Representative Volume Element Method Research Articles

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.

Study on the Estimation of Mechanical Properties with Porous Rate using the Representative Volume Element Method

Study on the Estimation of Mechanical Properties with Porous Rate using the Representative Volume Element Method

A Geometry-Dependent Void Closure Model Considering Void Deformation and Orientation Changes during Hot Metal Formation

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

The effects of single-walled carbon nanotubes dispersion and agglomeration in aluminum matrix: Fabrication and finite element simulation

This paper provides novel research on the effect of full dispersion and agglomeration of single-walled carbon nanotubes (SWCNT) in the Aluminum (AL) matrix. The effect was investigated using the representative volume element (RVE) and finite element method (FEM). The acquired findings were compared to the experimental method (EXP) to assess the correctness of the employed method. In the investigation to anticipate the SWCNT rule in AL/SWCNT mechanical properties, RVE and FEM approach focused on two primary conditions: SWCNT complete dispersion and via agglomeration. Al/SWCNT was manufactured using powder technology. SEM images revealed that there were local SWCNT agglomerations within the composites at greater carbon nanotube concentrations, resulting in a decrease in the specimens' elastic modulus and mechanical strength. Based on RVE and EXP methods, the elastic modulus was increased until dispersed SWCNTs were added up to 2 wt%, after which the modulus was decreased as more SWCNTs were added. The elastic modulus with EXP was compared to the RVE curve cylinder SWCNT full dispersion and curve cylinder with SWCNT agglomeration results under periodic boundary conditions (PBC). The comparison demonstrated that EXP and RVE were in an acceptance agreement. In addition, AL-SWCNT RVEs were studied under damage condition.

Bias in the Representative Volume Element method: Periodize the Ensemble Instead of Its Realizations

AbstractWe study the representative volume element (RVE) method, which is a method to approximately infer the effective behavior$$a_{\textrm{hom}}$$ahomof a stationary random medium. The latter is described by a coefficient fielda(x) generated from a given ensemble$$\langle \cdot \rangle $$⟨·⟩and the corresponding linear elliptic operator$$-\nabla \cdot a\nabla $$-∇·a∇. In line with the theory of homogenization, the method proceeds by computing$$d=3$$d=3correctors (ddenoting the space dimension). To be numerically tractable, this computation has to be done on a finite domain: the so-called representative volume element, i.e., a large box with, say, periodic boundary conditions. The main message of this article is: Periodize the ensemble instead of its realizations. By this, we mean that it is better to sample from a suitably periodized ensemble than to periodically extend the restriction of a realizationa(x) from the whole-space ensemble$$\langle \cdot \rangle $$⟨·⟩. We make this point by investigating the bias (or systematic error), i.e., the difference between$$a_{\textrm{hom}}$$ahomand the expected value of the RVE method, in terms of its scaling w.r.t. the lateral sizeLof the box. In case of periodizinga(x), we heuristically argue that this error is generically$$O(L^{-1})$$O(L-1). In case of a suitable periodization of$$\langle \cdot \rangle $$⟨·⟩, we rigorously show that it is$$O(L^{-d})$$O(L-d). In fact, we give a characterization of the leading-order error term for both strategies and argue that even in the isotropic case it is generically non-degenerate. We carry out the rigorous analysis in the convenient setting of ensembles$$\langle \cdot \rangle $$⟨·⟩of Gaussian type, which allow for a straightforward periodization, passing via the (integrable) covariance function. This setting has also the advantage of making the Price theorem and the Malliavin calculus available for optimal stochastic estimates of correctors. We actually need control of second-order correctors to capture the leading-order error term. This is due to inversion symmetry when applying the two-scale expansion to the Green function. As a bonus, we present a stream-lined strategy to estimate the error in a higher-order two-scale expansion of the Green function.

A deep learning empowered smart representative volume element method for long fiber woven composites

In response to the global trend of carbon reduction over the last few years, various industries, including the aviation and automobile industries, have gradually begun research, design, and production of carbon fiber composite materials. These have excellent mechanical properties, such as being lightweight, high strength, and of high rigidity, which provide weight reduction and energy savings in applications across many fields. When used as a load-beam structure, the weave pattern determines the primary mechanical properties of the composite material. Therefore, the production of diverse products and components can be carried out using different patterns of weaving and manufacturing according to an application’s requirements. The mechanical properties of woven fiber composites can be obtained by using simulation analysis software, which can reduce unnecessary waste during design and manufacturing. However, difficulties arise in the simulation analysis due to the complexity of the weaving method. With the continuous improvement of computer technology in recent years and the enormous amount of training data available, many research teams have begun to implement artificial intelligence (AI) technology, which has been widely used to overcome long-standing obstacles in many different fields. For example, the problems involved in the prediction of protein folding sequences and the prediction of the physics of structural materials have all been resolved by AI. We implement a convolutional neural network (CNN), a deep learning method, to establish a model that utilizes a representative volume element for the prediction of the mechanical properties of a woven fiber composite material. The predictive model significantly streamlines the computational complexity involved in analyzing woven composite materials, resulting in a substantial reduction in processing time compared to conventional methods. Unlike traditional finite element simulations, which necessitate intricate boundary conditions and interactions on a case-by-case basis, our research simplifies these complex procedures and accommodates a wide range of scenarios. This research offers substantial advantages for industrial manufacturing, particularly in the design and mass production of woven fiber composite materials.

Functionally graded structure design for magnetic field applications

This study presents topology optimization methodology of anisotropic magnetic composites, which consist of two ferromagnetic materials with low and high reluctivity values, considering the nonlinear magnetic saturation effect. Instead of employing the asymptotic homogenization theory, the representative volume element method combined with the machine learning is used to build the continuous function model and it is applied to obtain the material property according to the design variable change. Finally, the micro-scale functionally graded structure composed of two ferromagnetic materials with the macro-scale topological morphology is simultaneously designed to improve the magnetic performance of actuators. Numerical examples for symmetric and asymmetric magnetic actuator models are provided to validate the effectiveness of proposed design process. In the numerical results, optimized configurations and objective values obtained with the nonlinear magnetic composite material, which depend on the intensity of the magnetic flux density, are compared with those of the linear magnetic composite material.

FREE VIBRATION INVESTIGATION ON RVE OF PROPOSED HONEYCOMB SANDWICH BEAM AND MATERIAL SELECTION OPTIMIZATION

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