Short Fiber Composites Research Articles

Comparative estimation of fracture resistance of teeth restored with new fiber impregnated composite, short fiber composite, and nanohybrid composite – An in-vitro study

INTRODUCTION. Composite resins, used in restorative dentistry, offer enhanced esthetic and mechanical qualities. Nevertheless, the significant issue of volumetric shrinkage during polymerization remains a concern. Shrinkage-induced stress has the potential to cause marginal defects and enamel and cuspal fractures, especially in high stress-bearing areas. The present study aimed at assessing and comparing the fracture resistance and fracture patterns of teeth restored with new impregnated cubical composite, short fiber reinforced composite, and nanohybrid composite in mesio-occlusal-distal (MOD) cavities.MATERIALS AND METHODS. This was an in-vitro study comprising 45 extracted premolars cleaned and mounted in resin blocks. The MOD cavities were prepared in all the samples and were divided into three groups; Group I samples restored using ESPE Filtek Z350 XT restorative composite syringeTM, Group II using GC EverX posterior compositeTM (4mm), and Group III using Fibrafill cube S. Restorations were finished and polished.RESULTS. The mean fracture resistance was 844.5±264.8, 1249.7±518.3, and 1240.8±453.3 in Group I, II, and III, respectively. Group II and III fracture resistance was comparable (p=1.00) but higher than Group I (p=0.03 with Group II, p = 0.04 with Group III). No significant difference was present in the favourable and nonfavourable fracture patterns between the three groups (p=0.108).CONCLUSIONS. Short fiber and cubic fiber integrated composites performed similarly in terms of fracture resistance resulting in favourable fracture, however better over conventional nanohybrid composites.

Three-Dimensional Printing Limitations of Polymers Reinforced with Continuous Stainless Steel Fibres and Curvature Stiffness

This study investigates the printability limitations of 3D-printed continuous 316L stainless steel fibre-reinforced polymer composites obtained using the Materials Extrusion (MEX) technique. The objective was to better understand the geometric printing limitations of composites fabricated using continuous steel fibres, based on a combination of bending stiffness testing and piezoresistive property studies. The 0.5 mm composite filaments used in this study were obtained by co-extruding polylactic acid (PLA), with a 316 L stainless steel fibre (SSF) bundle. The composite printability limitations were evaluated by the printing of a series of ’teardrop’ shaped geometries with angles in the range from 5° to 90° and radii between 2 and 20 mm. The morphology and dimensional measurements of the resulting PLA-SSF prints were evaluated using μCT scanning, optical microscopy, and calliper measurements. Sample sets were compared and statistically examined to evaluate the repeatability, turning ability, and geometrical print limitations, along with dimensional fluctuations between designed and as-printed structures. Comparisons of the curvature bending stiffness were made with the PLA-only polymer and with 3D-printed nylon-reinforced short and long carbon fibre composites. It was demonstrated that the stainless steel composites exhibited an increase in bending stiffness at smaller radii. The change in piezoresistance response of the PLA-SSF with load applied during the curvature bending stiffness testing demonstrated that the 3D-printed composites may have the potential for use as structural health monitoring sensors.

Properties of Multiple-Processed Natural Short Fiber Polypropylene and Polylactic Acid Composites: A Comparison

Natural fiber composites have gained increasing attention due to sustainability considerations. One often neglected aspect is the potential for the mechanical recycling of such materials. In this work, we compounded injection-molded polypropylene (PP) and polylactic acid (PLA) short cellulose fiber composites with fiber shares up to 40 percent by weight. Both matrix materials were reinforced by the addition of the fibers. We investigated a trifold full recycling process, where we subjected the materials produced in the first place to compounding, injection molding, testing, and shredding, and then repeated the process. Although the materials’ properties assigned to degradation were found to decrease with progressive recycling, attractive mechanical properties could be preserved even after the third reprocessing cycle.

Influential reinforcement parameters, elemental mapping, topological analysis and mechanical performance of lignocellulosic date palm/epoxy composites for improved sustainable materials

The value of biomaterials for green products has begun to develop more ecofriendly and renewable sustainable materials for a better circular economy and to reduce carbon footprints. This work presents integrated investigations of the lignocellulosic date palm/epoxy composites at various reinforcement condition parameters for sustainable structural materials where elemental mapping, topological analysis, and mechanical performance have been performed. Mapping energy dispersive X-ray spectroscopy was utilized to assess the composite composition properly. Elemental mapping and a scanning electron microscope were employed to evaluate the chemical composition of the composites. The mechanical performance of the produced composites was also explored in terms of ultimate tensile strength, tensile modulus, elongation at break, and impact energy properties. The effects of fiber loading, fiber length, and fiber width (as long fiber, short fiber, and long-thin fiber) were investigated for the date palm fiber/epoxy composites. Results have revealed that the composite behavior was affected by several influential reinforcement parameters. The energy dispersive X-ray spectroscopy maps by C–K, O–K, Si–K, K-K, and Ca-K demonstrated that the composites contain mainly carbon, silicon, and oxygen. It was evident that the modulus of elasticity property of short fiber composites exhibits an increasing trend with higher fiber content, even at 35 wt%. Moreover, the enhancement of tensile strength for the short fiber size composites reached 72.5 %. However, such tensile strength of thin fiber size/epoxy composites achieved 135.7 % at 25 wt% indicating superior development of this mechanical property. The long date palm fiber composites demonstrated the best value of modulus of elasticity and the maximum impact energy of 15.3 kJ/m2 attained at 25 wt%, which is about 112.5 % enhancement. Scan electron microscope was capable of confirming that broken fibers were not separated from the matrix indicating the good adhesion between the fiber and the matrix that supports their good mechanical performance.

Microscopic instabilities in single crystal matrix composites

A finite strain micromechanical analysis is presented for the prediction of the loss of microscopic stability of a class of metal matrix composites that are subjected to axial compressive loading and undergoing large deformations. The metallic constituent behavior is modeled by the single crystal anisotropic plasticity theory in which, due to the resolved shear stresses, plastic deformations occur along certain pre-defined slip planes. Thus, this incremental plasticity theory is capable of providing the effect of the applied axial loading on the induced shear stresses which dominate the microbuckling. The composites are assumed to possess slight imperfections at the interfaces, and in order to satisfy the interfacial conditions, a perturbation expansion is employed which yields zero and first order micromechanical analysis problems. The zero order problem corresponds to the micromechanical modeling of the composite with no imperfections, whereas the solution of the first order problem is utilized to obtain the critical stresses and deformations at which bifurcation buckling occurs. Both problems are solved by employing the finite strain high-fidelity generalized method of cells (HFGMC) micromechanics. Applications are given for various types of single crystal matrix composites including layered, particulate, continuous and short fiber composites. Finally, a comparison between the compressive strengths of a standard metal matrix boron/aluminum and SiC/single crystal composites is presented and discussed.

Feasibility problems with the differential Mori-Tanaka method and modifications for refining inclusion stress predictions

Prevalent mean-field homogenization techniques excel in approximating effective stiffness, they fall short in predicting the stress states of individual inclusions within the same phase. Differential Mori-Tanaka (DMT) method presents possibilities for estimating stresses/strains in individual inclusions, which can be used for improved micromechanics of short fibre composites. This paper showcases inherent physical admissibility problems associated with DMT and proposes a novel modification to address them. The two schemes viz. DMT and modified-DMT are benchmarked using full-FE results. The modified-DMT effectively circumvents the physical admissibility problems with the DMT and is shown to results in qualitatively superior predictions of stresses in individual inclusions.

Piezoresistive modeling of orthotropic 3D-printing composite line extrusions with non-affine reorientation of fibers

This work introduces a micromechanical semi-analytical model to estimate piezoresistive constants in 3D-printable short-fiber composites, extending the Mori–Tanaka scheme with two innovative components. Firstly, the model incorporates non-affine reorientation of fibers, controlled by a parameter η, which significantly impacts texture coefficients. This parameter introduces an additional layer of complexity, modifying texture coefficients beyond traditional affine fiber reorientations. Observational data illustrate a linear relationship between piezoresistivities and η, leading to the development of a statistical model that calculates η based on the fiber aspect ratio. Secondly, the model accounts for preferential fiber orientation in the undeformed state, resulting in an orthotropic material model. This anisotropy is quantified using an Orientation Distribution Function (ODF) derived from X-ray scans, which is parameterized to maintain symmetry across three orthogonal planes. Initial investigations indicate that the inherent anisotropy introduced by the printing process substantially affects the initial resistivity of 3D-printed composites. Utilizing a Gaussian transversely isotropic model, we find that neglecting this anisotropy could lead to significant errors in understanding and predicting piezoresistive behavior. The model’s incorporation into advanced nanocomposite frameworks offers preliminary reconciliation with experimental data. Additionally, our results emphasize the necessity to refine wavy fiber models by incorporating non-affine rotations, particularly crucial for fibers with small aspect ratios, thereby enhancing predictive accuracy. The findings lay a robust foundation for future research, emphasizing the need for comprehensive experimental validation and setting the stage for nuanced applications in piezoresistive composite materials.

Numerical modeling of fiber orientation in multi-layer, isothermal material-extrusion big area additive manufacturing

Fiber orientation is a critical factor in determining the mechanical, electrical, and thermal properties of 3D-printed short-fiber polymer composites. However, the current numerical studies on predicting fiber orientation are limited to straight single-strand configurations, while the actual printed parts are often composed of complex multi-layer structures. To address this issue, we conducted numerical simulations of material extrusion in multi-layer big-area additive manufacturing without any post-deposition strand morphology modification mechanism. By examining the effects of material properties and printing conditions when extruding and depositing strands on a fixed substrate as well as previously deposited layers, it was possible to observe the complex interplay between multiple layers and its impact on fiber orientation. The work and methodology presented in this paper can be used to identify optimal extrusion-to-nozzle speed ratios, material rheology, fiber content, and fiber aspect ratio to achieve the desired performance and thermo/mechanical properties of additively manufactured parts. This work is an important contribution towards the manufacture of high-performance, short-fiber polymer composites as the presented methodology can enable engineers to precisely predict and tailor the fiber orientation in 3D printed parts.

Response of short jute fibre preform based epoxy composites subjected to low-velocity impact loadings

This work aimed to investigate the low velocity impact behaviour of short jute fibre non-woven preform epoxy matrix composites experimentally. Dry fibre preforms were developed using an optimised process and a laboratory made preforming device. The effects of alkali and poly vinyl alcohol (PVA binder) treatments on impact performances of jute composites were investigated and compared at 3 J and 6 J impact energy levels. To identify the failure modes of tested composites, the X-ray µCT tomography was employed. The results demonstrated that the developed untreated short jute fibre preform reinforced composites absorbed a higher impact energy, when they were compared to treated (alkali or PVA binder) composites. For untreated composites, maximum impact forces at 3 J and 6 J energies, were found as ⁓2478 N and ⁓2319 N, respectively; for the PVA treatment these values were measured as ⁓2457 N and ⁓2216 N, while, at same energy levels, alkali treated composites showed the lowest values as ⁓1683 N and ⁓1440 N, respectively. Untreated jute fibre contains natural matrices such as hemicellulose, lignin and waxes, which ensured a positive response to absorb more energy upon impact loading. In contrast, the alkali treatment facilitates a highly fibre packed composite structure, which accelerated the impact crack propagation in tested composites, resulting in lower resistance to impact energy. Although, PVA treated composites showed reduced impact properties compared to untreated composites due to the PVA polymer brittleness on the treated fibre surface during the impact incidents, this treatment demonstrated better impact responses over the alkali treatment. The application of PVA binder on alkali-treated fibres provided an extra support to fibres and a better fibre/matrix interface and hence, this combined treatment demonstrated a slightly better impact resistance (⁓2027 N and ⁓1874 N impact forces at 3 J and 6 J respectively) compared to only alkali treated fibre composites. The SEM fracture images and the X-ray µCT damage analysis revealed different impact damage modes, which supported the observed impact results. The obtained results from this investigation could be helpful for using short jute fibre composites in various load demanding applications where impact incidents are likely to be happened.

Investigation of the hybridization effect on mechanical properties of natural fiber reinforced biosourced composites

Hybridizing the natural fibers with stronger synthetic fibers could significantly improve the properties of the natural fiber-reinforced composites. The improved mechanical capabilities of fiber reinforced polymers result from the fiber’s capacity for withstanding a more substantial portion of the mechanical load compared to the matrix it replaces. In order to guarantee the efficient transfer of the mechanical load from the matrix to the reinforcement, it is necessary to incorporate a fibrous filler. Transference takes place when the length of the fiber is longer than a specific critical length. Fibers which are shorter than the critical length will pull out from the matrix when tested to a tensile load. In some cases, complete transfer of the load is not performed. The goal of this study is to learn more about flax (FF), glass (GF), and mixtures of flax and glass (FF + GF) short fiber-reinforced PLA-PBS composites. This is performed to find out how the flax/glass combination affects the mechanical properties of PLA-PBS-reinforced short fiber composites. In order to extend their use for industrial applications, these composites were manufactured via extrusion and, afterward, injection molding. Fiber aspect ratios were followed after compounding and injection processing. The analysis of fiber lengths reveals a noteworthy observation: the proportion of fibers exceeding their critical length of 531 µm and 772 µm for FF and GF, respectively, is more significant when flax fibers (FF) and glass fibers (GF) are combined compared to when they reinforce the composite individually. Specifically, the composite containing both FF and GF exhibits a higher percentage of fibers surpassing their critical length, compared to their individual reinforcement in the composite. The results reveal that 27% of individually extracted single FF exceed their critical length, whereas a higher proportion, at 34%, is observed when FF is part of the composite mixture. In contrast, the critical length is surpassed by only 4% of individually extracted single GF, whereas the combined presence of GF in the composite results in a notably higher percentage, at 19%. The tensile properties of these composites were investigated considering the effect of the hybridization by flax/glass short fibers. It was noted that the tensile properties of the hybrid composites increase comparing to the flax composites from 42.4 MPa to 53 MPa for the tensile strength and from 4.9 GPa to 5.4 GPa for the tensile modulus. In contrast, the elongation at break of the hybrid composites decreases from 1.7% to 1.5% with the incorporation of glass fibers. The experimental results were compared with the predictions of the mixture law and the Cox-Krenchel model. The findings indicate that mixing synthetic fibers with natural fibers is an excellent approach to enhancing mechanical properties.

Mixed experimental-numerical method for quantitative measurement of mode II fibre/matrix interface debonding and comparison of fibre sizings in single short fibre composites

In short fibre composites, debonding cracks usually initiate from fibre tips and their growth is governed by the properties of the fibre/matrix interface. These properties are ideally acquired from a model test similar to the real composite, while excluding the effects of fibre fractures and the induced debonding interactions. Therefore, in this study, debonding growth was examined in detail, using novel single short fibre specimens, which were fabricated using a new methodology. These experiments were further complemented with a continuous fibre case study, where the established single fibre fragmentation specimens were evaluated. The progression of debonding and pull-out damages versus remote stress was studied for two fibre sizings utilizing real-time in-situ polarized light microscopy. A finite element model was built to obtain the fibre/matrix interfacial fracture toughness considering thermal residual stresses, friction and matrix plasticity, and a very good correlation was obtained between the model and the experiments.

Manufacturing, characterization, and macromechanical modeling of short flax/hemp fiber-hybrid reinforced polypropylene

The present work focuses on the manufacturing, mechanical characterization, and modeling of hybrid Flax/Hemp/Polypropylene (PP) composites under dry conditions. Geometric parameters of the fibers were measured both before and after the melt processing. The results indicated that the processed fibers, especially the hybrid ones, had a narrowed length distribution with an average fiber length of 0.48 mm for hybrids compared to 0.62 mm for non-hybrids. The hybrid composites were mechanically characterized using basic and loading-unloading tensile tests with various fiber combinations and weight percentages. The study also examined the effect of strain rate and cutting angle on the behaviors of the composites. The results demonstrated the significance of fiber orientation as the primary factor in explaining mechanical variations. The tensile strength and Young's Modulus of FH30 composites (PP + 15 wt% flax + 15 wt% hemp) increased by about 24.1 % and 10.9 %, respectively, when the plates were cut into dumbbell shapes at a 90° angle to the injection molding flow direction, compared to a cut at 0° The study also showed that the tensile strength is directly proportional to the mass fraction of reinforcements, with an increase in tensile strength by 7.9 % for 0° cut angle specimens between FH10 (PP + 5 wt% flax + 5 wt% hemp) and FH30 bio-composites, while the uniform strain is inversely proportional to the mass fraction of reinforcements, evidenced by a reduction in uniform strain of 30 % between FH10 and FH30 samples. Morphological observations revealed the presence of bands indicating the propagation of micro-cracks, as well as debonding or cohesive failure. Finally, a Perzyna-type elasto-viscoplastic constitutive model was applied to accurately predict the overall mechanical response of a hybrid composite material. Specifically, the model successfully captured the tension deformation behavior of hybrid natural short-fiber thermoplastic composites, including the elastic stage, yield stress, and nonlinear hardening.

An Experimental Study on the Hardness, Inter Laminar Shear Strength, and Water Absorption Behavior of Habeshian Banana Fiber Reinforced Composites

ABSTRACT The current study examines the effect of NaOH treatment on the hardness, inter-laminar shear strength (ILSS) and water absorption behavior of epoxy composites reinforced with banana pseudostem fibers. Using the hand-lay-up method, six distinct samples are created that are composed of layers of woven and short banana fibers in both a plain and hybrid form. Plain- treated woven composites reveal the highest hardness and ILLS properties followed by the hybrid and short fiber composites. The random orientation of the fiber structure in short fiber composites results in the largest moisture absorption; this behavior is further supported by elucidating the kinetic parameters and diffusion coefficient parameters. SEM analysis confirms the improved surface of the NaOH-treated composite material.

Short fibre/unidirectional hybrid thermoplastic composites: Experimental characterisation and digital analysis

This paper explores the use of compression moulding to produce structural hybrid composites based on short-fibre composites, combining a short-fibre core and uni-directional (UD) skins. A parametric study on processing parameters found low consolidation pressures provided a higher repeatability of the manufacturing process. The best mechanical response of the hybrid laminate was obtained through a 2-step consolidation process due to an increased fibre volume fraction. Despite a moderate 21.5% increase in cost compared to the short fibre material, the hybrid panels showed large increases in mechanical properties with an outstanding increase in flexural modulus of 330.4%. A semi-analytical constitutive model of the short fibre composite was developed to determine the variability in the mechanical response due to the stochastic microstructure. The results predicted a low scatter in strength, compatible with the requirements of structural applications. This study opens the path to the development of sustainable thermoplastic composites from recycled short-fibre compounds.

A data-driven model based on the numerical solution of the equivalent inclusion problem for the analysis of nonlinear short-fibre composites

The paper introduces a novel data-driven homogenization model developed for the computation of stress-strain curves for composites featuring arbitrary orientation distributions, aspect ratios, and volume fractions of fibres. The objective of the proposed model is to deliver both time-efficient and accurate results while taking into account a relatively small database. The database is generated through numerical solutions of the equivalent inclusion problem, encompassing results for predefined orientations and aspect ratios of the single inclusion (fibre). The database created for a specific matrix-fibre system can be employed by the surrogate model to predict outcomes for various cases involving different fibre configurations. The surrogate model comprises four key modules: aspect ratio interpolation, a discrete orientation averaging procedure involving a genetic algorithm, a spatial transformation procedure, and an iterative Mori-Tanaka scheme. The validity of the proposed data-driven model has been confirmed by comparing the obtained results with those acquired through analysis of the complex representative volume element (RVE) using Fast Fourier Transform (FFT)-based homogenization, as well as through comparisons with experimental results from the existing literature.

Predicting failure in injection-moulded short-fibre subcomponents under varied environmental conditions through fracture mechanics

Injection-moulded short-fibre composites are lightweight materials suitable for high-volume applications; however, current simulation methods (based on failure initiation criteria) to design components using these materials cannot yet accurately predict failure. This work presents a methodology to predict failure of injection-moulded short-glass-fibre reinforced thermoplastic (IM-SFRP) composite subcomponents, based on experimentally measured properties. The material's fracture toughness was characterised by Compact Tension tests for different fibre orientations and environmental conditions. These fracture toughnesses were used as the input for cohesive zone modelling in Finite Element simulations of subcomponents representative of automotive applications, coupled with fibre orientation fields predicted by an injection-moulding process simulation. These coupled simulations presented excellent agreement with the experimental results for subcomponents both in terms of (i) the peak load (highlighting the importance of accounting for the finite fracture toughness of the material to accurately predict the ultimate failure of the subcomponents), and (ii) the pre- and post-peak sequence of failure events (verified using fractographic analyses). This work also verified the applicability of temperature-moisture equivalence, not only for material characterisation using coupons including the material's fracture toughness, but also for the mechanical response of subcomponents until final failure. The methodology demonstrated in this paper contributes to designing safer and more efficient damage-tolerant IM-SFRP components.

Methodology to establish a forming process window for thermoset aligned discontinuous fiber composites

Highly aligned discontinuous fiber composites have been pursued with the goal of achieving high performance properties with the formability of short fiber composites. The feedstock consists of a highly aligned discontinuous fiber preform which can be combined with thermoplastic or thermoset resins to create prepreg that can extend in the fiber direction. With this added benefit of lamina extensibility in the fiber direction, a methodology is needed to determine the degradation of material quality with applied forming strain. A framework is established to define a forming process window which sets the optimal process conditions—temperature and strain rate—for maintaining lamina uniformity after deformation. Digital image correlation was used to measure strain uniformity for samples stretched in uniaxial tension at constant temperature and strain rate. The experimental results show that forming strain rate should increase with increasing process temperature. The process window established in this work will be used to ensure that material uniformity can be optimized in manufacturing trials and other material characterization evaluations.

Experimental method for in-situ real-time measurement of mixed mode fibre/matrix interface debonding and comparison of fibre sizings in single short fibre composites

In short fibre composites, off-axis fibres are potentially subject to mixed-mode loading, which results in interactive debonding growth in opening and sliding modes. This synergy might differ for strong and weak fibre/matrix bondings inducing discrete debonding patterns. This study employed an optical visualization technique to investigate, for the first time, the mixed-mode debonding growth for short fibres with different sizings and off-axis angles, through in-situ real-time measurements. For this purpose, embedded single short-fibre specimens were fabricated using E-glass fibres and an epoxy matrix, with a novel and more efficient manufacturing method than done so far in literature. E-glass fibres with two different sizings were utilized, including a polypropylene-compatible (weak) sizing and an epoxy-compatible (strong) sizing. While there was a relatively rapid debonding growth for the transverse fibres with the weak sizing, the strong sizing experienced a gradual debonding growth independent of the fibre angle. For the weak sizing, partial debonding cracks were initiated at different locations along the length of the fibres, where they coalesced into dominant debonding cracks. For the strong sizing, debonding was always initiated and localized at the fibre tip, and there was a clear synchronous propagation of debonding in the arc and length of the fibre.

Study of self-heating and local strain rate in polyamide-6 and short fibre glass/polyamide-6 under tension through synchronised full-field strain and temperature measurements

This paper studies thermomechanical coupling during room-temperature tensile testing of polyamide-6 (PA6) and 50 wt% short glass fibre/PA6. The tests were performed for different fibre angles (0°, 45°, 90°), moisture contents (dry, 50%RH), and strain rates (10−4, 10−2, 10−1s−1). Digital image correlation (DIC) was coupled with infrared thermography. The contribution of the local strains, strain rates and temperatures to the global mechanical behaviour was investigated throughout deformation. The initial thermoelastic response was used to estimate the coefficient of thermal expansion. In PA6, neck development caused significant self-heating at high strain rates, differently between dry and 50%RH. In glass/PA6, however, temperature rises were always small (<+3 °C) despite local strain rate peaks in the fracture zone. This was ascribed to limited plastic deformation, as confirmed by post-mortem microscopy. The full-field data can be highly valuable for the development of advanced constitutive models for both pure polymer and short fibre composite.

A numerical multi-scale method for analyzing the rate-dependent and inelastic response of short fiber reinforced polymers: Modeling framework and experimental validation

This research presents a numerical multi-scale approach that efficiently addresses the inelastic and time-dependent mechanical response of short fiber reinforced polymers (SFRPs) under monotonic loading conditions by linking the mechanical analysis from microscale analysis to a continuum model. To do so, first, the mechanical performance of a recently suggested unit cell, considering the intrinsic mechanical characteristics of both fiber and matrix, is studied to address the inelastic and rate-dependent mechanical behavior of completely aligned SFRPs. Then, the evaluated mechanical response is linked to the Hill's plasticity and two-layer viscoplastic (TLVP) models to represent the anisotropic mechanical response of SFRPs. Furthermore, an easy-to-use multi-step homogenization process is considered to numerically incorporate the influence of fiber misalignments. Finally, the suggested multi-scale technique is thoroughly validated at different strain rates, by using experimental observations of short fiber composites with high volume fraction and direct FE simulations of RVEs with complex microstructures.