Volume Element Research Articles

Analyzing the Impact of Multiple Foundation Stiffness Correlation on the Natural Frequency of Offshore wind turbines

The analysis of wind turbine behavior should avoid unplanned resonance, as it can increase fatigue damage. It is essential to rigorously evaluate the natural frequency of wind turbines in the initial design stage. This estimation can be done through two steps, the first one is the computing of the fixed base natural frequency of the wind turbine. The second is the estimation of the foundation stiffness effect. This paper examines the error margin of four correlations of foundation stiffness namely Randolph, Davies and Budhu, DNV, and Higgins in the estimation of the natural frequency of wind turbines. The fixed base natural frequency was estimated in this paper using a special-purpose finite element computer program called TurbiSoft through beam and volume elements. A reference 5.0 MW offshore wind turbine and 9 other turbines from different wind farms have been analyzed. For the fixed base natural frequency, obtained results demonstrate the reliability of the finite element program TurbiSoft through an error margin between 1-4% for the reference 5.0 MW offshore wind turbine. For the natural frequency of the whole system, the estimated error marking was between 9-20% which is an important value.This significant error is attributed to the low accuracy of these four correlation formulas for predicting the foundation flexibility contribution. The results from the four correlation formulas used are quite similar, with a difference in the error margin of less than 1%. However, the largest error margins are observed with the Higgins formula, which has been originally developed for short monopiles, even though the analyzed monopiles can be considered short, with monopile slenderness ratios less than 8.

An introduction for non-experts on using X-ray micro computed tomography as a tool for pore scale digital subsurface characterisation of siliciclastic materials

This paper presents an overview of using X-ray micro computed tomography (μCT) as a valuable tool for micro scale investigation of siliciclastic materials. When processed using digital image analysis (DIA), valuable quantitative data can be extracted from μCT 3D images. Subsurface reservoirs are of great importance to society as fluid-bearing formations, but also as storage reservoirs for carbon dioxide. μCT imaging has the capability to perform preliminary, highly detailed investigations of potential reservoirs. This approach has a range of benefits when compared to traditional 2D techniques, such as optical and scanning electron microscopy (SEM). Key advantages include the technique being non-destructive and capable of 3D and 4D visualisation. This facilitates rapid repeated digital measurements and experiments on microstructures. Digital samples can also be readily shared within the scientific community to replicate results and quickly launch new investigations. However, limitations still exist, posing challenges to the wider application of such a methodology. Such limitations include the identification of a representative elementary volume (REV), computational cost, and suitable processing of the output image data. Here, we highlight the value of using μCT and DIA, from our first experiences, to facilitate pore scale siliciclastic reservoir characterisation, but also highlight our perceived limitations and barriers to its much wider application. This paper introduces the key processing stages, opportunities and limitations of these techniques.

A FEM-based model for failure initiation in the microstructure of gray cast iron under uniaxial compression

PurposeThe purpose of this study was to validate the feasibility of the proposed microstructure-based model by comparing the simulation results with experimental data. The study also aimed to investigate the relationship between the orientation of graphite flakes and the failure behavior of the material under compressive loads as well as the effect of image size on the accuracy of stress–strain behavior predictions.Design/methodology/approachThis paper presents a microstructure-based model that utilizes the finite element method (FEM) combined with representative volume elements (RVE) to simulate the hardening and failure behavior of ferrite-pearlite matrix gray cast iron under uniaxial loading conditions. The material was first analyzed using optical microscopy, scanning electron microscopy (SEM), energy-dispersive X-ray spectroscopy (EDS) and X-ray diffraction (XRD) to identify the different phases and their characteristics. High-resolution SEM images of the undeformed material microstructure were then converted into finite element meshes using OOF2 software. The Johnson–Cook (J–C) model, along with a damage model, was employed in Abaqus FEA software to estimate the elastic and elastoplastic behavior under assumed plane stress conditions.FindingsThe findings indicate that crack initiation and propagation in gray cast iron begin at the interface between graphite particles and the pearlitic matrix, with microcrack networks extending into the metal matrix, eventually coalescing to cause material failure. The ferritic phase within the material contributes some ductility, thereby delaying crack initiation.Originality/valueThis study introduces a novel approach by integrating microstructural analysis with FEM and RVE techniques to accurately model the hardening and failure behavior of gray cast iron under uniaxial loading. The incorporation of high-resolution SEM images into finite element meshes, combined with the J–C model and damage assessment in Abaqus, provides a comprehensive method for predicting material performance. This approach enhances the understanding of the microstructural influences on crack initiation and propagation, offering valuable insights for improving the design and durability of gray cast iron components.

A novel algorithm for generating random fiber distributions for fiber reinforced composites based on lattice partition

AbstractThis paper propose a random fiber distribution generation algorithm based on lattice partition, which addresses the issue of limited increase in fiber volume fraction caused by the random movement of fibers in previous methods. By partitioning the representative volume element (RVE) window into lattices and moving fibers directionally, the proposed algorithm significantly increases the number of fibers within the RVE window. The generated fiber distribution achieves a fiber volume fraction of up to 80%, with an average execution time of 243.4 s. The influence of algorithm parameters on the randomness of fiber distribution is examined through statistical analysis of the generated distributions. Finite element models with various parameters are established to predict the elastic properties of the composites. The average relative error between the predicted values and the experimental results is 8.6%, demonstrating the effectiveness of the proposed algorithm. This algorithm offers a simple and effective approach for generating fiber distributions in the numerical study of the micromechanics of composites.Highlights A new lattice‐partition method is proposed to generate fiber distributions. The fiber volume fraction of generated fiber distribution is up to 80%. The randomness of fiber distribution is analyzed through statistical analysis. The algorithm predicts elastic properties with an average relative error of 8.6%.

Comparative analysis of direct search methods for material design optimization

This paper contributes to the field of optimization for periodic composite material design by systematically evaluating the performance of four direct search algorithms: greedy, simulated annealing (SA), genetic algorithms (GA), and particle swarm optimization (PSO). The central goal is to determine the optimal arrangement of two material domains inside a representative volume element (RVE) while respecting the constraint that half volume of the domains is composed of a specific material, with the effective shear modulus as the objective function. The main contribution of this work is the detailed comparison of these algorithms in terms of success rates and computational efficiency, providing critical insights into their suitability for different problem scales. For a small-scale problem (16 cells), PSO achieves a 100% success rate, while SA demonstrates over 90% success but at a higher computational cost. The greedy algorithm, despite its simplicity, achieves a 72% success rate with the lowest computational effort, requiring an average of 256 objective function evaluations. GA, however, exhibits the lowest success rate at 52% and requires the highest average number of evaluations (5003.2). Furthermore, the paper extends the analysis to a more complex problem (36 cells), where the adaptability and efficiency of the algorithms are tested. This investigation highlights the trade-offs between algorithmic complexity, success rate, and computational cost, offering practical guidelines for selecting suitable optimization methods based on problem size and characteristics.

A unified method to generate representative volume elements with tailored random fibre arrangements to estimate the shear and transverse behaviours of unidirectional continuous fibres composite plies

Axial compressible strength is a key design parameter of CFRP laminate structures, especially for Aerospace where maximum flexure on wings is driven by the global margin of safety on compressive loads. One of its main limiting contributors is the non-linear shear behaviour of the unidirectional ply. This shear response can be predicted by using generated (quasi-)random microstructures set within representative volume elements (RVE). Different microstructures with or without clusters of fibres (resulting from manufacturing processes) are necessary to quantify the mechanical variability. The variability of the microstructures is characterised by the variation of the arrangement, the volume fraction and the misalignment of the fibres. This leads to significant variations in the mechanical performance, in particular for the shear behaviour. In this study, we propose a unified algorithm that makes it possible to generate all the different positions of fibres in microstructures with very high fibre volume fractions. The microstructural parameters responsible for variations in mechanical behaviour are identified to establish a correlation between fibre distribution and the mechanical response. Finally, a composite cross-section is analysed to estimate the local non-linear shear behaviour as well as the compressive strength as an example to illustrate the benefit of complex microstructures modelling.

Study of the residual stress distribution in SiCp/Al composites under thermal cycling conditions

In this study, a three-dimensional random representative volume element model was constructed using the finite element method combined with Python script to investigate the residual stress distribution in SiCp/Al composites with varying volume fractions, particle shapes, and particle size under thermal cycling conditions. The model has two different particle morphologies: spheres and irregular polygons. The results show that the irregular polygonal SiC particles exhibit higher residual stresses than spherical particles before and after thermal cycling due to their complex load transfer pathways and higher stress concentration at particle corners, which makes them more consistent with the characterization of SiCp/Al composites under practical application conditions. As the volume fraction of SiC particles increases, the particle spacing decreases, hindering the release of thermal stresses through plastic deformation. Notably, the relief rate of residual stress reached 53% in the 12 vol% SiCp/Al composites, with the stress decreasing from 698 MPa to 328 MPa after 50 thermal cycles. In contrast, the reduction rate for 18 vol% composites is only 13% after thermal cycling. Furthermore, compared to larger particles (7.3 µm, 8.9 µm), the smaller particles (4.3 µm, 5.9 µm) exhibit a more uniform stress distribution and lower thermal stresses before and after thermal cycling. Consequently, our work provides a significant theoretical basis for the design and application of SiCp/Al composites, especially for the application of materials under extreme temperature changes.

Fine‐Tuning of Elastic Properties by Modifying Ordering of Parallel Nanolayer Inclusions in Hard Sphere Crystals

It is known that changes on the microscopic, structural level of materials exert changes on their macroscopic properties, in particular elastic ones. This approach can be used to alter the elastic properties of materials. However, it is not easy to predict the impact of a particular change in the structure of crystals. The recent studies show that depending on the size, shape, and orientation of inclusions used, the resulting elastic properties may differ. Inclusions may enhance, weaken, or eliminate the auxetic properties in a hard sphere model. This study is focused on the influence of the spatial distribution of planar inclusions within the hard sphere crystal and its impact on its elastic properties. Periodic systems containing two nanolayer inclusions in the representative volume element, oriented orthogonally to ‐direction and in various spatial ordering, are considered. It has been shown that introducing layer inclusions causes the deterioration of auxetic properties in the ‐direction. However, the latter weakly depends on the spatial ordering of the inclusion layers. Moreover, changes in the size of the inclusion particles, combined with different ordering of the inclusion layers, can be used to coarsely and finely tune the elastic properties of the model crystal.

A unified framework for the analysis of accuracy and stability of a class of approximate Gaussian filters for the Navier–Stokes equations

Abstract Bayesian state estimation of a dynamical system utilising a stream of noisy measurements is important in many geophysical and engineering applications. In these cases, nonlinearities, high (or infinite) dimensionality of the state space, and sparse observations pose key challenges for deriving efficient and accurate data assimilation (DA) techniques. A number of DA algorithms used commonly in practice, such as the Ensemble Kalman Filter (EnKF) or Ensemble Square Root Kalman Filter (EnSRKF), suffer from serious drawbacks such as catastrophic filter divergence and filter instability. The analysis of stability and accuracy of these DA schemes has thus far focused either on finite-dimensional dynamics, or on complete observations in case of infinite-dimensional dissipative systems. We develop a unified framework for the analysis of several well-known and empirically efficient DA techniques derived from various Gaussian approximations of the Bayesian filtering schemes for geophysical-type dissipative dynamics with quadratic nonlinearities. We establish rigorous results on (time-asymptotic) accuracy and stability of these algorithms with general covariance and observation operators. The accuracy and stability results for EnKF and EnSRKF for dissipative PDEs are, to the best of our knowledge, completely new in this general setting. It turns out that a hitherto unexploited cancellation property involving the ensemble covariance and observation operators and the concept of covariance localization in conjunction with covariance inflation play a pivotal role in the accuracy and stability for EnKF and EnSRKF. Our approach also elucidates the links, via determining functionals, between the approximate-Bayesian and control-theoretic approaches to DA. We consider the ‘model’ dynamics governed by the two-dimensional incompressible Navier–Stokes equations (NSEs) and observations given by noisy measurements of averaged volume elements or spectral/modal observations of the velocity field. In this setup, several continuous-time DA techniques, namely the so-called 3DVar, EnKF and EnSRKF reduce to a stochastically forced NSEs. For the first time, we derive conditions for accuracy and stability of EnKF and EnSRKF. The derived bounds are given for the limit supremum of the expected value of the L 2 norm and of the H 1 Sobolev norm of the difference between the approximating solution and the actual solution as the time tends to infinity. Moreover, our analysis reveals an interplay between the resolution of the observations (roughly, the ‘richness’ of the observation space) associated with the observation operator underlying the DA algorithms and covariance inflation and localization which are employed in practice for improved filter performance.

A two‐scale numerical analysis of intra‐yarn hybrid natural/synthetic woven composites

AbstractThis paper investigates how combining natural and synthetic fibers within yarns, altering the degree of hybridisation, and varying weave architectures affect the homogenized elastic properties and stress distributions in 2D woven composite laminae using a two‐scale homogenization scheme. The novelty lies in integrating a micro‐scale representative volume element model with a meso‐scale repeating unit cell model to capture intra‐yarn natural/synthetic fiber hybridisation. The study focuses on 2/2 twill and 5‐harness satin woven laminae with flax/E‐glass, hemp/E‐glass and basalt/E‐glass hybrid yarns, all with a total fiber volume fraction of 0.6. Fiber distributions are created through a random sequential expansion algorithm for hybrid RVEs, while periodic meso‐structures are used to define weave architectures for RUCs. Results show that yarn‐level fiber hybridisation significantly influences matrix stress distributions, with variations of up to 22%. In contrast, weave architecture has a minimal effect, with variations in homogenized properties below 2%. Varying fiber types, degrees of hybridisation and weave architectures allow for the tailoring of yarn and lamina properties and altering the stress distributions at micro‐ and meso‐scales and potentially influencing damage mechanisms. The modeling approach for analyzing the mechanical behavior of intra‐yarn hybrid natural/synthetic woven laminae could potentially be used to tailor their tolerance to damage.Highlights Two‐scale homogenization integrates RVE and RUC for 2D woven hybrid composites. Analyzed flax/E‐glass, hemp/E‐glass, basalt/E‐glass in twill and satin weaves. Intra‐yarn hybridisation significantly affects properties and stress fields. Hybridizing fibers offers tailored properties and may improve damage tolerance.

Hydrodynamic theory of premixed flames propagating in closed vessels: flame speed and Markstein lengths

A hydrodynamic theory of premixed flame propagation within closed vessels is developed assuming the flame is much thinner than all other fluid dynamic lengths. In this limit, the flame is confined to a surface separating the unburned mixture from burned combustion products, and propagates at a speed determined from the analysis of its internal structure. Unlike freely propagating flames that propagate under nearly isobaric conditions, combustion in a closed vessel results in continuous increases in pressure, burning rate and flame temperature, and a progressive decrease in flame thickness. The flame speed is shown to depend on the voluminal stretch rate, which measures the deformation of a volume element of the flame zone, and on the rate of pressure rise. Both effects are modulated by pressure-dependent Markstein numbers that depend on heat release and mixture properties while capturing the effects of temperature-dependent transport and stoichiometry. The model applies to flames of arbitrary shape propagating in general flows, laminar or turbulent, within vessels of general configurations. The main limitation of hydrodynamic flame theories is the assumption that variations inside the flame zone due to chemistry or turbulence, which could potentially alter its internal structure, are physically unresolved. Nonetheless, the theory, deduced from physical first principles, identifies the various mechanisms involved in the combustion process as demonstrated in detailed discussions of planar flames propagating in rectangular channels and spherically expanding flames in spherical vessels. It also enables the construction of instructive models to numerically simulate the evolution of multi-dimensional and corrugated flames under confinement.

Evaluating the deformation modulus at representative elementary volume using electrical resistivity tomography

The deformation modulus of rock mass is an essential parameter for evaluating the bearing capacity and deformations. A deformation modulus obtained through conventional approaches, including empirical equations and in situ tests, cannot present the deformation modulus at representative elementary volume (DREV) due to limited test coverage and technical difficulties in harsh geological or topographic conditions. This study utilized electrical resistivity (ER) tomography and numerical back-analysis to investigate DREV at the Asmari-Jahrum formation. We employed geoelectrical contrasts to detect proper locations for installing extensometers at excavated galleries. The deformations recorded by extensometer were used to back-calculate the DREV values by finite difference numerical modeling. We established a correlation between ER and DREV to predict DREV, which were 30–80 % more accurate than those obtained through conventional approaches at the study site. The tested area, anisotropy, creep, ER inaccuracies, and plastic deformations are evaluated as statistically significant factors that can influence DREV. Our methodology provides a systematical approach to assess DREV, which applies to geoengineering projects within the Asmari-Jahrum formation or similar sedimentary units (ER below 200 Ω⸱m). This methodology is also replicable for other geological formations with harsh geology or limited access without exposing an extreme financial burden or environmental issues.

Representative elementary volume (REV) and flow-dependent solute transport in homogenous porous media

Representative elementary volume (REV) and flow-dependent solute transport in homogenous porous media

Hierarchical Deformation and Anisotropic Behavior of (α+β) Ti Alloys: A Microstructure-Informed Multiscale Constitutive Model Study

In this study, the hierarchical deformation and anisotropic behavior of (α+β) Ti alloys are investigated using a novel microstructure-informed multiscale constitutive model. State-of-the-art crystal plasticity finite element (CPFE) models, due to their emphasis on a single length scale, are inadequate for capturing the complex hierarchical behavior of additively manufactured (AM) (α+β) titanium alloys, which are characterized by columnar grains and lamellar subgrain features at distinct length scales. To overcome this limitation, a decoupled multiscale framework was developed, integrating representative volume elements (RVEs) for both the columnar grain structure at the higher length scale and the subgrain microstructure at the lower length scale, with equal emphasis on each. The material behaviors at these scales were modeled using an anisotropic classical plasticity model and a mechanism-based CPFE model, respectively. The framework was experimentally validated for Directed Energy Deposition (DED) manufactured Ti-6Al-4V and used to investigate microscopic stress/strain fields, deformation localizations at grain and subgrain levels, and stress partitioning among neighboring grains. Insights from these studies led to the proposal of a new theory of anisotropy in AM (α+β) titanium alloys.

An analysis of the bilinear finite volume method for the singularly-perturbed convection-diffusion problems on Shishkin mesh

In this paper, we study the bilinear finite volume element method for solving the singularly perturbed convection-diffusion problem on the Shishkin mesh. We first prove that the finite volume element scheme is ϵ-uniformly stable. Then, based on new expression of the finite volume bilinear form and some detailed integral calculations, an ϵ-uniform error estimation is derived in the ϵ-weighted gradient norm, including the L2-norm. This error estimate is better than the known result. Moreover, we also give the L∞-error estimate near the boundary layer regions. At last, numerical experiments show the effectiveness of our method.

A numerical conductive network model for investigating the strain-sensing response of graphene nanoplatelets-filled elastomeric strain sensors

Strain sensors have attracted great attentions for practical applications such as human-machine interface. It is challenging to model the electrical behavior of elastomeric strain sensors modified with nanomaterials. This study presents a finite element simulation to explore the piezoresistivity of graphene nanoplatelet (GNP)-filled elastomeric nanocomposites. The percolation network model is employed to determine the critical distance necessary for electrical percolation. The finite element percolation network model uses the Euclidian distance between GNPs distributed inside the representative volume element to calculate the resistivity. The influence of various parameters, including GNP alignment direction, aspect ratio, and volume fraction, on the resistivity changes of the nanocomposite is investigated. Results demonstrate that nearly 20% more tunneling distance is allowed for percolation of nanocomposite with 30% larger aspect ratio GNPs. Findings reveal that as the volume fraction of GNPs increases, the critical distance for the electrical percolation decreases significantly.

Experimental and numerical characterization of E-glass/epoxy plain woven fabric composites containing void defects

The presence of voids in woven fabric composite (WFC) significantly affects the mechanical and thermomechanical properties. Void defects are introduced during the resin infiltration process due to various controlling parameters involved in the curing process, i.e., pressure, temperature, resin flow etc. In this study, the mechanical constants of 2D woven fabric composite were experimentally determined. A finite element (FE) based representative volume element (RVE) model has been validated against these experimental results. A multiscale-based FE model has been developed, and periodic boundary conditions are applied to the RVE model to evaluate the homogenized thermomechanical properties of WFC containing void defects. Present numerical model incorporates the geometrical microstructures of the post-cured woven composite and void contents obtained from X-ray microtomography. The influence of void defect and resin infiltration have been incorporated to evaluate the thermomechanical properties of plain WFC. A parametric study has been carried out with respect to the variation of void defects on thermoelastic properties of E-glass/epoxy plain WFC. The variation of void defects has been considered in micro and mesoscale models. Monte Carlo simulations further quantified the effects of void content on the thermomechanical constants of WFC. The presence of voids has been observed to have significant influences on the thermomechanical constants of yarn and woven fabric composites.

Application of Numerical Integration in Analysing the Volume of Reinforcement Particles in Algorithms for Generating Representative Volume Elements (RVEs)

Abstract The paper focuses on spatial modelling of composites with discontinuous reinforcement. The algorithm for creating a representative volume element (RVE) must consider random distribution and size of reinforcing particles (RP), prevention of RP interpenetration, and maintaining the desired volume fraction of the reinforcing phase (Vp) in the composite microstructure. Assuming fixed RVE dimensions and randomly determined RP size, the actual Vp value needs to be continuously determined. If the assumed (desired) Vp is lower than the current value, additional reinforcement is added to the RVE. As the RP location is random, some particles may extend beyond the RVE limits, affecting Vp calculation. The research aims to determine the RP volume within the RVE boundaries when RP extends outside. The RVE was discretized with N points, and the number of Ni points within the area occupied by RP was determined. The sought value was calculated using the ratio Ni /N = Vp /VRVE, where VRVE, is the volume of the RVE. Two discretisation methods, systematised (RI) and random (Monte Carlo (MC)), were employed. The study investigated the effects of discretisation type and number N points on calculation accuracy and microstructure generation time for particle-reinforced composites in sphere, cylinder, and ellipsoid shapes. Systematised discretisation yielded higher accuracy/stability, with number N dependent on RP dimensions. The MC method reduced generation time but introduced instability and significant errors.

Microstructure and mechanical-property evolution of the explosive welding joint from the same RAFM steels under explosive welding and post-weld heat treatment

This study investigated the morphological evolution behaviors and the mechanical property of the weld interface during explosive welding for the flyer plate and base plate sourcing from the same reduced activation ferrite/martensitic (RAFM) steel. The relationship between fine-grain formation and the occurrence of dynamic recrystallization was analyzed based on the strain and temperature field distributions at the explosive-weld interface. Although post-weld tempering (PWT) treatment eliminated bent martensite laths, but it did not eliminate fine equiaxed grains and δ ferrite grains near the explosive-weld interface; therefore, the PWT treatment improved the mechanical properties of the explosive-weld RAFM steel joint only minimally. However, implementation of a normalizing process after the explosive welding process (“PWN” treatment) significantly eliminated the gradient structure and the residual δ ferrite grains at the explosive-weld interface of the RAFM steel joint. Based on the PWN state, the inclusion of a tempering treatment (“PWNT” treatment) promoted the uniform precipitation of M23C6 carbides, which significantly improved the tensile strengths of the explosive-weld RAFM steel specimens under both room and high temperatures. To study the influence of different microstructures on the plastic deformation behavior at the explosive-weld interface, the representative volume element (RVE) models basing on crystal plasticity finite element (CPFEM) method was constructed for different post-weld heat treatments (PWHTs). At the explosive-weld interface of the PWT-state RAFM steel joint, the plastic deformation was mainly concentrated in the δ ferrite grains, rather than in the fine equiaxed grains. In addition, only minimal deformation concentration was observed for the PWNT-state RAFM steel joint. In order to reveal the independent influence of the fine equiaxed grains at the weld interface on the mechanical properties of explosive-weld RAFM steel joint, the microstructural and mechanical distinctions between the RAFM steel joints in the N-PWT and PWNT states were investigated detailly. Finally, through optimization of the PWHT method, an explosive-weld RAFM steel (PWNT state) joint with a uniform microstructure and ideal mechanical properties was obtained.

Review of contemporary fluorescence correlation spectroscopy method in diverse solution studies.

Fluorescence correlation spectroscopy (FCS) is a well-known and established non-invasive method for quantification of physical parameters that preside over molecular mechanisms and dynamics. It combines maximum sensitivity and statistical confidence for the analysis of speed, size, and number of fluorescent molecules and interactions with surrounding molecules by time-averaging fluctuation analysis in a well-defined volume element. The narrow compass of this study is to acquaint the basic principle of diffusion and the FCS method in general regarding variable magnitudes and standardization adjustment. In this review, we give a theoretical introduction, examples of experimental applications, and utensils in solution systems with future perspectives.