Meso-scale Representative Volume Element Research Articles

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.

A multi-scale stochastic model for damage analysis and performance dispersion study of a 2.5D fiber-reinforced ceramic matrix composites

This paper presents a stochastic approach to study the damage evolution and performance dispersion of a 2.5D woven fiber-reinforced ceramic matrix composite in a multi-scale framework. The mechanical behavior of the composite depends on the constituent properties, fiber volume fraction, weave architecture and loading conditions. The dispersion behavior of the material was investigated with: i) a full-thickness meso-scale representative volume element (RVE) model which is established based on the weave architecture of the material, and ii) the Monte-Carlo method to obtain the effective mechanical properties of the material which are influenced by the dispersion in its constituents. The simulations reveal the damage initiation and propagation process of the material at micro/meso-scale. The results show that there are significant relationships between the constituent properties and the effective mechanical properties; the effective properties of material can be predicted with small errors, which would guide the design and optimization of composite materials.

Refine reconstruction and verification of meso-scale modeling of three-dimensional five-directional braided composites from X-ray computed tomography data

This paper proposes a statistical approach to generate the refine meso-scale representative volume element of three-dimensional (3D) five-directional braided composites considering the fabric compaction and the axial yarn torsion. The method firstly extracts the regions of interest to obtain the reference model (R-model) from the X-ray computed tomography (Micro-CT) data. Then, the geometric parameters of the collected yarns of R-model are statistically analyzed based on the scanning tomograms. Consequently, the meso-scale statistical model (S-model) are reconstructed after being fitted with the appropriate function. Moreover, for the validation of S-model, the traditional ideal model (I-model) and the experimental tests are considered. The results show that the proposed S-model is capable of accurately presenting the effects of the fabric compaction and yarn torsion on the mechanical behaviors of 3D braided composites, validated by the elastic constants and the damaged modes.

Hybrid woven carbon-Dyneema composites under drop-weight and steel ball impact

In this study, the impact behavior and damage mechanism of novel carbon-Dyneema hybrid fabric reinforced plastic composites are investigated using drop-weight and steel ball impact tests. The force-displacement response, energy absorption and damage mechanisms of the hybrid composite were analyzed and compared with those of woven carbon laminates. The experimental results suggest that the impact resistance of the hybrid composites has been improved when benchmarked with carbon fiber composites. The Dyneema fibers suppress the splitting of bottom surfaces during impact but are susceptible to buckling due to the low compressive strength of Dyneema fibers. A multi-scale approach is proposed for modelling impact damage of hybrid woven composite accounting for the interweave patterns. A meso-scale representative volume element of the interwoven hybrid structure is analyzed and discretized into several sub-sections, each regarded as a type of laminate. Then, a macro-scale impact model is established based on the homogenized effective properties of the sub-sections using continuum shell elements. The failure of the material is modelled using energy-based continuum damage mechanics. Overall, the numerical simulations show good agreement with experimental data in terms of impact force history and damage features, providing insight into the impact damage behavior of hybrid composites.

Predicting damage initiation in 3D fibre-reinforced composites – The case for strain-based criteria

Three dimensional (3D) fibre-reinforced composites have shown weight efficient strength and stiffness characteristics as well as promising energy absorption capabilities. In the considered class of 3D-reinforcement, vertical and horizontal weft yarns interlace warp yarns. The through-thickness reinforcements suppress delamination and allow for stable and progressive damage growth in a quasi-ductile manner.With the ultimate goal of developing a homogenised computational model to predict how the material will deform and eventually fail under loading, this work proposes candidates for failure initiation criteria. It is shown that the extension of the LaRC05 stress-based failure criteria for unidirectional laminated composites, to this class of 3D-reinforced composite presents a number of challenges and leads to erroneous predictions. Analysing a mesoscale representative volume element does however indicate, that loading the 3D fibre-reinforced composite produces relatively uniform strain fields. The average strain fields of each material constituent are well predicted by an equivalent homogeneous material response. Strain based criteria inspired by LaRC05 are therefore proposed. The criteria are evaluated numerically for tensile, compressive and shear tests. Results show that their predictions for the simulated load cases are qualitatively more reasonable.

Digital-Image-Driven Stochastic Homogenization for Recycled Aggregate Concrete Based on Material Microstructure

In this paper, a digital-image-driven stochastic homogenization method is developed to analyze elastic heterogeneous media such as recycled aggregate concrete (RAC), etc. This linking can be accomplished in an efficient manner by exploiting the excellent synergy of finite pixel-element method and Monte Carlo simulation for the computation of the effective properties of the random five-phase composite. The pixel-point discretization of system geometry is used for the approximation of the mechanical response of the elastic heterogeneous microstructure. Using nanoindentation technique and scanning electron microscopy, tens of digital images of modulus map of the five-phase heterogeneous material are made. Using the moving window technique and the Monte Carlo method, the random elastic moduli of the five phases at micro-scale are obtained. Then the effective elastic modulus of the meso-scale representative volume element (RVE) is computed based on spectral stochastic finite element method. Finally, the effective modulus is used to analyze the global behavior of RVE at macro-scale. Then the finite pixel-element method is used to investigate the effect of microscopic covariance noise on the global material properties, as well as the computational efficiency. The results show that the digital image method is an accurate and efficient tool to investigate the random material properties across scales.

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.

Multi-scale material modelling to predict the material anisotropy of multi-phase steels

In this article, a novel material modelling approach to predict the anisotropic material response of multi-phase steels is developed. The macroscopic material behaviour of the model is characterized by the homogenized response of a meso-scale Representative Volume Element (RVE), derived by Finite Element (FE) simulations. The RVE holds the most relevant microstructural features of the material under consideration, such as phase distribution, grain orientation, morphology etc., in sufficient detail, in order to capture the anisotropy and phase interactions. The micro-scale material models of individual phases are described with specific plastic potential functions, the components of which are derived from Crystal Plasticity (CP) laws. The plastic potential functions are constructed using the Facet method for each phase in the microstructure at the level of single grains, and are used in conjuncture with phase specific, isotropic grain hardening laws. The proposed model is evaluated through numerical experiments performed on a synthetic microstructure of Duplex steel, constructed from statistical material parameters extracted from literature. The RVE flow curves depicted very good correspondence with the experimental data reported for the same grade of Duplex Stainless Steel. The anisotropy prediction was further assessed through comparison between virtual diffraction experiments performed on the statistical microstructure and the actual Neutron Diffraction (ND) experimental data of the reference material. It was found that the model captured the overall trend of the diffraction curves for the individual phases with good accuracy, but obtaining an exact correspondence to the experimental values was not feasible with the performed simulations on statistical microstructures. Finally, an approach to predict the anisotropic yield locus of a multi-phase material is also presented.

Progressive failure of inter-woven carbon-Dyneema fabric reinforced hybrid composites

This study investigates the in-plane mechanical behavior of a twill 2,2 carbon-Dyneema fabric reinforced hybrid composite. A finite element (FE) model of a meso-scale representative volume element (RVE) is developed for simulating the in-plane behavior of the composite. The development of damage in both carbon and Dyneema yarns is modeled through progressive damage models with linear softening laws and the non-linear response of the Dyneema yarn is experimentally determined and described by the Ramberg-Osgood equation. The epoxy resin is regarded as an elasto-plastic material. The damage development in different constituents of the composite is analyzed and correlated with experimental observations. In addition, the role of RVE size in modeling the behavior of the hybrid composite is investigated. It is found that a minimum of size of about five basic units of RVEs is necessary to achieve acceptable predictive results due to shear lag effects.

Multi-scale constitutive modeling of natural fiber fabric reinforced composites

Natural fiber reinforced structural composites have a hierarchical structure made from stacked fabrics of interwoven yarns formed by twisting together discontinuous natural fibers. We develop multi-scale constitutive models to investigate the mechanical properties of plain woven composites. The multi-scale constitutive modeling is carried out in two steps: the effective micromechanical properties of a micro-scale representative volume element (RVE) of the twisted yarn are calculated using an orientation averaging method, which are subsequently transferred to a meso-scale RVE of the final composite to compute the elastic constants by homogenization over the RVE. 3D finite element models of the meso-scale RVEs of composites are developed to verify the accuracy of the proposed model. The multi-scale modeling results show that the yarn twist angle has significant effects on the elastic properties of the composites. The predicted results from the multi-scale constitutive model show good agreements with that from finite element analysis and experiment.

A multi-scale stochastic fracture model for characterizing the tensile behavior of 2D woven composites

In this paper, a multi-scale stochastic fracture model is presented to study the nonlinear mechanical behaviors of two-dimensional (2D) woven C/SiC composites under uniaxial tension. This model considers the randomly distributed intrinsic flaws and the complex braided structure of composites. In the model, the micro-scale representative volume element (RVE) is developed to compute the effective properties of yarns, which are then used in the meso-scale RVE to capture the macroscopic stress response of woven composites. Weibull distribution law is applied to the material elements to reflect the random flaws. The failure mechanism of composites is identified by analyzing the damage rates and the fracture morphologies of fiber, matrix, and interface. The effects of fiber volume fraction and temperature on fracture strength are predicted and the results demonstrate that the failure location varies as the temperature increase due to the relief of thermal residual stress. The presented model provides an efficient tool for evaluating the mechanical properties of textile composites.

Mechanical modelling of a sheared textile composite unit cell

Composites made using carbon fibre textile reinforcement give an anisotropic material with directional mechanical properties that are dependent on the fabric architecture. The directional properties of a 2D textile are primarily based on weave pattern: The direction of warp and weft yarns, undulation of the tows, and the change in fibre orientation during dry fabric forming process.During dry fabric forming processes, shear is the dominant deformation mechanism as the 2D fabric conforms to 3D shapes. As the fabric changes its shape to match that of the tool, the fibres rotate away from the orthogonal axes as a function of the shear angle. The modified fibre orientation is carried through the curing process and ends up in the finished composite component. This has an influence on the mechanical properties of a cured composite in localised regions of high deformation. Currently the effect of shear during fabric forming is not usually taken into account when modelling the performance of the finished composite at the macro-scale. Through the development of a novel, robust virtual tool, it is possible to identify the change in mechanical properties for a given shear angle. This will allow the macro FE models to give more accurate results. High deformation regions can be identified from a forming simulation (e.g. a sheet of fabric draped over a tetrahedron tool and causes severe shear near the intrusion) and the change in mechanical properties of these local regions can be adjusted accordingly.Using the digital element method previously developed in University of Bristol, the dry fabric architecture can be accurately predicted. The current work has created the ability to shear this virtual unit cell to update the unit cell geometry. This deformed woven geometry is then mapped onto a sheared voxel mesh and combined with an epoxy resin matrix to obtain the meso-scale Representative Volume Element (RVE) model. By applying periodic load cases to the model, the stiffness matrix and therefore the mechanical properties of the composite can be determined. This tool is applicable for any 2D woven resin-infused composite.

Multiscale surrogate modelling of the elastic response of thick composite structures with embedded defects and features

This paper presents a multiscale modelling approach for thick composite structures containing internal defects and features. The proposed approach was developed using a surrogate model to represent the composite response on the meso-scale. A set of Representative Volume Element (RVE) models under periodic boundary conditions were used to sample the response at specified locations across the composite design space. As an example of its application, wrinkle defects of various severities were introduced to the RVE models to assess the defect contribution to the composite response. The homogenized responses from the meso-scale RVE models were then used as input to the surrogate model. To link the macro and meso scales, a set of 3D lamination parameters representing the composite layup were developed. A surrogate model using the 3D lamination parameters and the defect severity as input was built to link the macro-model to the meso-scale responses. The proposed multi-scale approach was verified against a set of high fidelity models with different levels of wrinkle defect severity. Good agreement was found between the new multi-scale approach and the more computationally expensive high-fidelity models.

Multiscale finite element modeling of sheet molding compound (SMC) composite structure based on stochastic mesostructure reconstruction

Predicting the mechanical behavior of the chopped carbon fiber Sheet Molding Compound (SMC) due to spatial variations in local material properties is critical for the structural performance analysis but is computationally challenging. Such spatial variations are induced by the material flow in the compression molding process. In this work, a new multiscale SMC modeling framework and the associated computational techniques are developed to provide accurate and efficient predictions of SMC mechanical performance. The proposed multiscale modeling framework contains three modules. First, a stochastic algorithm for 3D chip-packing reconstruction is developed to efficiently generate the SMC mesoscale Representative Volume Element (RVE) model for Finite Element Analysis (FEA). A new fiber orientation tensor recovery function is embedded in the reconstruction algorithm to match reconstructions with the target characteristics of fiber orientation distribution. Second, a metamodeling module is established to improve the computational efficiency by creating the surrogates of mesoscale analyses. Third, the macroscale behaviors are predicted by an efficient multiscale model, in which the spatially varying material properties are obtained based on the local fiber orientation tensors. Our approach is validated through experiments at both meso- and macro-scales, such as tensile tests assisted by Digital Image Correlation (DIC) and mesostructure imaging.

A representative volume element based micromechanical analysis of a Bi-layered Ganoid Fish scale

The Mississippi Alligator gar (Atractosteus spatula) possesses a flexible exoskeleton armor consisting of overlapping ganoid scales used for predatory protection. Each scale is a two-phase biomineralized composite containing bio-modified hydroxyapatite (hard) minerals and collagen (soft) fibers. The protective layer consists of a stiff outer ganoine layer, a characteristic “sawtooth” pattern at the interface with the compliant bone inner layer. The garfish scale exhibits a decreasing elastic modulus from the external to the internal layers. Scanning electron microscopy (SEM) images of the cross-section revealed a two-layered structure. Elastic moduli, measured from nanoindentation experiments, were correlated to structural changes across each layer. The “material” symmetry of this materially and geometrically nonlinear biomineralized composite is unknown. Therefore, to be able to determine the stiffness tensor requires the use of finite element analysis (FEA). The gar fish scale was computationally modeled using the representative volume element (RVE) based approach. As a result, the unknown symmetry induced by the architecture and material layering require the use of complex FEA boundary conditions. The simulation was conducted in the pure uniaxial strain regimes of tension and shear, which necessitated the mathematical determination so appropriate surface loading conditions could be applied. This paper provides the results from a highly-resolved mesoscale RVE model based on iso-strain boundary conditions (ISBC) to determine the elastic stiffness tensor for the composite system. By assuming isotropic behavior in individual elements, the results for the RVE reveal the fish scale has an “orthotropic symmetry” with slight local strain variations occurring at the sawtooth interface.

Multi-scale finite element analyses on the thermal conductive behaviors of 3D braided composites

The thermal conductive behaviors of 3D braided composites along in-plane and out-of-plane directions were characterized and analyzed by multi-scale finite element analyses (FEA) and also validated by experimental. Micro-scale representative volume element (RVE) was used to calculate the thermal conductivities of braiding yarns, and the meso-scale RVE and full-scale braided model were developed to research the thermal conductive behaviors of the whole braided composites. The differences of the two models are also analyzed in this paper. Another attention of this paper was focused on revealing the thermal conductive structural effects of braided composites. It is found that the thermal conductivities along out-of-plane direction are larger than that of in-plane direction. The temperature distribution and heat flux transmission are mainly along fiber orientation direction. With the increment of temperature, the thermal conductivities of the braided composites are increased. As the existence of surface and corner regions, the thermal conductivities calculated from full-scale model are closer to experimental by comparison with meso-scale RVE. In addition, the temperatures in interior regions are slightly higher than those in surface and corner regions of the braided composites. This paper could make for further understanding the thermal conductive behaviors of braided composites.

Comparing experimental results to a numerical meso-scale approach for woven fiber reinforced plastics

Meso-mechanical analysis, allowing for the study of local phenomena, is one of the strongest tools for the investigation of woven carbon fiber reinforced plastics (CFRP). A meso-scale representative volume element (RVE) of a twill weave CFRP ply is modeled, which consists of the yarn part, and the surrounding matrix region. The yarns are considered to be elastic and transversely isotropic. To obtain the material properties of the yarn, a hexagonal dense packing (HDP) RVE representing the microstructure inside a tow, is homogenized. Furthermore, isotropic elasto-plastic behavior is assumed for the neat matrix region at the meso-scale. The material model accounts for different yield strengths in tensile and compressive direction as well as pressure dependence. For the verification of the meso-model and their homogenized results, experiments are conducted, which provide strains in a very high local resolution as well as the global response. The numerically and experimentally obtained strain fields as well as the global stress–strain responses are compared.

A determination of the minimum sizes of representative volume elements for the prediction of cortical bone elastic properties

At its highest level of microstructural organization-the mesoscale or millimeter scale-cortical bone exhibits a heterogeneous distribution of pores (Haversian canals, resorption cavities). Multi-scale mechanical models rely on the definition of a representative volume element (RVE). Analytical homogenization techniques are usually based on an idealized RVE microstructure, while finite element homogenization using high-resolution images is based on a realistic RVE of finite size. The objective of this paper was to quantify the size and content of possible cortical bone mesoscale RVEs. RVE size was defined as the minimum size: (1) for which the apparent (homogenized) stiffness tensor becomes independent of the applied boundary conditions or (2) for which the variance of elastic properties for a set of microstructure realizations is sufficiently small. The field of elastic coefficients and microstructure in RVEs was derived from one acoustic microscopy image of a human femur cortical bone sample with an overall porosity of 8.5%. The homogenized properties of RVEs were computed with a finite element technique. It was found that the size of the RVE representative of the overall tissue is about 1.5mm. Smaller RVEs (~0.5mm) can also be considered to estimate local mesoscopic properties that strongly depend on the local pores volume fraction. This result provides a sound basis for the application of homogenization techniques to model the heterogeneity of cortical microstructures. An application of the findings to estimate elastic properties in the case of a porosity gradient is briefly presented.

Improved parameter selection method for mesoscopic numerical simulation test of direct tensile failure of rock and concrete

In order to numerically simulate the failure process of rock and concrete under uniaxial tension, an improved method of selecting the mechanical properties of materials was presented for the random mechanic parameter model based on the mesoscopic damage mechanics. The product of strength and elastic modulus of mesoscale representative volume element was considered to be one of the mechanical property parameters of materials and assumed to conform to specified probability distributions to reflect the heterogeneity of mechanical property in materials. With the improved property parameter selection method, a numerical program was developed and the simulation of the failure process of the rock and concrete specimens under static tensile loading condition was carried out. The failure process and complete stress-strain curves of a class of rock and concrete in stable fracture propagation manner under uniaxial tension were obtained. The simulated macroscopic mechanical behavior was compared with the available laboratory experimental observation, and a reasonable agreement was obtained. Verification shows that the improved parameter selection method is suitable for mesoscopic numerical simulation in the failure process of rock and concrete.

A multi-scale approach for the stress analysis of polymeric separators in a lithium-ion battery

The separator is a critical component to the durability and safety of a battery. In a Li-ion battery, the dimensional change of the electrodes due to Li insertion/removal and the thermal expansion mismatch between components may induce stresses in the separator. Currently, there is no method to evaluate the stress inside a battery. This paper presents a finite element based multi-scale approach for the stress analysis of the separator in a battery cell. In this approach, the stress and deformation due to Li intercalation in electrode particles and separators is computed with a meso-scale representative volume element (RVE) battery cell sub-model coupled to a 1D macroscopic battery in the multi-physics code COMSOL ®. A LiC 6/LiPF 6/Li y Mn 2O 4 battery cell is analyzed. As the first step, only the effect of dimensional change due to Li insertion/removal is considered. The simulation results revealed that the stress in the separator vary in phase with the battery cycles. Its state and magnitude depended upon the Young's modulus of the separator, electrode particle size, packing, and the pressure of the cell. The results also suggested that the net cyclic dimensional variation of the battery cell accompanied with Li insertion/removal can be controlled by battery design.