Microstructural Model Research Articles

Determination of the REV size for heterogeneous rocks with different grain sizes: Deep learning and numerical approaches

Accurate determination of the representative elementary volume (REV) size plays a pivotal role in analysing the mechanical properties and failure processes of heterogeneous rocks in complex engineering environments. In this study, a novel microstructure modelling strategy (NMMS) for determining the REV size is proposed by combining deep learning and an improved phase-field method (PFM). Micro- and macroscale experiments are systematically conducted to determine the real microstructural characteristics and mechanical properties of heterogeneous rocks with different grain sizes. On the basis of this experimental evidence, geometric models of different sizes were reconstructed through deep learning to avoid the limitations of human-based methods, and an improved PFM was used for numerical calculations. These models were then employed to perform numerical tests under uniaxial loading conditions, and the coefficient of variation was introduced to determine the REV size of heterogeneous rocks with different grain sizes. The research findings indicate that the final REV size is the maximum value of the REVs defined by the evaluation properties within an acceptable coefficient of variation. At a criterion of 5% for the coefficient of variation, the REV sizes are 60 mm×60 mm, 70 mm×70 mm, and 90 mm×90 mm for fine-medium-grained (FMG), medium-grained (MG), and coarse-grained (CG) rocks, respectively. Furthermore, the REV determined by the NMMS was applied to investigate the effects of microstructure on macromechanical properties and damage evolution under triaxial loading conditions. The numerical results show that the NMMS can accurately predict the macromechanical properties and microcracking patterns of heterogeneous rocks, especially the intracrystalline cracks in feldspar, the interfacial cracks in gravel, and the “voids” of cracks in biotite. This research can provide some basic references for the optimal choice of the REV size of heterogeneous rocks.

High-fidelity reconstruction of porous cathode microstructures from FIB-SEM data with deep learning

Accurate modeling of lithium-ion battery (LIB) electrode microstructures provides essential references for understanding degradation mechanisms and optimizing materials. Traditional segmentation methods often struggle to accurately capture the complex microstructures of porous LIB electrodes in focused ion beam scanning electron microscopy (FIB-SEM) data. In this work, we develop a deep learning model based on the Swin Transformer to segment FIB-SEM data of a lithium cobalt oxide electrode, utilizing fused secondary and backscattered electron images. The proposed approach outperforms other deep learning methods, enabling the acquirement of 3D microstructure with reduced particle elongated artifacts. Analyses of the segmented microstructures reveal improved electrode tortuosity and pore connectivity crucial for ion and electron transport, emphasizing the necessity of accurate 3D modeling for reliable battery performance predictions. These results suggest a path toward voxel-level degradation analysis through more sensible battery simulation on high-fidelity microstructure models directly twinned from real porous electrodes.

Predictive Modeling and Optimization of Hot Forging Parameters for AISI 1045 Ball Joints Using Taguchi Methodology and Finite Element Analysis

This study focused on optimizing the hot forging process for AISI 1045 medium carbon steel ball joints, which is crucial for enhancing both their mechanical properties and production efficiency. Traditional hot forging processes often face challenges due to variations in flow stress and microstructural outcomes, which can result in a suboptimal product performance. To address these challenges, this research employed the Taguchi method in conjunction with a finite element (FE) simulation to identify the optimal forging parameters. The Arrhenius constitutive model, based on the Zener–Hollomon parameter, was applied to predict the flow stress with a high level of accuracy, achieving a coefficient of determination (R2) of 0.968 and an average absolute relative error (AARE) of 7.079%. An analysis of variance (ANOVA), a statistical innovation that partitions the total variation into components linked to key process factors, was utilized to determine the significance of these parameters. The ANOVA revealed that the billet temperature played a significant role in influencing the preforming force, finishing force, and mean stress, with a maximum impact of 62.30%, 59.50%, and 94.20% on the variation in the response variable, respectively. Additionally, the friction factor significantly affected the preforming and finishing forces, contributing 36.19% and 38.28%. The validation of the model through both simulations and practical experiments is a testament to the reliability of this research, demonstrating the accuracy of the model with minimal discrepancies in the forging forces and exhibiting errors of just 2.88% and 3.40%. Furthermore, microstructure modeling successfully predicted the key outcomes, such as the grain size and pearlite volume fraction, validating the effectiveness of the simulation in forecasting microstructural characteristics.

Cellular solids and prestressed affine networks as models of the elastic behavior of soft biological structures.

We reviewed two microstructural models, cellular solid models and prestressed affine network models, that have been used previously in studies of elastic behavior of soft biological materials. These models provide simple and mathematically transparent equations that can be used to interpret experimental data and to obtain quantitative predictions of the elastic properties of biological structures. In both models, volumetric density and elastic properties of the microstructure are key determinants of the macroscopic elastic properties. In the prestressed network model, geometrical rearrangement of the microstructure (kinematic stiffness) is also important. As examples of application of these models, we considered the shear behavior of the cytoskeleton of adherent cells, of the collagen network of articular cartilage, and of the lung parenchymal network since their ability to resist shear is important for their normal biological and physiological functions. All three networks carry a pre-existing stress (prestress). We predicted their shear moduli using the microstructural models and compared those predictions with existing experimental data. Prestressed network models of the cytoskeleton and of the lung parenchyma provided a better correspondence to experimental data than cellular solid models. Both cellular solid and prestressed network models of the cartilage collagen network provided reasonable agreements with experimental values. These findings suggested that the kinematic stiffness and material stiffness of microstructural elements were both important determinants of the shear modulus of the cytoskeleton and of the lung parenchyma, whereas elasticity of collagen fibrils had a predominant role in the cartilage shear behavior.

The Evolution of Dilatant Shear Bands in High-Pressure Die Casting for Al-Si Alloys

Bands of interdendritic porosity and positive macrosegregation are commonly observed in pressure die castings, with previous studies demonstrating their close relation to dilatant shear bands in granular materials. Despite recent technological developments, the micromechanism governing dilatancy in the high-pressure die casting (HPDC) process for alloys between liquid and solid temperature regions is still not fully understood. To investigate the influence of fluid flow and the size of externally solidified crystals (ESCs) on the evolution of dilatant shear bands in HPDC, various filling velocities were trialled to produce HPDC samples of Al8SiMnMg alloys. This study demonstrates that crystal fragmentation is accompanied by a decrease in dilatational concentration, producing an indistinct shear band. Once crystal fragmentation stagnates, the enhanced deformation rate associated with a further increase in filling velocity (from 2.2 ms−1 to 4.6 ms−1) localizes dilatancy into a highly concentrated shear band. The optimal piston velocity is 3.6 ms−1, under which the average ESC size reaches the minimum, and the average yield stress and overall product of strength and elongation reach the maximum values of 144.6 MPa and 3.664 GPa%, respectively. By adopting the concept of force chain buckling in granular media, the evolution of dilatant shear bands in equiaxed solidifying alloys can be adequately explained based on further verification with DEM-type modeling in OpenFOAM. Three mechanisms for ESC-enhanced dilation are presented, elucidating previous reports relating the presence of ESCs to the subsequent shear band characteristics. By applying the physics of granular materials to equiaxed solidifying alloys, unique opportunities are presented for process optimization and microstructural modeling in HPDC.

Buoyancy driven motion of non-coalescing inertial drops: microstructure modeling with nearest particle statistics

Buoyancy driven motion of non-coalescing inertial drops: microstructure modeling with nearest particle statistics

2-D Microstructure Modeling based on Micrographs of Laser Powder Bed Fusion Melted Specimens

2D microstructural modeling based on the optical micrographs was successfully carried out. Creating a realistic microstructural model containing microstructural features such as fusion boundaries and phases makes it possible to analyze the relationship between the microstructure and property. We implemented this method to the 316 stainless steel (SS) laser powder bed fusion melted specimens. The optical micrographs were meshed and imported into finite element (FE) software. According to the results, the orientation of the fusion boundaries significantly influenced the mechanical properties of the printed parts. Stress localization was significant when the fusion boundaries were parallel to the loading direction. The situation differed when the fusion boundaries were perpendicular to the loading direction. In this case, the large amount and size of fusion boundaries showed significant ductility with homogenously distributed straining.

Adaptively remeshed multiphysical modeling of resistance forge welding with experimental validation of residual stress fields and measurement processes

Welding processes used in the production of pressure vessels impart residual stresses in the manufactured component. Computational modeling is critical to predicting these residual stress fields and understanding how they interact with notches and flaws to impact pressure vessel durability. In this work, we present a finite element model for a resistance forge weld and validate it using laboratory measurements. Extensive microstructural changes, near-melt temperatures, and large localized deformations along the weld interface pose significant challenges to Lagrangian finite element modeling. The proposed modeling approach overcomes these roadblocks in order to provide a high-fidelity simulation that can predict the residual stress state in the manufactured pressure vessel; a rich microstructural constitutive model accounts for material recrystallization dynamics, a frictional-to-tied contact model is coordinated with the constitutive model to represent interfacial bonding, and adaptive remeshing is employed to alleviate severe mesh distortion. An interrupted-weld approach is applied to the simulation to facilitate comparison to displacement measures. Several approaches are employed for residual stress measurement in order to validate the finite element model: neutron diffraction, the contour method, and the slitting method. Model-measurement comparisons are supplemented with detailed simulations that reflect the configurations of the residual-stress measurement processes themselves. The model results show general agreement with experimental measurements, and we observe some similarities in the features around the weld region. Factors that contribute to model-measurement differences are identified. Finally, we conclude with some discussion of the model development and residual stress measurement strategies, including how to best leverage the efforts put forth here for other types of related weld problems.

Effect of curing behaviors on performances of phthalonitrile resins: A deep molecular dynamics exploration with experiment

The curing process and mechanism of high-performance phthalonitrile (PN) thermosetting resin are crucial for its excellent mechanical and thermal-oxidation properties. The complicated polymerization reactions of PN resins were effectively controlled to obtain three types of major cured products (triazine, polyindoline and phthalocyanine). The corresponding cross-linking evolution processes and atomistic microstructural models were dynamically constructed and visualized through a creatively self-compiled procedure. Molecular dynamics simulations combined with experiment were properly conducted on two typical PN resins to illustrate the relationship between cross-linked microstructures and performance. The cross-linking degree and types of final products are positively correlated with the mechanical strength of PN resin. The hydrogen bonds present in the cross-linked structure mainly consolidate the cured networks of PN resin and the unique phenolic hydroxyl groups in PN75 enhance the hydrogen bonding contribution. The dominant pyrolysis gases were experimentally detected and distinguished as H2O, NH3, HCN, CH4, CO2 and CO during the thermal pyrolysis process of PN resin as the temperature rose. This work provides a new approach to probe the curing process and generated species, and further tailor the mechanical behavior and thermal-oxidation properties of resins or composites.

Plastic deformation and damage modeling of AA7075 synthetic 3D microstructure created using generative AI

3D microstructures provide valuable insight into material behavior which is essential in elucidating microstructural phenomena, such as particle morphology and void damage, and consequent macroscopic material response. However, creating 3D microstructures is extremely laborious and expensive, requiring complex microstructural characterization and imaging techniques such as Focussed-Ion Beam based Scanning Electron Microscopy (FIB-SEM) or X-ray Computed Tomography (XCT). To this end, synthetic 3D microstructures were rapidly generated from orthogonal 2D images using SliceGAN, which proved a practical and cost-effective method. In this study, multiple synthetic microstructures of AA7075-O, a complex microstructure of various strengthening precipitates within a softer aluminum matrix, were post-processed, meshed, and modeled for different damage behavior in FEA using advanced constitutive material models. Subsequently, the synthetic and real microstructures were qualitatively and quantitatively analyzed for their elastoplastic deformation and ductile void damage responses.This study illustrates the viability of an integrated AI-FE methodology in studying microstructural micromechanics, demonstrating that synthetic microstructures exhibited a very similar stress-strain response, especially when using a free boundary condition, and comparable stress distribution and void damage, albeit with some discrepancies. Also, it emphasizes the influence of particle morphology on strength and damage, where highly irregular particles play a dual role in increasing strain hardening by restricting matrix flow at the cost of increased ductile damage induced by decohered particles. Lastly, the more advanced FE models, with multiple voiding mechanisms, reduced the discrepancy between real and synthetic microstructures compared to simpler models

The Cahn–Hilliard model of coherent lamellar microstructure: application to alkali feldspar

The temporal evolution of coherent lamellar microstructures is significantly influenced by their elastic properties, particularly when the exsolved phases are coherent. This research utilizes the Cahn–Hilliard model to examine the morphological and energetic evolution of binary alkali feldspar, integrating anisotropic elastic energy into the Gibbs energy equation. The Cahn–Hilliard model successfully simulated the orientation of lamellae observed in natural samples and the elastic strain was consistent with previous research. We also computed the coherent solvus from the annealing simulation of various precursor compositions and temperatures. The temperature difference (ΔT\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta T$$\\end{document}) between the strain-free solvus and the coherent solvus was ΔT=85∘C\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\Delta T = 85\\,{}^\\circ \ ext {C}$$\\end{document}, which is slightly lower than previously reported values obtained from similar parameters. This discrepancy is likely due to the presence of non-planar lamellae at the onset of phase separation, which are more stable than planar ones. We also simulated the binodal curves of the coherent solvi for different precursor phase compositions. The computed solvi were not unique but varied depending on the precursor composition. Our model is flexible because it does not assume any specific shapes for the lamellar interfaces and is applicable to various coherent binary systems.

Three-dimensional reconstruction of porous media by fusing multi-grid image features based on extended feature pyramid network

Microstructural analysis of porous media has significant research value in the study of their macroscopic properties. An accurate reconstruction of the digital microstructure model is a prerequisite for understanding their physical properties and transport properties. Deep learning can accurately extract features from training images for a fast and precise reconstruction of porous media. The reconstruction methods based on deep learning have yielded important achievements in the reconstruction of porous media. Aiming at the complex morphology and multi-scale image information of porous media, this paper proposes a generic end-to-end deep learning-based encoder–decoder generative method for the reconstruction of porous media from a single 2D image. This paper designs an extended feature pyramid network encoder to extract image features of different resolutions and different scales, and a generator network incorporating multi-scale image information. Through the training process of the network, the final three-dimensional images that meets certain requirements are generated by means of confrontation. By introducing the loss function of the pattern density function and the loss function of Wasserstein distance with gradient penalty, we constrain the reconstructed 3D structures. Finally, the reconstructed 3D structures and the target 3D structures are visualized to compare their similar morphologies. The morphological parameter indicators of the reconstructed 3D structures were line with those of the target 3D structure. The microstructure parameters of the 3D structures were also compared and analyzed. For complex porous media images, our method can achieve diverse, accurate, and stable 3D reconstruction.

Investigation of failure analysis on fatigue crack initiation influenced by critical resolved shear stress in X10CrMoVNb9-1 steel

This study investigates the influences of the critical resolved shear stress (CRSS) values on calculating the number of cycles for the fatigue crack initiation cycle of X10CrMoVNb9-1 (P91) under cyclic loading conditions at room temperature while considering varied surface roughness on microstructure models. The micropillar compression test was utilized to calculate the CRSS values, incorporating the Schmid factor, the Frank–Read source together with the Hall–Petch effect, measuring the diameter of the micropillar after compression, and the Mlikota and Schmauder equation. Two primary microstructure surface roughness – plane surface roughness (PS) and surface roughness (SR) with an average of 1 µm – were generated using the Voronoi Tessellation (VT) method. Finite Element Method (FEM) simulations were conducted to identify different stress distributions across these artificial microstructures. These stress distributions were subsequently analyzed using the physics-based Tanaka-Mura model (TMM) to estimate the number of cycles for fatigue crack initiation at several stress amplitudes and six types of microstructure. The number of cycles varies significantly at lower stress amplitudes and convergence at higher stress amplitudes. The study of the CRSS of steel P91 offers a significant advancement in fatigue research, particularly with implications for power plants.

Special Issue on Quantitative Metallography and Microstructure Modeling

Special Issue on Quantitative Metallography and Microstructure Modeling

Multiscale modelling and characterisation of fused filament fabricated neat and graphene nanoplatelet reinforced G-polymers

AbstractIn this study, the fused filament fabrication of novel biodegradable G-polymer is investigated, including also filaments reinforced by graphene nanoplatelets. A combined framework of computational multiscale modelling and experimental studies is applied to characterise and model the mechanical behaviour of composite and nanocomposite materials, fabricated using a 3D-printer by depositing G-polymer filaments in +45$$^\circ$$ ∘ and $$-45^\circ$$ - 45 ∘ angles. The investigation is performed on both hot-extruded single filaments and 3D-printed specimens. Experimental results of hot-extruded single filaments are utilized on the microscale to extract the macroscale constitutive models. At the microscale level, representative volume elements with different percentages of penetration are analyzed to compute the effective orthotropic elastic material properties. A comprehensive comparison study is conducted using different micromechanical models, multiscale simulation outputs, and the mechanical properties resulting from experiments. The accuracy of the results obtained from the homogenization technique is validated against realistic finite element microstructural models and experimental measurements. The results demonstrate that computational homogenization, when coupled with accurate property characterisation, serves as a reliable tool for predicting the elastic response of 3D-printed parts. Furthermore, the proposed framework reduces the need for extensive experimental replication and lowers manufacturing costs.

Research on Alkali-Activated Slag Stabilization of Dredged Silt Based on a Response Surface Method.

To improve the resource utilization of dredged silt and industrial waste, this study explores the efficacy of using ground granulated blast furnace slag (GGBS), active calcium oxide (CaO), and sodium silicate (Na2O·nSiO2) as alkali activators for silt stabilization. Through a combination of addition tests, response surface method experiments, and microscopic analyses, we identified key factors influencing the unconfined compressive strength (UCS) of stabilized silt, optimized material ratios, and elucidated stabilization mechanisms. The results revealed the following: (1) CaO exhibited the most pronounced stabilization effect, succeeded by Na2O·nSiO2, whereas GGBS alone displayed marginal efficacy. CaO-stabilized silt demonstrated rapid strength augmentation within the initial 7 d, while Na2O·nSiO2-stabilized silt demonstrated a more gradual strength enhancement over time, attributable to the delayed hydration of GGBS in non-alkaline conditions, with strength increments noticeably during later curing phases. (2) Response surface analysis demonstrated substantial interactions among GGBS-CaO and GGBS-Na2O·nSiO2, with the optimal dosages identified as 11.5% for GGBS, 4.1% for CaO, and 5.9% for Na2O·nSiO2. (3) X-ray diffraction (XRD) and scanning electron microscopy (SEM) analyses clarified that the hydration reactions within the GGBS-Na2O·nSiO2 composite cementitious system synergistically enhanced one another, with hydration products wrapping, filling, and binding the silt particles, thereby rendering the microstructure denser and more stable. Based on these experimental outcomes, we propose a microstructural mechanism model for the stabilization of dredged silt employing GGBS-CaO-Na2O·nSiO2.

A numerical simulation method for ultrasonic transmission in cancellous bone based on a four-parameter random growth method

Abstract Quantitative ultrasound (QUS) has been widely used in non-destructive evaluation of bone health in research and clinical practice. To make a more accurate bone evaluation, the transmission characteristics of ultrasound in the bone need to be understood in detail. In the two-dimensional finite element model, cancellous bone is usually simulated by a non-porous structure solid or by approximating bone trabeculae as ellipses, which is different from real bone. However, although the error of the model constructed by bone CT images is small, it needs to be based on real bone samples, and the samples are limited. Therefore, a modeling method of cancellous bone based on four-parameter random growth method was proposed in this paper, and on this basis, numerical simulation of ultrasonic transmission was carried out. Firstly, based on the four-parameter random growth method, the aggregation algorithm is used to concentrate discrete pixels and smooth the edge of pores. Meanwhile, the built-in algorithm ensures the same porosity before and after processing to reduce the discrete pore structure. Secondly, based on COMSOL to establish the simulation model of ultrasonic propagation in cancellous bone, we analyzed the change of acoustic field distribution, discussed the correlation between the porosity of cancellous bone and backscattering coefficient (BSC) based on the ultrasonic backscattering method, and compared the experimental results of CT scan images of bone samples. The experimental results show that the cancellous bone modeling method in this paper has the same conclusion as the method based on CT images, which verifies the feasibility of this method. This method can generate a geometric model of the cancellous bone microstructure with specified porosity and different bone trabecular distribution, which is similar to the real bone structure, and can be directly imported into the finite element software to facilitate the study of bone microstructure related problems. It provides a more convenient method to study the mechanism of ultrasonic propagation in cancellous bone and has important significance in solving the inverse problem of recovering effective bone parameters from the received ultrasonic signals.

A multiscale discrete fiber model of failure in heterogeneous tissues: Applications to remodeled cerebral aneurysms

Damage-accumulation failure models are broadly used to examine tissue property changes caused by mechanical loading. However, damage accumulation models are purely phenomenological. The underlying justification in using this type of model is often that damage occurs to the extracellular fibers and/or cells which changes the fundamental mechanical behavior of the system. In this work, we seek to align damage accumulation models with microstructural models to predict alterations in the mechanical behavior of biological materials that arise from structural heterogeneity associated with nonuniform remodeling of tissues. Further, we seek to extend this multiscale model toward assessing catastrophic failure events such as cerebral aneurysm rupture. First, we demonstrate that a model made up of linear elastin and actin and nonlinear collagen fibers can replicate bot the pre-failure and failure tissue-scale mechanics of uniaxially-stretched cerebral aneurysms. Next, we investigate how mechanical heterogeneities, like those observed in cerebral aneurysms, influence fiber and tissue failure. Notably, we find that failure occurs and the interface between regions of high and low material stiffness, suggesting that spatial mechanical heterogeneity influences aneurysm failure behavior. This model system is a step toward linking structural changes in growth and remodeling to failure properties.

Design of Steel-Cu composites for enhancing thermal properties of plastic processing tools by using a numerical model of the microstructure

Limitationsof conventional materials used for plastic processing tools, particularly related to thermal conductivity, significantly influence production efficiency, with the cooling time of moulded parts appearing as one of the key factors. Therefore, this study focuses on designing Steel-Cu composites with the aid of a numerical model of the composite's microstructure for enhancing their overall thermal properties. We present a novel procedure for designing such composites, which facilitates the identification of the optimal shape for the phases to improve overall thermal conductivity. We have developed a data-driven homogenization model to aid the optimization process and ensure time-efficient solutions. The data has been generated through numerical homogenization based on the finite element method. The proposed shape optimization procedure has been applied to determine the optimal shape of the Cu phase across various volume fractions. We found out that the optimal shape of the Cu phase is not constant but depends on its volume fraction. Emphasizing the practical utility of the proposed procedure, it is noteworthy that once the data-driven model is established, it enables a time-efficient optimization of the Cu phase shape for arbitrary volume fractions of phases. Consequently, this may expedite the decision-making process for material manufacturers.

Freeze-thaw cycling of nano-SiO2-modified recycled aggregate in concretes: Hydro-thermal-mechanical modeling

The freeze-thaw cycling in the cold region causes severe damage to the concrete, which seriously affects the durability of concrete. In this paper, nano-SiO₂ (NS) modified RAC (NS-RAC) specimens were prepared by impregnating RCA with a 3 % NS dispersion for 48 h with following frost resistance assessed experimentally. To further fully understand the performance of NS-RAC under freeze-thaw (F-T) cycles, a comprehensive hydro-thermal-mechanical coupling model was established to simulate the damage behavior of NS-RAC under F-T conditions. A random polygon microstructure model of RAC was developed, and the characteristics of RCA and three types of ITZs were discussed. The damage control equation for RAC during the F-T process was defined based on the coupling effects of percolation, temperature, and stress in a porous medium. The F-T cycle tests show that the compressive strength of NS-RAC samples after 100 F-T cycles is 9.04 MPa higher than that of RAC. Numerical simulation results indicate that, compared to RAC without NS, the maximum pore pressure, crystallization pressure, and maximum principal stress of samples with 3 % NS after the first F-T cycle are reduced by 3.84 %, 4.36 %, and 2.26 %, respectively. During the F-T cycle, with increases in ITZ width, aggregate gradation range, RCA replacement rate, and temperature difference, the internal stress of NS-RAC specimens increased to varying degrees. This study provides insights into the F-T damage of RAC in severe cold regions and promotes the practical engineering application of RAC in such environments.