Micro-scale Representative Volume Element Research Articles

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.

Data-physics driven multiscale approach for high-pressure resin transfer molding (HP-RTM)

We present a multiscale computational framework for high-pressure resin transfer molding of fiber-reinforced composites. Due to the relatively rapid speed of resin flow and the significant convective effects, this process is governed by the nonlinear steady-state Navier–Stokes equations, as opposed to the linear Stokes equations commonly adopted for the simulation of classical resin transfer molding processes. To overcome the computational challenge of directly solving the high-pressure resin filling problem through the fiber preform, we developed a data-driven nonlinear homogenization approach where the average velocity and instantaneous permeability computed from the microscale representative volume element problem provide solution-dependent coefficients for the macroscale problem. The proposed data-physics driven computational framework has been validated against the direct numerical solution of the steady-state Navier–Stokes equations.

Numerical simulation and experimental validation of ratchetting deformation of short fiber-reinforced polymer composites

This paper proposes a micromechanical model based on the finite element method (FEM) to analyze the ratchetting deformation of short glass fiber-reinforced polymer composites (SFRPCs). To reasonably consider the complex mechanical characteristics of the polymeric matrix under asymmetrical stress-controlled cyclic loading, a damage-coupled nonlinear viscoelastic-viscoplastic (VE-VP) cyclic constitutive model was constructed. The cyclic constitutive model of the matrix was introduced into the FEM model utilizing a user-defined material, and the corresponding experimental validation of the matrix was conducted. Subsequently, the cyclic constitutive model was introduced into the analysis of the micro-FEM model of the composites. The random orientation was considered to generate fibers in the FEM. Based on the analysis of the microscale representative volume element (RVE) model, the effects of different fiber content and cyclic peak stress on the ratchetting of SFRPCs were studied in detail. After validation, the effects of the fiber length and fiber stiffness on the ratchetting deformation of SFRPCs are discussed based on the developed micro-FEM model. The results show that the increase in the fiber length and fiber stiffness reduced the ratchetting deformation of SFRPCs within a specific content range. The model can assess the ratchetting deformation and damage evolution within the composites to provide more accurate predictions of the ratchetting deformation of SFRPCs and guide the expanded application of SFRPCs in structures.

Voids effect on micromechanical response of elastoplastic fiber-reinforced polymer composites using 1D higher-order theories

This work investigates the effect of voids within the matrix of composite materials. Effects on local stress and plastic strain values are evaluated by conducting a micromechanical analysis. The microscale Representative Volume Element (RVE) is modeled through refined 1D elements based on the Carrera Unified Formulation (CUF). Using 1D models for the RVE leads to a significant reduction in computational costs compared to standard 3D elements. Fibers are modeled as orthotropic, and the matrix has an elastoplastic behavior. Random distributions of voids are considered, and statistical analyses are carried out. Furthermore, the influence of the depth of the RVE is investigated. The results show significant mean and peak stress values increases as the void volume fraction grows. Also, the use of deeper RVE leads to higher stress values.

Research into the thermal expansion behavior of spread tow woven pierced carbon/carbon composites at high temperature

Textile-reinforced carbon/carbon composites are frequently used for thermal safety due to their superb thermophysical properties. The coefficient of thermal expansion (CTE) is a fundamental performance metric of spread tow woven pierced carbon/carbon composites (STWPs). The multiscale representative volume element (RVE) models constructed as part of this work were used for investigating the CTEs of STWPs at high temperature. The temperature displacement coupling analysis step was established to predict the CTEs of STWPs considering the high-temperature environment. In addition, periodic displacement boundary conditions were adopted as node constraints with the spatial periodicity of RVE models. The influences of pore positions and configurations on the CTEs of the matrix were considered through two different matrix RVE model. The CTEs of the spread tow (ST) and fiber rod were computed using two microscale RVE models with an unequal fiber volume fraction. A novel modeling strategy for the mesoscale RVE model was put forth in order to calculate the CTEs of the STWPs due to the remarkable lightness and thinness of the ST. Only 9.64% and 7.92% errors in the in-plane and out-of-plane directions were found when the experimental findings were compared to those predicted by numerical models, demonstrating the accuracy and effectiveness of the multiscale RVE models. Moreover, the impacts of areal density of ST woven fabric on the CTEs of STWPs were discussed. The fundings demonstrated that the in-plane and out-of-plane CTEs both decreased as the areal density increased.

Multiscale Analysis of the Highly Stretchable Carbon−Based Polymer Strain Sensor

In this paper, a multiscale analysis method was proposed to simulate carbon nanoparticles (CNPs)-filled polymers which can be strain sensors applied in wearable electronic devices, flexible skin, and health monitoring fields. On the basis of the microstructure characteristics of the composite, a microscale representative volume element model of the CNPs-filled polymer was established using the improved nearest-neighbor algorithm. By finite element analysis, the variation of the junction widths of adjacent aggregates can be extracted from the simulation results. Then, according to the conductive mechanism of CNP-filled polymers, the composite was simplified as a circuit network composed of vast random resistors which were determined by the junction widths between adjacent aggregates. Hence, by taking junction widths as the link, the resistance variation of the CNPs-filled polymer with the strain can be obtained. To verify the proposed method, the electromechanical responses of silicone elastomer filled with different CNPs under different filling amounts were investigated numerically and experimentally, respectively, and the results were in good agreement. Therefore, the multiscale analysis method can not only reveal the strain-sensing mechanism of the composite from the microscale, but also effectively predict the electromechanical behavior of the CNPs-filled polymer with different material parameters.

Elastoplastic analysis of AA7075-O aluminum sheet by hybrid micro-scale representative volume element modeling with really-distributed particles and in-situ SEM experimental testing

• Presents a novel computationally-efficient reconstruction of 3D RVE model of second-phase particle-strengthened AA7075-O sheet with real distribution of particles based on FIB-SEM techniques. • Three types of second-phase particles (i.e., irregularly-shaped iron-rich particle Al 3 Fe, elliptically-shaped particle MgZn 2 , and needle-like particle CuAl 2 ) are determined using SEM-based EDS and EBSD techniques. • Presents a systematic study of the overall elastic-plastic response by developing and applying a hybrid experimental analysis and computational modeling framework. • Good agreement is observed in the comparison of RVE results with that of in-situ SEM tensile tests, indicating that the real 3D microstructure-based RVE models can accurately predict the plastic deformation and interfacial failure evolution in AA7075-O sheet. This paper addresses the challenge of reconstructing randomly distributed second-phase particle-strengthened microstructure of AA7075-O aluminum sheet material for computational analysis. The particle characteristics in 3D space were obtained from focused ion beam and scanning electron microscopy (FIB-SEM) and SEM-based Electron Backscatter Diffraction/Energy Dispersive X-ray Spectrometry (EBSD/EDS) techniques. A theoretical framework for analysis of elastic-plastic deformation of such 3D microstructures is developed. Slip-induced shear band formation, void initiation, growth and linkage at large plastic strains during uniaxial tensile loading were investigated based on reconstructed 3D representative volume element (RVE) models with real-distribution of particles and the results compared with experimental observations. In-situ SEM interrupted tension tests along transverse direction (TD) and rolling direction (RD), employing microscopic-digital image correlation (μ-DIC) technique, were carried out to investigate slip bands, micro-voids formation and obtain microstructural strain maps. The resulting local strain maps were analyzed in relation to the experimentally observed plastic flow localization, failure modes and local stress maps from simulations of RVE models. The influences of particle size, shape, orientation, volume fraction as well as matrix-particle interface properties on local plastic deformation, global stress-strain/strain-hardening curves and interfacial failure mechanisms were studied based on 3D RVE models. When possible, the model results were compared with in-situ tensile test data. In general, good agreement was observed, indicating that the real 3D microstructure-based RVE models can accurately predict the plastic deformation and interfacial failure evolution in AA7075-O aluminum sheet.

Numerical Tensile Damage Procedure Analysis of Angle-Ply Laminate Using Multi-Scale RVEs with Smear Crack Models.

This paper reported the tensile failure strengths and damage procedure of composite laminate manufactured from the toughened-epoxy T800 prepreg at multi-scale levels. According to the exterior and interior distinction of each layer in laminate, the macro/mesoscale representative volume element (macro-RVE, meso-RVE) was first constructed, respectively. Then the micro-scale representative volume element (micro-RVE) with a hexagonal fiber-packed pattern in the interior zone of each layer in the laminate was finally determined on the principle of the same fiber volume fraction between the composite laminate and multi-scale RVEs. In the multi-RVEs analysis, the mechanical failure strengths of each scale model were transmitted from the last-scale model’s homogenization, such as the meso-RVE from micro-RVE and the macro-RVE from meso-RVE. Based on our previous report, the innovative multi-scale damage and post-damage models on the concept of the smear crack were improved fully and incorporated by user-defined material subroutines (UMATs), such as in the addition of multiple cracks co-coupled, which makes it predict the element damage procedure. The averaged mechanical responses with damage mechanism of multi-scale RVEs under tensile, compressive, or shear loadings were obtained wholly by the homogenization method. The macroscale tensile damage initiation and propagation procedure were analyzed in detail including their global/local responses, being extended to comparison with experimental results.

Analysis of nonlinear shear and damage behaviour of angle-ply laminates with Direct FE2

In this paper, non-linear shear and damage behaviour of angled ply laminates is studied and simulated with the Direct FE2 approach. The FE2 method allows dual scale modelling of composite laminates by coupling micromechanical models of Representative Volume Element (RVE) of unidirectional fibre reinforced polymer composite with a macroscale laminate level model. Angled ply laminates under uniaxial tension are chosen because their non-linear behaviour arises from matrix plasticity and fibre reorientation under tension in addition to constituent damage and becomes important particularly for large deformation. This requires additional effort to account for fibre rotation to existing homogenized ply damage models. The FE2 approach requires only constituent (matrix and reinforcement) properties as input, thus removing the need for homogenized laminate and ply-level constitutive properties. At the macroscale, the FE2 model gave good prediction of experimental stress-strain response of laminates under uniaxial tension, while concurrently, the microscale RVEs captured fibre rotation, micro-cracks and fibre rupture.

Multi-scale Modeling of Polymeric Composites Including Nanoporous Fillers of Milled Anodic Alumina

A polymer composite based on an innovative filler consisting of microscale powder of nanoporous alumina is modeled. The passing-through nanoscale pores in this system—roughly columnar cylindrical, with diameter of the order of 100 nm—are fully penetrated by the resin, which is not bonded to the inner pore walls by any chemical agent. This system, previously assessed by laboratory experiments, is modeled here for the first time, based on a computational multi-scale hierarchical approach. First, microscale representative volume element (RVE) is modeled in two steps using finite element modeling. Then, the macro-scale RVE is characterized, using a combination of micromechanical rules. The elastic response of the composite is simulated to predict its Young’s modulus. This simulation confirms the former experimental results and helps to shed light on the response of the investigated material, which may represent a novel system for use in disparate composite applications. In particular, the nanoporous microfillers composite is compared with a composite material containing the fillers of the same material yet nonporous, bonded to the matrix. It appears that, with respect to this standard concept of three-phase composites, the presence of the nanopores can compensate for the absence of the bonding agent.

Longitudinal compression failure of 3D printed continuous carbon fiber reinforced composites: An experimental and computational study

Fused filament fabrication (FFF) with continuous carbon fiber filaments has proven to be a promising manufacturing technique in engineering applications. To provide guidance in the design of 3D printed carbon fiber reinforced polymer (CFPR) components, the longitudinal compression failure of continuous CFPR composites using the FFF technique is investigated systematically. First, longitudinal compression tests are performed for 3D printed continuous CFRP composites with and without designed waved filaments. The degradation of the failure strength is remarkable when the waved filaments are introduced. Nevertheless, further degradation is limited when more waved filaments are adopted. Next, the fracture morphologies are analyzed, and in-plane and out-of-plane kink-bands are observed in the microscopic images. For the specimens with waved filaments, fracture occurs at the cross-section with the contact region of the waved and regular filaments, as well as the cross-section with the maximum misalignment angle. Correspondingly, a computational framework for 3D printed continuous CFPR composites is established to explore the longitudinal compression failure mechanisms. The meso-scale computational models are reconstructed according to the geometric features of the deposited continuous CFRP filaments and the actual void volume fraction. The elastic properties of the filament are calculated by a micro-scale representative volume element (RVE) model, which is based on the fiber random distribution algorithm. The plastic deformation and failure is described by a filament constitutive model which is established by the Liu-Huang-Stout yield criterion and a simplified Tsai-Wu failure criterion. The experimental validation demonstrates the feasibility of the computational models to predict the stress-strain curves of 3D printed materials, and also capture the realistic longitudinal compression failure behavior.

An integrated modeling of the curing process and transverse tensile damage of unidirectional CFRP composites

In this work, an integrated numerical approach for predicting the damage mechanism of unidirectional CFRP composites at the micro-scale level has been developed using a multi-scale modeling strategy, where the curing residual stresses induced in autoclave curing process is taken into account. This research frames of the curing residual stresses development and the transverse tensile damage development through finite element computation. The curing residual stresses of CFRP composites induced in the curing process are characterized by coupling thermal-chemical analysis at macro-scale level and thermal–mechanical at micro-scale level. Then, the obtained residual stresses are combined with the micro-scale representative volume element (RVE) to compute the transverse tensile damage of CFRP composites. The predicted homogenized stress–strain curve at micro-scale fits the experimental results well. The microscopic damage distribution caused by the introduction of curing residual stresses reveals the intrinsic mechanisms of CFRP composites from fabrication to service. In addition, the influence of curing process on the strength performance of CFRP composites are further studied using the proposed approach.

Capsule based self-healing composites: New insights on mechanical behaviour based on finite element analysis

We have investigated the reinforcement mechanics of capsule-based self-healing composites (CSC) comprising poly(urea–formaldehyde) (PUF) capsules embedded in epoxy matrix using a micro-scale representative volume element (RVE) model. Finite element analysis was used to model four stages of loading, corresponding to elastic loading and fracture of pristine CSC (containing epoxy-filled capsules) and, following healing, of repaired CSCs (containing capsules depleted of healants), respectively. Predictions of the elastic modulus (E) during elastic loading and the local damage pattern within the CSC during fracture were obtained. The E was most sensitive to capsule volume fraction (Vp) but least sensitive to capsule distribution pattern. The E also depended on the state of the capsule. The E increased with increasing Vp in epoxy-filled capsule composite, suggesting that epoxy-filled capsules could provide reinforcement to the epoxy-based composite. However, E decreased with increasing Vp in empty capsule composites, indicating that empty capsules could not be depended upon for reinforcing the composite. When fracture began, capsules at close proximity, especially in agglomerates, could interact to promote further damage regardless of whether they were filled or empty; the damage pattern observed could be a prelude to mode 1 type fracture. These predictions led to wider implications concerning how agglomerates in the CSC could influence the mechanics of elastic loading and fracture of the composite.

Multiscale Modeling of Asphalt Concrete and Validation through Instrumented Pavement Section

In this study, macroscale responses of asphalt concrete (AC) are predicted from the responses of its corresponding microscale representative volume element (RVE) within a finite element framework using quasi-static and dynamic analyses. Nanoindentation test was performed on the mastic and aggregate phase of an AC sample to determine the viscoelastic and elastic properties of RVE elements. Aggregate-mastic proportions in the RVE were obtained from the morphological image analysis. Macroscale model responses were compared with the AC pavement responses obtained from an instrumented pavement section subjected to falling weight deflectometer loading and a class 9 vehicle. Model responses are very close to the actual responses. The multiscale analyses show that tensile strain in microscale RVE is 5–10 times higher than that in a macroscale element. Furthermore, multiscale analyses also show that variations in the microscale RVE, such as the reduction in the aggregate-mastic ratio or increment in the voids, can increase the maximum tensile strain at the bottom of the AC in macroscale model by around 25%.

Microscale representative volume element based numerical analysis on mechanical properties of fused deposition modelling components

Among additive manufacturing techniques, Fused Deposition Modelling (FDM) has emerged as an economical method capable of fabricating functional components. The thermoplastic filament material used in FDM and the fabrication criterion such as infill density, layer height, raster orientation etc. influence the print attributes. The directional characteristics of the component needs to be determined for designing functional components. The primary aspiration of the study is to numerically investigate the influence of infill density, layer height and raster orientations on the elastic behaviour of FDM components. The study also develops a predictive model to estimate the elastic characteristics of FDM components. Using cross-section morphology of FDM print, micro-scale Representative Volume Element (RVE) are modelled for 0/90 degree raster configuration. The characteristics determined over the RVE could be considered as the characteristics of the FDM component. The components exhibited directional behaviour with higher layer height at lower infill densities. The significance of the build parameters and their relationship on the characteristics of the part is estimated. The Response Surface Methodology (RSM) based predictive model developed can anticipate the directional peculiarities of FDM prints. This predictive model could be effectively used for optimizing the components for functional applications.

Three-scale asymptotic homogenization of short fiber reinforced additively manufactured polymer composites

In this research, prediction of mechanical properties of short fiber-reinforced composites manufactured with the help of fused filament fabrication (FFF) process is investigated. Three-scale formulation of asymptotic homogenization is employed to upscale the properties from microscale to mesoscale and from mesoscale to macroscale. Since generating microscale representative volume element (RVE) infused with short fibers requires sophisticated modeling tools, the algorithm for the microscale RVE generation is presented and discussed. Homogenization was performed for microscale RVEs with random and aligned (fibers aligned with the beads on mesoscale) fiber orientations, and for mesoscale RVEs with unidirectional and 0/90 layup formation. Tensile tests were performed for different short carbon fiber concentrations 5, 7.5 and 10% (by volume) to validate predicted homogenized properties. Moreover, to analyze the morphology of 3D printed specimens, microstructural analysis using SEM was performed on all the printed specimens. Surface morphology helped to gain more insight into the bead structure and fiber distribution. It was concluded that Young's modulus prediction using random fiber orientation has low relative errors tested in bead direction. Overall, this study has unique contribution to mechanical property prediction for FFF-made short fiber-reinforced composite parts.

Multiscale homogenization method for the prediction of elastic properties of fiber-reinforced composites

An analytical approach based on multiscale homogenization is proposed to enable efficient and accurate characterizations of fiber-reinforced composites with imperfect interfaces. Micromechanical formulations are developed to evaluate transversely isotropic properties of a microscale representative volume element (RVE) consisting of a fiber, the surrounding matrix and their interfaces. We utilized the shear-lag model to derive the longitudinal Young’s modulus, the composite cylinder assemblage (CCA) model to get the in-plane bulk modulus and the axial shear modulus, and the generalized self-consistent (GSC) scheme for the transverse shear modulus. Numerical results given by the detailed finite element analysis (FEA) demonstrate the high accuracy of the obtained material properties. To scale up-to macro-level, the RVEs are homogenized to equivalent inclusions that are perfectly bonded to the matrix, followed by the application of the Mori–Tanaka method to obtain bulk properties of the overall composites. The large-scale FEA model that allows incorporation of periodic boundary conditions and cohesive interfaces between fiber and surrounding matrix confirms the good accuracy of the proposed multiscale homogenization strategy. The proposed strategy does not depend on any computational simulations, providing a very efficient tool to understand effects of imperfect interfaces and an alternative to determine mechanical properties of composites only based on geometric and material parameters.

Multiscale modeling of strength and failure behavior of carbon nanostructure reinforced epoxy composite adhesives in bonded systems

In this study, atomistic based continuum (ABC) multiscale modeling approach is presented for strength and failure prediction of carbon nanotube (CNT) reinforced epoxy composite adhesives in bonded systems. Assuming that the CNTs are uniformly dispersed in the epoxy matrix, the mechanical properties of the nanocomposite adhesive are determined utilizing a two-step sequential homogenization procedure. In the first step, effective mechanical properties of a nanoscale representative volume element (RVE) are determined. The RVE comprises a CNT embedded in the epoxy matrix separated by an interphase. The structure-property relationship at the nanoscale is captured through ABC modeling approach wherein a CNT is modeled as a space-frame structure with beam elements and the epoxy is modeled using solid elements. The interphase between the CNT and the epoxy is modeled using non-linear spring elements to account for non-bonded van-der Waals interactions. In the second step, CNT inclusions with random orientations in the matrix are considered to create a microscale RVE of the nanocomposite. In both the steps, different boundary conditions were applied on the RVEs, and finite element (FE) analyses were conducted to estimate the effective mechanical properties through numerical homogenization. Furthermore, the strength of CNT/epoxy composite is estimated using modified Kelly-Tyson theory. Finally, modeling scheme proposed here is utilized to assess the load carrying capacity and failure behavior of a single lap-joint (SLJ) comprising composite adherends and CNT/epoxy nanocomposite adhesive by conducting continuum scale FE analyses. Results show over 30% improvement in strength for the SLJ with CNT/epoxy bondlayer comprising 2 vol% CNT. The findings of the study indicate that both strength and damage tolerance of the bonded joints can be significantly optimized utilizing nanoreinforced bondlayer.

Homogenisation of elastic properties in FDM components using microscale RVE numerical analysis

Fused deposition modelling (FDM) is an additive manufacturing method having the potential to fabricate functional components. As the inherent nature of additive structures, the component stiffness depends on the build parameters such as layer height and raster orientation in addition to the filament material properties. Even on FDM prints with 100% infill density, voids are formed along the interface of rasters and contribute to the characteristics of the component. The primary role of the present work is to determine elastic characteristics such as Young’s modulus, shear modulus and Poisson’s ratio of FDM components and study the effect of build parameters. The void geometry identified from the cross-sectional morphology was used to create a microscale representative volume element (RVE) model capturing the characteristics of the FDM print. The elastic constants of the microscale model RVE were estimated by volume average method and homogenised over the entire structure. The study also investigated the influence of layer height on the elastic behaviour of FDM components in two different raster orientations of 0° and 0°/90°. Both the conditions exhibited directional characteristics and the elasticity constants approaches filament characteristics with decreases in the layer height. The modulus of elasticity was found maximum in the direction of raster orientation, whereas the elasticity modulus along vertical direction exhibited the lowest. The components with 0°–90° raster orientation exhibited transversely isotropic characteristics. Thus, the actual cross-sectional morphology-based microscale numerical analysis can effectively predict the directional attributes of FDM prints.

Prediction of non-linear mechanical behavior of shear deformed twill woven composites based on a multi-scale progressive damage model

In this paper, the non-linear mechanical behavior of shear deformed woven composite was predicted using a representative volume element (RVE) model based on multi-scale progressive failure analysis. The micro-scale RVE model, consisting of single fiber and a matrix, was employed to determine the stress amplification factor and distinguish the failure of each fiber and the matrix constituent. Then, a meso-scale RVE model of shear deformed twill woven composite was developed to predict non-linear behavior using micro-stress transferring with finite element simulation. Fiber yarn shapes were observed with respect to the shear angle of the twill fabric. Based on the observed yarn geometry, shear deformed twill composite was modeled by using the open source software TexGen. To prove validity of the proposed model, shear deformed twill woven composite was fabricated using a picture frame, followed by a vacuum assisted resin transfer molding process. Mechanical tests were conducted and the failure progress during the tests was observed to determine their failure analysis. As a result, a good correlation between the multi-scale progressive damage model and experimental results such as mechanical properties, the non-linear stress-strain curve, and failure modes were achieved.