGs of NSR effectively. These results are validated by computations of the frequency response function under various average strains. Overall, this design presents a promising approach for developing mechanical metamaterials with tunable functionality.

A multiscale hydro-elastoplastic model for large floating structures in two-dimension

A novel fluid–structural model was presented considering hydro-elastoplastic behavior, which coupled multiple hydro-structural-material scales. A large floating sandwich structure (LFSS) comprising upper and lower high-strength panels and a low-weight core was considered as an illustration. The mesoscale characteristics of materials and elastoplastic parameters of the low-weight perforated components were coupled by utilizing the representative volume element (RVE) method. Through the parameterized relations from RVE analysis, the flexure dynamics model for the floating sandwich structure with an equivalent homogenized core was deduced. With the flexure dynamic equation, yield criterion, and potential flow model, a multiscale hydro-elastoplasticity theoretical model was established, which combined the wave action, hierarchical component, material configuration, and structural behavior. The dynamic responses of the large floating structure under fluid–structure interaction were calculated, and the internal deformation (i.e., core strain) was set as the determining variable for the plastic region. The initially intact floating structure became hinged multi-modules after plastic cracking, and the high-strength layers at the cracking positions behaved as flexible hinges, which was defined as a hydro-elastoplastic process. The elastoplastic state evolutions of the LFSSs with different structural parameters and material configurations were solved for practical optimization. The results indicated that the multiscale coupled calculation model can provide great scientific guidance for designing large floating structures.

Effect of graphene reinforcement on the tensile and flexural properties of thermoplastic polyurethane nanocomposite using experimental and simulation approach

ABSTRACT This study investigates the integration of graphene (Gr) nanoparticles into polyurethane (PU) matrices to enhance mechanical properties, focusing on Young’s modulus, tensile strength, and flexural strength. Utilising a Representative Volume Element (RVE) analysis with 1 × 1 × 1 μm dimensions, the research evaluates PU/Gr composites at varying volume fractions. Results indicate substantial improvements in mechanical properties, with the 0.05 PU/Gr composite exhibiting the highest enhancements, including a 25% increase in Young’s modulus and 26% and 31% enhancements in tensile and flexural strengths, respectively, compared to pure PU. Fractography confirms the transition from ductile to brittle behaviour with Gr incorporation. The RVE method accurately predicts Young’s modulus, aligning closely with experimental and micromechanical model data. Additionally, ANSYS simulation tests show results within a 10% error margin. The findings suggest significant potential for the development of high-performance composite materials applicable across industries like aerospace, automotive, and construction.

Nonlinear bending characteristics of multidirectional functionally graded porous panels using higher-order finite element solution with parametric optimization

The current study aims to investigate the nonlinear bending behavior of unidirectional (1D) and multidirectional (2D/3D) functionally graded porous shell panels. Here, the material properties of the multidirectional functionally graded (FG)-panels are estimated by employing the representative volume element method and Voigt’s micromechanical homogenization scheme. The nonlinear mathematical model of the FG-panel is developed by incorporating Green-Lagrange type nonlinear strains in higher-order-midplane kinematics. The minimum potential energy principle is used to obtain the final form of the equilibrium equation for the multidirectional FG shell panel and further solved by using Picard’s iterative-based 2D-isoparametric finite element method via quadrilateral Lagrangian elements. The efficacy and robustness of the present model are checked by comparing its results with previously reported literature. Numerous examples are solved to analyze the impact of material parameters, such as volume fraction index and porosity index, and geometrical parameters, such as aspect ratio and support conditions, on the nonlinear deformation behavior of multidirectional FG shell panels. In addition, parametric optimization is carried out to minimize the flexural response by using the response surface methodology and, hence, determining the optimal values of multidirectional porous FG-panel. The results demonstrate that, within the defined ranges of FG-panel, lower values of porosity index and volume fraction index yield lesser deflection.

Three-Dimensional Columnar Microstructure Representation Using 2D Electron Backscatter Diffraction Data for Additive-Manufactured Haynes®282®.

This study provides a methodology for exploring the microstructural and mechanical properties of the Haynes®282® alloy produced via the Powder Bed Fusion-Electron Beam (PBF-EB) process. Employing 2D Electron Backscatter Diffraction (EBSD) data, we have successfully generated 3D representations of columnar microstructures using the Representative Volume Element (RVE) method. This methodology allowed for the validation of elastic properties through Crystal Elasticity Finite Element (CEFE) computational homogenization, revealing critical insights into the material behavior. This study highlights the importance of accurately representing the grain morphology and crystallographic texture of the material. Our findings demonstrate that created virtual models can predict directional elastic properties with a high level of accuracy, showing a maximum error of only ~5% compared to the experimental results. This precision underscores the potential of our approach for predictive modeling in Additive Manufacturing (AM), specifically for materials with complex, non-homogeneous microstructures. It can be concluded that the results uncover the intricate link between microstructural features and mechanical properties, underscoring both the challenges encountered and the critical need for the accurate representation of grain data, as well as the significance of achieving a balance in EBSD area selection, including the presence of anomalies in strongly textured microstructures.

Multiscale homogenization of aluminum honeycomb structures: Thermal analysis with orthotropic representative volume element and finite element method

This study develops a thermal homogenization model for an aluminum honeycomb panel using the representative volume element (RVE) concept, considering the orthotropic nature of the structure. The RVE thermal homogenization method is a numerical approach for analyzing heterogeneous materials. It employs a constitutive model based on RVE performance to represent thermal behavior. Effective parameters are determined through averaging techniques, and the finite element method solves the thermal problem, accounting for structure topology and material behavior. The resulting heat conduction problem is solved using the finite element method (FEM) to evaluate the effective thermal characteristics. A 3D RVE is generated based on the honeycomb panel's geometry, evaluating thermal conductivity tensor and describing the medium's thermal performance. Numerical tests validate the model by comparing it with the real honeycomb structure under sinusoidal heat flux. Results show good correlation, with maximum temperatures of 1101.9 °C in the real structure and 1096.4 °C in the medium. The homogeneous medium is further used to investigate thermal performance under convective conditions with varying panel thicknesses, achieving over 77 °C temperature reduction with the thickest panel. Natural vibration behavior is considered, demonstrating strong correlation between modal responses and natural frequencies. This modeling approach efficiently analyzes thermal behavior in large honeycomb structures, reducing computational time significantly.

Investigation into the anisotropic damage behavior of LA103Z Mg‐Li alloy rolling sheet using X‐ray computed tomography and numerical modeling

AbstractThe anisotropic damage behavior has a great influence on the formability of rolling sheets. This work aimed to investigate the anisotropic damage mechanism of the LA103Z Mg‐Li alloy rolling sheet by combining mesoscale detection and modeling. The X‐ray computed tomography (XCT) and scanning electron microscope (SEM) were applied to characterize the evolution of damage morphology and volume fraction in RD, DD, and TD directions of the rolling sheet. The GTN damage model was calibrated by the experimental results with the representative volume element (RVE) method. The anisotropic damage mechanism was revealed via experimental and modeling results. The micro void nucleation strain εN was critical to determine the initiation moment of the anisotropic damage. The continuous nucleation in RD direction, the severe growth in DD direction, and the massive coalescence in TD direction were the micro void evolution competition results that caused the anisotropy for damage mechanism and fracture strain.

Multiscale modeling of shape memory polymers foams nanocomposites

Shape memory polymer foams (SMPFs) are defined as lightweight cellular materials with the ability to recover their undeformed shape by applying an external stimulus like light, temperature, magnetic field, etc. Reinforcement of the material with nano-clay filler leads to a significant improvement in its physical properties. As a result, a wide range of applications is occupied by SMPFs, especially in industry and biomedical applications. Because of the heterogeneous nature of the SMPFs at different scale levels, modeling the material with one scale numerical model which able to capture all the effects of the lower scale material structure is really a complex task. Within this work, a full multiscale modeling approach is employed to investigate the thermomechanical response of the SMPFs. Furthermore, a combination of the 3D Representative Volume Element (RVE) and finite element method is used to explore the effects of the nano-filler weight fractions and the material's cellular structure at different length scales on the material dynamics. The multiscale modeling process gives great and promising results with good agreement with the experimental results. Moreover, the model shows relatively high sensitivity parameters that are initiated from the lower scale level.

Research on Representative Volume Element Fex-Cy High-Temperature Mechanical Model Based on Response Surface Analysis

In this research, a multi-scale representative volume element method is introduced that combines the temperature and stress fields to analyze the force field distribution around microcracks in low-carbon steel using a combination of molecular dynamics and finite element analysis. Initially, an orthogonal experimental design was used to design the molecular dynamics simulation experiments. Next, a nano-level uniaxial tensile test model for mild steel was established based on the experimental design, and the uniaxial tensile behavior of low-carbon steel was investigated using molecular dynamics. Lastly, mathematical models of the modulus of elasticity E and yield strength Q of mild steel at a high temperature were obtained statistically using the response surface methodology. Meanwhile, a finite element model with a coupled temperature–stress field was established to investigate the force field distribution around the microscopic defects, and the microscopic crack stress concentration coefficient K was revised. The results indicate that regardless of the location of microcracks within the structure, the stress distribution due to size effects should be considered under high-temperature loading.

Bottom‐up analysis framework for the continuous multidirectional carbon fiber‐reinforced PEEK composite laminates

AbstractThe continuous carbon fiber‐reinforced polyether ether ketone (CCF/PEEK) composites have been widely utilized in aerospace structures due to their excellent properties. However, the main load‐bearing structure in the next‐generation aircraft needs to withstand high temperatures up to 200°C, and the mechanical properties of CCF/PEEK composites show significant time‐/temperature‐dependence due to the viscoelastic nature of the PEEK matrix. Therefore, accurate predictions of the mechanical performance of CCF/PEEK composites under high‐temperature service conditions are the key issue for structural safety and life assessments and have therefore become a recent research focus. To address these challenges, this study established a bottom‐up analysis framework for the CCF/PEEK composites and employed the theoretical model and the finite‐element representative volume element (FE‐RVE) method to investigate the anisotropic viscoelastic properties of CCF/PEEK composites. We first built an anisotropic viscoelastic model of the unidirectional CCF/PEEK composites by integrating the generalized Maxwell into the bridging model. Upon this foundation, we further developed a viscoelastic laminate model capable of accurately predicting the thermoviscoelastic properties of multidirectional laminates. To verify the developed model, different kinds of FE‐RVEs were built and analyzed. Overall, there is good agreement among the model predictions, the FE‐RVE simulations, and the experimental results within a temperature range of 25–250°C. The developed model can be used to design the high‐temperature performance of CCF/PEEK composites with different fiber volume fractions, laminated configurations, or loading directions.Highlights An anisotropic viscoelastic model of the unidirectional (UD) continuous carbon fiber‐reinforced polyether ether ketone (CCF/PEEK) composites is built. The viscoelastic laminate composite model is developed based on the UD CCF/PEEK composites model. The finite element representative volume element (FE‐RVE) simulation with fibers in a hexagonal or random array has better accuracy compared with the experimental results. The FE‐RVE simulation and the experimental results verified the developed model from 25°C to 250°C.

A multiscale optimization methodology for cyclic elastoplastic performance of beam-pile joint member in pile-supported wharf

A material-member-structure multiscale optimization methodology, which can be utilized for improving the elastoplastic behaviour of the beam-pile joint member in pile-supported wharf under cyclic loading, was developed on the base of the application of high-specific stiffness material. Based on the representative volume element (RVE) method, the parameterized relations between the mesoscale phases (e.g., steel fibers, interfacial transition zone, and matrix) and macroscale homogenized elastoplasticity of ultrahigh-performance concrete (UHPC) reinforced with steel fibers were obtained under periodic boundary conditions. The physical equivalence relation between material scale and member scale was established by utilizing the refined constitutive model with the macroscopic mechanical parameters and exponential decay damage evolution factors. UHPC material property tests and cyclic loading tests of small-scale beam-pile joint specimens were performed respectively, and the results were analyzed and utilized to validate the numerical model and multiscale optimization method. Using the computational platform ABAQUS, the cyclic elastoplastic performances of the novel beam-pile joint members were evaluated numerically by pseudo-static hysteretic loading. As an illustration, a multiscale modelling approach for the pile-supported wharf frame system was presented and employed to assess the seismic performance improvement through the optimization of the beam-pile joint members. The coupled solution of refined member damage and large-scale structural bearing capacity was realized by utilizing the deformation coordination condition and force balance equation, which bridges the member scale and structure scale. This study aims to provide a reference for future design and optimization of the joint members in marine frame structures, to enhance cyclic bearing capacities and reduce reinforcement consumptions.

Vibration and damping of carbon fiber reinforced polymer orthogonal lattice truss sandwich panels manufactured by a new manufacturing process

A new method of fabricating carbon fiber reinforced polymer (CFRP) orthogonal lattice truss sandwich panels is proposed. Inner trusses are inserted into outer trusses. Three structures are prepared using different adhesives: epoxy resin, ethylene–vinyl acetate copolymer (EVA), and nitrile butadiene rubber (NBR). The mode shapes, natural frequencies, and loss factors of the structures are tested and predicted using the finite element modal strain energy method with a solid model and two shell models, respectively. The shell stiffness matrixes are calculated using representative volume element (RVE) method and analytical method. The results show that these three theories can accurately predict the sandwich panels with epoxy or EVA adhesive, while the sandwich panel with rubber layer cannot be accurately predicted. The strain energy composition, shell stiffness matrices, influence of node offset and influence of adhesive layer thicknesses are studied. The EVA adhesive improves the loss factors of the structure within an acceptable reduction of natural frequency.