Representative Volume Element Approach Research Articles

Integrated model for simulating Coble creep deformation and void nucleation/growth in polycrystalline solids - Part I: Theoretical framework

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

Thermal modeling of porous medium integrated in PCM and its application in passive thermal management of electric vehicle battery pack

The integration of a composite of porous medium with phase change material (PCM) offers significant advantages in thermal management systems, enhancing heat transfer efficiency and addressing various thermal regulation challenges. This approach utilizes the PCM's latent heat absorption and the enhanced thermal conductivity provided by the porous medium, resulting in optimized system performance. Its applicability spans across electronics cooling and building insulation systems. However, predicting the thermal behavior of this composite material is challenging, necessitating computational tools to anticipate its response under different conditions and evaluate its influence on cooling strategies. The objective of this study is to create a computational tool specifically tailored to evaluate constitutive parameters of this composite material, thereby providing a comprehensive description of its thermal behavior. To achieve this goal, the multiscale homogenization principle is employed to assess the composite's effective thermophysical material properties using the representative volume element approach. The repeating unit cell of the aluminum lattice is incorporated into the PCM to define a representative volume element. The finite element method (FEM) is utilized to solve the three-dimensional homogenization problem, yielding an orthotropic effective thermal conductivity due to the inherent symmetry of the repeating material cell. Moreover, the study leverages the apparent heat capacity method to effectively manage the phase transitions within the PCM domain, utilizing smooth and temperature-dependent functions to accurately describe the thermophysical properties of the PCM. Integrating the composite into battery pack thermal management, this study thoroughly examines thermal dynamics by comparing outcomes with and without PCM integration. The transient thermal problem is accurately tackled using the FEM, employing the evaluated effective constitutive parameters of the homogenized composite to minimize computational effort. The results indicate a notable decline in the highest temperatures of the battery pack, leading to a reduction of about 14 °C at the specific moment when the phase change material fully transitions into its liquid form. The obtained results emphasize the effectiveness and practical feasibility of the proposed thermal management strategy. The modeling approach presented provides a robust tool with significant efficiency in reducing computational time for analyzing the thermal behavior of large models, as the utilization of the homogenization technique notably decreases the computational time.

Investigation of Macroscopic Mechanical Behavior of Magnetorheological Elastomers under Shear Deformation Using Microscale Representative Volume Element Approach.

Magnetorheological elastomers (MREs) are a class of smart materials with rubber-like qualities, demonstrating revertible magnetic field-dependent viscoelastic properties, which makes them an ideal candidate for development of the next generation of adaptive vibration absorbers. This research study aims at the development of a finite element model using microscale representative volume element (RVE) approach to predict the field-dependent shear behavior of MREs. MREs with different elastomeric matrices, including silicone rubber Ecoflex 30 and Ecoflex 50, and carbonyl iron particles (CIPs) have been considered as magnetic particles. The stress-strain characteristic of the pure silicon rubbers was evaluated experimentally to formulate the nonlinear Ogden strain energy function to describe hyper-elastic behavior of the rubbery matrix. The obtained mechanical and magnetic properties of the matrix and inclusions were integrated into COMSOL Multiphysics to develop the RVE for the MREs, in 2D and 3D configurations, with CIP volume fraction varying from 5% to 40%. Periodic boundary condition (PBC) was imposed on the RVE boundaries, while undergoing shear deformation subjected to magnetic flux densities of 0-0.4 T. Comparing the results from 2D and 3D modeling of isotropic MRE-RVE with the experimental results from the literature suggests that the 3D MRE-RVE can be effectively used to accurately predict the influence of varying factors including matrix type, volume fraction of magnetic particles, and applied magnetic field on the mechanical behavior of MREs.

Effect of plant short fibers on the mechanical properties of carbon fiber reinforced epoxy matrix by using FEM based numerical homogenization technique

In this study, we utilized the material design library in Ansys Product 2022 R1 to analyze the impact of short plant fibers on the mechanical properties of epoxy resin. We employed the representative volume element (RVE) approach and examined different volume fractions up to 50%. The technique employed in this study was multi-scale modeling based on the finite element method (FEM) for numerical homogenization. Subsequently, we used the same software to develop a five-layer laminated composite. The samples were based on epoxy resin enriched with short plant fibers at fractions of 20% and 30%, as well as pure epoxy resin. The laminated composites were reinforced with carbon fibers. The objective of this study was to analyze the mechanical response of each sample during a tensile test, focusing on multiple parameters. The sought-after results included total deformation, directional deformation, equivalent and elastic stress (Von-mises). The samples containing epoxy resin enriched with 30% of short hemp fibers exhibited remarkable mechanical strength compared to the other samples. These results suggest that the incorporation of short hemp fibers into the matrix led to a significant improvement in the mechanical strength of the composite.

Combined RVE-Cohesive elements approach to the multi-scale modelling of FDM 3D-printed components

Mechanical strength of 3D-printed components dramatically depends on printing process parameters. These can be usually set over a relatively wide range, in combinations that determine the microstructure morphology and the resulting mechanical behaviour. The present investigation focuses on the relationship between revealed structure and resulting mechanical properties of FDM-printed ABS specimens. The peculiar structures, examined at the meso- and microscale, are modelled by a finite-element Representative Volume Element (RVE) approach, in conjunction with cohesive elements to reproduce the sealing efficiency between fused filaments. The simulation of the tensile response up to failure falls within the 95% of confidence with experiments. Also, homogenized response of RVE determines spatial material constants useful for the effective numerical simulations of functional components, and intra- and inter-layer damage mechanisms are distinguished providing hints for the structural optimization.

Study on Interfacial Interaction of Cement-Based Nanocomposite by Molecular Dynamic Analysis and an RVE Approach

There is an increased demand for cement nanocomposites in the twenty-first century due to their composition, higher strength, high efficiency, and multiscale nature. As carbon nanotubes (CNTs) possess extremely high strength, resilience, and stiffness, inclusion of carbon nanotubes in small quantities to the concrete mix makes them a multifunctional material. A molecular level understanding is significant to capacitate the macrolevel properties of these composites. In the proposed work, molecular dynamics (MD) simulations are used to understand the behaviour of the composites at the atomic level and continuum mechanics with representative volume element (RVE) homogenization modelling is carried out for interfacial interaction study of composites. The mechanical properties such as Young’s modulus, shear modulus, and poisons are evaluated using previous methods of simulations for different compositions of nanomaterials in cement matrix. The FORCITE module of MD simulation and square RVE model is used to determine the mechanical, electrical properties, and elastic constants of the cement nanocomposite. The MD simulation describes the linking effect of CNT into cement matric, and the RVE modelling study reveals the pull-out effect of CNT from matrix. From experimental and analytical studies, it is found that increase in CNT till 0.5% weight fraction increases the mechanical properties about 12% and further increasing of CNT weight fraction causes a reduction in mechanical properties about 5% due to the agglomeration of nanotubes. The density of states method in MD simulation indicates that mobility of the electrons increases with an increase in carbon nanotube proportion in the composites. The experimental test results substantiate the analytical studies, and the error obtained from both approaches is less than 20%. From the analytical study, the average maximum Young’s modulus, shear modulus, and bulk modulus are obtained as 46 GPa, 31 GPa, and 32 GPa for 0.5% weight fraction of CNT in cement matrix. Hence, it is concluded that 0.5% weight fraction of CNT is considered as optimum dosage to obtain better electrical and mechanical properties.

Finite element modeling of the effective creep compliance of carbon nanotube-polymer nanocomposites: A critical microstructure-level investigation

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

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.

Marble waste reinforced composite with tunable physico-mechanical and thermal properties: micromechanical simulation assisted experimental investigation

ABSTRACT This paper investigates the development of waste marble dust-reinforced particulate composites through an integrated approach of investigation. Samples of marble-epoxy composites were prepared with systematic variations in filler content to achieve tunable mechanical, physical, and thermal properties. Increasing ceramic filler's loading level resulted in superior properties of composite samples, as demonstrated by macroscale characterization such as compressive and flexural strength. Microstructural characterizations such as Fourier transform infrared spectroscopy (FT-IR), Field emission scanning electron microscopy (FE-SEM), thermogravimetric analysis (TGA), and X-ray diffraction (XRD) analysis were used to better understand the results. FT-IR results indicate chemical linkages forming between the epoxy resin and marble dust in the composite, while FE-SEM images suggest strong interfacial bonding between filler and matrix. TGA analysis shows enhancement of thermal properties with increasing filler content, while XRD indicates enhancement of crystallinity. Micro-mechanical modeling using the representative volume element (RVE) approach was also carried out using a commercial simulation package, determining Young’s modulus and comparing it with experimental results.

Chemical and Mechanical Characterization of Unprecedented Transparent Epoxy–Nanomica Composites—New Model Insights for Mechanical Properties

Two nanomicas of similar composition, containing muscovite and quartz, but with different particle size distributions, have been used to prepare transparent epoxy nanocomposites. Their homogeneous dispersion, due to the nano-size, was achieved even without being organically modified, and no aggregation of the nanoparticles was observed, thus maximizing the specific interface between matrix and nanofiller. No exfoliation or intercalation has been observed by XRD, despite the significant dispersion of the filler in the matrix which produced nanocomposites with a loss in transparency in the visible domain of less than 10% in the presence of 1% wt and 3% wt of mica fillers. The presence of micas does not affect the thermal behavior of the nanocomposites, which remains similar to that of the neat epoxy resin. The mechanical characterization of the epoxy resin composites revealed an increased Young's modulus, whereas tensile strength was reduced. A peridynamics-based representative volume element approach has been implemented to estimate the effective Young's modulus of the nanomodified materials. The results obtained through this homogenization procedure have been used as input for the analysis of the nanocomposite fracture toughness, which has been carried out by a classical continuum mechanics-peridynamics coupling approach. Comparison with the experimental data confirms the capability of the peridynamics-based strategies to properly model the effective Young's modulus and fracture toughness of epoxy-resin nanocomposites. Finally, the new mica-based composites exhibit high values of volume resistivity, thus being excellent candidates as insulating materials.

Evaluation of tensile properties of spherical shaped SiC inclusions inside recycled HDPE matrix using FEM based representative volume element approach

In the current study, a FEM-based representative volume element (RVE) technique is used to evaluate the elastic modulus of recycled high-density polyethylene (rHDPE) filled spherical-shaped shaped silicon carbide (SiC). In the ANSYS 2019, the material designer (MD) module is used to generate a 3D RVE of 500 × 500 × 500 μm cuboid, with randomly dispersed spherical SiC particles (i.e., 10, 15, 20, and 30% volume fractions) inside rHDPE. The Young's modulus values extracted from the RVE technique at various volume % are substantially nearer to experimental data than other micromechanical models. The tensile performance of the composite is simulated, and it was noted that the maximum equivalent stress of 4.1133 MPa for rHDPE/30% SiC composite, which is decreased to 13.8, 7.8 and 6.8% for rHDPE/10% SiC, rHDPE/15% SiC and rHDPE/20% SiC composite respectively. The results are astounding for immediate application in the relevant field of interest.

Multi-scale modelling and life prediction of aged composite materials in salt water

Tidal turbine infrastructure is currently in the large-scale prototype and short-term demonstration phase. However, the immediate requirement is to develop materials, processes and long-term life predictive facilities for tidal turbine plant that has decades of operational lifetime requirements. Computational modelling is a key tool to interpret the experimental data, understand the relevant mechanisms and provide a predictive capability for the performance of aged components for industries. The goal of this paper is a prediction of the long-term life of marine-based glass/epoxy and carbon/epoxy composite laminates aged in artificial seawater with 3.5% salinity based on Arrhenius degradation theory and tensile strength retention over 180 days ageing at room temperature and 60°C. Three different analytical models (linear and exponential) were implemented to calculate time shift factors and corresponding life in a real marine environment. Additionally, multi-scale modelling has been implemented via a representative volume element approach for square and hexagonal cells, and two-step homogenization of textile composites in accordance with nanoindentation testing for matrix/resin cells and fibre constraint cells after 90 days of immersion in saltwater. In general, the multi-scale modelling in ABAQUS and TexGen4SC was able to approximate (with about 10% difference) the mechanical properties of dry and aged composite laminates.

Fabrication and finite element simulation of aluminum/carbon nanotubes sheet reinforced with Thermal Chemical Vapor Deposition (TCVD)

This study aims to grow the carbon nanotubes (CNTs) on the aluminum substrate (sheet) using Thermal Chemical Vapor Deposition (TCVD) so that the aluminum sheets can be clad together. Besides, finite element simulation (FEM) was used to evaluate the damage progression, and fracture initiation in AL-CNT composites. AL-CNT Representative Volume Element (RVE) was studied to numerically get an appropriate micro-scale Al-CNT composite simulation. To forecast the statistical connection between material microstructure and effective constitutive properties, the RVE approach was developed. AL/CNT RVE models were studied to determine the most effective carbon nanotube weight percentage as a contender to reinforce the aluminum matrix. The experimental technique was then used to investigate the results found in the RVE models. According to the experimental procedure, AL/CNT shows the maximum mechanical strength and material behavior in the CNT weight percentage reported by the RVE model analysis. Furthermore, regarding the importance of continuum mechanical simulation of microstructural damage processes in the ductile fracture mechanics research, the effect of stress triaxiality ratios, such as the ratio of mean stress to equivalent stress, on the damage growth rate was studied. The experimental results show that the composite mechanical behavior is appropriate at each CNT weight percentage simulations were conducted, and the results were compared to the numerical and experimental approaches in the literature, yielding satisfactory agreements. Based on the experimental findings, ultimate strength and young modulus of AL-5 wt.% CNT are 239 MPa and 73 GPa respectively. By adding more CNT concentration, CNT agglomerations are appeared inside the samples based on SEM. Therefore AL-5 wt.% CNT is the final candidate with the best physical properties.

A numerical study on the effects of DP steel microstructure on the yield locus and the stress–strain response under strain path change

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

Representative volume element homogenisation approach to characterise additively manufactured porous metals

Additive manufacturing represents a great candidate to boost smart materials expansion in the Industry 4.0 era through 4 D printing technologies. However, to fully exploit the benefits of these technologies, increasing knowledge is needed on how internal defects condition the overall behavior of the component. In this work, the Representative Volume Element approach is presented to investigate, through Finite Element Analyses, how micro-voids influence the stress-strain behavior of an AlSi10Mg additively manufactured through the Selective Laser Melting technique. An in-house code on the commercial software ANSYS Parametric Design Language APDL was developed to model a random pore distribution inside the RVE and to apply the boundary conditions necessary for the RVE periodicity; comparison with reference case studies from the literature are reported.

A multiscale peridynamic framework for modelling mechanical properties of polymer-based nanocomposites

In this work, a peridynamics-based representative volume element approach is implemented to estimate the effective tensile modulus of nanomodified epoxy resins. The results obtained through this homogenization procedure are then used as input for the analysis of nanocomposite fracture toughness, which is carried out by exploiting a classical continuum mechanics-peridynamics coupling strategy. In the coupled model, the small-scale heterogeneity of the crack tip region is preserved by implementing the recently proposed intermediately-homogenized peridynamic model. Comparison to experimental data confirms the capability of the peridynamics-based approaches to properly model the effective tensile modulus and fracture toughness of polymer-based nanocomposites.

Finite element modeling of fatigue properties of polymer nanocomposites

This paper presents a 3-dimensional finite element modeling of fatigue properties of polymer nanocomposites with a Representative Volume Element (RVE) approach using ANSYS. Epoxy was used as a matrix, and alumina nanoparticles of spherical shape (diameter 33 nm) were used as reinforcement. Convergence analysis was conducted to select the proper size of RVE. A geometric model of a flat dog bone specimen was created to model the fatigue properties. MATLAB code was used to generate randomly distributed nanoparticles. The sample was loaded in uniaxial tension-tension fatigue loading with a stress ratio of 0.1. S-N data for epoxy and alumina were given as input to determine the fatigue life of polymer nanocomposites. The results obtained from modeling were compared with experimental data. The fatigue life was determined by taking the average life at five different locations in the gauge region for a sample. The average of five different samples was calculated for each wt.% (0.5, 1.0, and 1.5). Reinforcement of nanoparticles up to 1 wt.% caused an increment in the fatigue life of nanocomposites, and fatigue life decreased at 1.5 wt.% of nanoparticles. The finite element modeling was able to predict the trend of improvement provided by the alumina nanoparticles (similar to experimental data).

Detailed structural analysis for fiber-reinforced polymer with singularities via FETI domain decomposition

The conventional representative volume element approach may not be accurate enough in examining stress distribution near singularity in a composite. However, enormous number of degrees of freedom (DOFs) is usually required to discretize the subcomponents within the composite structure; hence, it may not be handled in a single CPU. In this study, the finite element tearing and interconnecting algorithm, a domain decomposition method, is proposed to address the challenges posed by such enormous number of DOFs via parallel computation. Owing to the message passing interface, analyses in this study will be conducted on the parallel computing environment. Furthermore, the METIS algorithm is adopted to automatically divide the solid domain into certain number of subdomains. Consequently, the fiber-reinforced polymer which possesses either a crack or notch discretized by over 10 million DOFs will be readily analyzed. The computational time is reduced significantly compared against the original one. Also, the stress and stiffness predictions show good agreement with those by the other existing analyses or experiments. Therefore, this study is expected to be fast and accurate in analyzing composite structures with enormous number of DOFs.

Three-dimensional shear angle determination with application to shear-frame test

The shear frame test is very often used in the context of plastics engineering to examine only the fiber construction for its deformability. Here, it is common to assume a homogeneous deformation, which apparently exists as a global deformation due to the shear frame. This results in the assumption of a constant overall shear angle. In this paper, we compare two analytical approaches to describe the deformation and the resulting strains in detail, particularly, the local shear angle calculation. As a second step, the extension of the shear angle computation based on curvilinear, three-dimensional surface deformations is applied to optical results of the experimental deformation behavior. For this purpose, a three-dimensional image correlation system is drawn on to determine the local, tangential shear angle even for folded fabrics. This requires an approach which is different to the classical digital image correlation method since the speckle varnish influences the deformation of the very compliant fiber bundles. In a third step, the same procedure is applied to the results of three-dimensional finite element computations since the programs do not provide the shear angle measure. The shear angle determination is discussed at various examples. As a side result of the investigations, the material parameters for orthotropic elasticity are determined using a representative volume element approach exploiting μ-CT data. Although the wrinkling prediction calculations depend on the pre-deformation, finite element discretization, and uncertainties of the specimens, calculation results might be used as an indicator to improve the specimen geometries.

Mechanical Properties of Polyester Toughened with Nano-Silica

The fabrication of nanocomposites has played role to the development of the nanotechnology and the technology of advanced composite materials. Thermoset polymers are used in engineering applications widely. Their mechanical properties can be change with adding particles. The mechanism of toughening polymers has been suggested recently by reinforcing well dispersed particles to the plain polymer. Nano-silica particles were added to thermoset polymer of polyester to evaluate their influence on the mechanical properties of the toughened polymer using both experimental and numerical methods. The Representative Volume Element (RVE) approach, which employs finite element models, has been developed to achieve that aim numerically for various types of nano-particle reinforcement ratios. In each case, the stiffness has been calculated with using the equivalent homogeneous material concept. Experimentally, toughened thermoset polymers of polyester reinforced with nano-silica were prepared with different particle content ratio. Several tests were conducted on the nanocomposite, and it was observed increasing nano-silica ratio caused increase in Young’s modulus and decrease in ductility.