Volume Element Research Articles

An efficient multi-scale method for failure mechanism analysis of SiCf/Ti composites with experimental validation

This study focuses on developing and validating a high-precision concurrent multi-scale finite element model considering the progressive damage model (PDM) and the cohesive zone model (CZM) for predicting the damage evolution of SiCf/Ti composites. At the macro-scale, a constitutive model describing the anisotropic damage criterion of SiCf/Ti composites was implemented by means of a user-defined subroutine (VUMAT). Meanwhile, based on the submodelling, a representative volume element (RVE) model was developed to systematically analyze the failure modes of the SiC fibers, the matrix, and the interface, respectively. Specifically, the crack initiation and propagation in the stress concentration zones were further discussed. Simultaneously, experimental methods were employed to verify the feasibility of the current model. During the uniaxial compression, the brittle fracture of the SiC fibers and ductile fracture of the matrix are the predominant failure modes of SiCf/Ti composites, with fiber fracture being the dominant factor. The crack initiates at the fibers, propagates rapidly to the fiber-matrix interface, and then extends into the matrix. Moreover, the fracture locations are suscepticle to stress concentrations, leading to the crack initiation and propagation. The predicted results show that the local damage has a significant effect on the failure mechanism of SiCf/Ti composites and this multi-scale model provides a scientific reference for the design and optimization of composites.

Comparative study of the experimentally observed and GAN-generated 3D microstructures in dual-phase steels

ABSTRACT In a deep-learning-based algorithm, generative adversarial networks can generate images similar to an input. Using this algorithm, an artificial three-dimensional (3D) microstructure can be reproduced from two-dimensional images. Although the generated 3D microstructure has a similar appearance, its reproducibility should be examined for practical applications. This study used an automated serial sectioning technique to compare the 3D microstructures of two dual-phase steels generated from three orthogonal surface images with their corresponding observed 3D microstructures. The mechanical behaviors were examined using the finite element analysis method for the representative volume element, in which finite element models of microstructures were directly constructed from the 3D voxel data using a voxel coarsening approach. The macroscopic material responses of the generated microstructures captured the anisotropy caused by the microscopic morphology. However, these responses did not quantitatively align with those of the observed microstructures owing to inaccuracies in reproducing the volume fraction of the ferrite/martensite phase. Additionally, the generation algorithm struggled to replicate the microscopic morphology, particularly in cases with a low volume fraction of the martensite phase where the martensite connectivity was not discernible from the input images. The results demonstrate the limitations of the generation algorithm and the necessity for 3D observations.

The mesoscale mechanics of compacted ductile powders under shear and tensile loads

A discrete numerical analysis of the yield and damage properties associated with a cohesive granular system composed of ductile particles is hereby presented. Such a modelling approach aims at better understanding damage mechanisms which are often encountered during the powder compaction process, widely used in the metallurgical and pharmaceutical fields. The analysis was based on the micromechanical modelling of an idealised granular system in the framework of the multi-particle finite element method, in which particle deformation was fully taken into account. An adhesive interaction law, presented in Audry et al. (2024), was used in the purpose of estimating the averaged mechanical properties associated with the modelled elementary volume. The focus was put on tensile and highly deviatoric loadings, which are usually related to the failure of powder compacts. The specific contact area developed through inter-particles contacts was used as an indicator of the mechanical strength of the elementary volume. Threshold surfaces corresponding to yielding and contact decohesion mechanisms were plotted in the stress space.

Can Stiff Matter Solve the Hubble Tension?

A new form of the mathematical expression for the co-moving volume element of a flat universe with cosmological constant, cold matter, and stiff matter is presented. It is used to determine the constraints from the Planck measurements of the Hubble parameter on the amount of stiff matter in the universe. These constraints are used to investigate whether the presence of stiff matter can solve the Hubble tension. It is found that the Planck measurements lead to an upper bound on the present value of the density parameter of stiff matter ΩS0<5⋅10−23, and that this is too small to solve the Hubble tension. Report. The main objective of this article is to introduce a novel mathematical expression for the co-moving volume element in a flat universe that includes a cosmological constant, cold matter, and stiff matter. This expression is utilized to derive constraints on the amount of stiff matter in the universe based on the Planck measurements of the Hubble parameter. These constraints are then examined to assess whether stiff matter could potentially resolve the Hubble tension. The findings indicate that the Planck measurements impose an upper limit on the current value of the density parameter of stiff matter, ΩS0<5⋅10−23, which is insufficient to resolve the Hubble tension.

From approximation of dissipative systems to representative space-time volume elements for metamaterials

From approximation of dissipative systems to representative space-time volume elements for metamaterials

Multiscale verification method for prediction results of mechanical behaviors in unidirectional fiber reinforced composites

At present, there is almost no reliable multiscale experiment method that can be used to verify the multiscale mechanical behaviors of unidirectional (UD) fiber reinforced composites (FRC). Therefore, a multiscale method was developed for verifying the prediction results of the macro-mechanical properties and micro-damage modes in UD FRC. Firstly, the fiber volume fractions were determined using the fiber content test for three different FRC. Secondly, the random fiber distributed representative volume elements (RFDRVEs) were generated corresponding to these fiber volume fractions. Moreover, the RFDRVEs were used to predict the macro-mechanical properties and micro-damage modes of UD FRC. Ultimately, the standard mechanical tests and scanning electron microscopy (SEM) were applied to verify the accuracy of the prediction for the macro-mechanical properties and micro-damage modes of UD FRC. The results show that the proposed multiscale method is feasible for the verification of the multiscale prediction results based on RFDRVEs.

A complementary approach to quantify the basic GSI chart considering scale effect on rock structure

Geological strength index (GSI) has been widely used as an input parameter in predicting the strength and deformation properties of rock masses. This study derived a series of equations to satisfy the original GSI lines on the basic GSI chart. Two axes ranging from 0 to 100 were employed for surface conditions of the discontinuities and the structure of rock mass, which are independent of the input parameters. The derived equations can analyze GSI values ranging from 0 to 100 within ±5% error. The engineering dimensions (EDs) such as the slope height, tunnel width, and foundation width were used together with representative elementary volume (REV) in jointed rock mass to define scale factor (sf) from 0.2 to 1 in evaluating the rock mass structure including joint pattern. The transformation of GSI into a scale-dependent parameter based on engineering scale addresses a crucial requirement in various engineering applications. The improvements proposed in this study were applied to a real slope which was close to the time of failure. The results of stability assessments show that the new proposals have sufficient capability to define rock mass quality considering EDs.

Representative Sample Size for Estimating Saturated Hydraulic Conductivity via Machine Learning: A Proof‐Of‐Concept Study

AbstractMachine learning (ML) has been extensively applied in various disciplines. However, not much attention has been paid to data heterogeneity in databases and number of samples used to train ML models in hydrology. In this study, we addressed these issues and their impacts on the accuracy and reliability of ML models in the estimation of saturated hydraulic conductivity, Ks. We selected 17,990 soil samples from the USKSAT database and created random subsets N = 2,000, 4,000, 6,000, 8,000, 10,000, 12,000, 14,000, 16,000, and 17,990, 80% of which were used for training. The random subset selection was repeated 50 times. The extreme gradient boosting (XGBoost) algorithm was used to estimate Ks from other soil properties, such as bulk density, soil depth, texture, and organic content. For each subset, we conducted the learning curve analysis on the training and cross‐validation data sets. Results showed that for all training sample sizes the number of samples was not enough for the training and cross‐validation curves to reach a plateau. We also applied the concept of representative elementary volume by plotting the average coefficient of determination, R2, and root mean square log‐transformed error, RMSLE, against the training sample size. For the testing data set, as the number of training sample size increased from 1,600 to 14,392 the average R2 value increased from 0.74 to 0.90, while the average RMSLE value decreased from 1.08 to 0.69. Either the learning curve or representative sample size analysis is required to investigate whether the number of samples is enough or not.

The role of Voronoi catalytic porous foam in reactive flow for hydrogen production through steam methane reforming (SMR): A pore-scale investigation

Complex pore structures in catalysts can significantly impact flow, heat transfer, and ultimately, reaction efficiency. In steam methane reforming (SMR) for hydrogen production, replacing simple catalyst geometries with intricate, interconnected structures can enhance heat transfer and optimize the SMR process. Reactive flow in Voronoi catalytic foams (VCFs) with conjugate heat transfer is investigated using OpenFOAM for pore-scale simulations. The study examines the impact of porosity, pore density (PPI), PPI distribution (uniform vs. gradient), flow direction, inlet velocity, and temperature on hydrogen production rates within a selected representative elementary volume (REV). The results show that reducing the porosity of the simple foam from 0.8 to 0.6 has led to a 25% increase in the hydrogen production mass flow rate. Additionally, replacing the simple foam with a porosity of 0.6 with a gradient foam with the same porosity can improve the hydrogen production rate by 17%. Also, it is observed that the inlet velocity has a more significant effect on the hydrogen production rather than the inlet temperature, such that increasing the inlet velocity from 0.5 to 2 m/s results in a remarkable 75% increase in the hydrogen production rate.

Characterization of pore model and percolation simulation of bulk grain pile porous media

AbstractTo ensure the quality of grain storage, researchers have developed a variety of models for the morphological structure of bulk grain piles. However, traditional characterization methods suffer from issues such as inaccurate models, limited size ranges, and low precision. In this study, x‐ray computed tomography was employed for the first time to capture real three‐dimensional (3D) images, revealing the surface porosity distribution ranging from 30% to 38% along the slice direction and a fractal dimension primarily distributed between 1.45 and 1.47. Moreover, the box counting method was used to determine the representative elementary volume (REV) comprising 600 × 600 × 600 pixels, effectively characterizing pore structure using porosity as an index. Connectivity analysis of the REV was conducted by integrating the refined central axis method and the 3D watershed algorithm. Equivalent diameters of connected pores were mainly distributed between 0.5 and 3.5 mm, with an average pore diameter of 2.22 ± 0.02 mm, an average coordination number of 7.04 ± 0.07, and an average tortuosity of 1.58 ± 0.01. Based on the characteristic parameters of connected pores, an equivalent pore network model (EPNM) was reconstructed for numerical simulation of single‐phase percolation of bulk grain pile. In addition, the constructed experimental platform demonstrates that the constructed EPNM closely corresponds to the real pore structure of the seed body, accurately reflecting pore–throat size, connectivity, and morphological characteristics within the grain pile. Furthermore, this research model can be applied to the study of gas flow, heat transfer, and mass transfer within porous media.

Determining the characteristics of representative volume elements in severely deformed aluminum-matrix composite

The accurate evaluation of the effective mechanical properties of composites mainly depends on the characteristics of representative volume elements (RVEs). This paper mainly investigates the RVE size. Additionally, the effect of volume fraction of reinforcement, the edge effect, and RVE types on the critical size are discussed. First, the Al/Ni multilayered composites were processed by nine cycles of the cross-accumulative roll bonding (CARB) method. Then, one type of RVEs was created based on cross-sectional micrographs of composites to consider their inhomogeneities. Another type was generated by using the random sequential adsorption (RSA) procedure. Thereafter, the homogenized effective elastic properties of both types of microstructure-based RVEs and RSA-based RVEs were computed and compared as a function of the volume fraction of Ni and RVE size. The results showed that by increasing the Ni fragments, the RVEs indicated stiffer elastic behavior. By increasing the volume fraction of Ni from 0.2 Vf to 0.8 Vf, the Poisson ratio decreased by 7 % and the elastic modulus increased by 83 % for RSA-based RVE. Regarding the size of microstructure-based RVE of Al/Ni (0.8 Vf), from the largest size (size 1) with a length of 575 μm and a width of 575 μm to the smallest size (size 5) with a length of 287.5 μm and a width of 287.5 μm, the elastic modulus and the Poisson ratio showed 16 % and 0.8 % decrease, respectively.

Numerical simulation and experimental validation of ICVI-C/C reaction process by methane/propane gas mixture source

This study aimed to optimize the preparation of carbon/carbon (C/C) composites by developing and validating a computational model for three-dimensional (3D) transient densification through an isothermal chemical vapor-phase infiltration (ICVI) process using a methane/propane mixture. Simplified multistep parallel reaction kinetics were employed to simulate the pore evolution using a two-dimensional representative volume element model and a 3D stochastic fiber model. The permeability, flow modeling, and material transfer behaviors were calculated using the Ergun, Brinkman, and mixing diffusion equations. The density was calculated to be 1.294 g/cm3 after 50 h of deposition with specific flow rates and temperatures. The experimental densities were lower than those predicted with an increased propane flow, highlighting the complex reaction kinetics. The numerical simulation results exhibited strong agreement with the experimental results at 1328 K, achieving a correlation of up to 5.918. This study provides a robust theoretical and experimental basis for optimizing the structure and process control of C/C composites.

Generation of two‐level representative volume element model for uncertainty analysis of composite materials

Generation of two‐level representative volume element model for uncertainty analysis of composite materials

Simulation analysis of cryogenic mechanical properties of carbon fiber reinforced silicon-containing epoxy resin composite

The use of carbon fiber-reinforced resin matrix composites instead of metals to manufacture cryogenic propellant tanks for spacecrafts is a development trend in the world aerospace industry. Cryogenic mechanical properties of the composites should be investigated in detail due to that the ultra-low temperature environment may cause micro cracks in the composites, leading to propellant leakage. In the present study, cryogenic tensile properties of a carbon fiber reinforced silicon-containing epoxy resin aomposite are investigated using experimental and numerical simulation methods. A silicon-containing epoxy resin with excellent cryogenic mechanical properties is developed by introducing a synthesized organic silicon polymer epoxidized polysiloxane and Nano-SiO2 into bisphenol F type epoxy resin. The tensile strength and modulus of the silicon-containing epoxy resin at −180 °C are 202.63 MPa and 7.81 GPa, which are 16.71% and 3.03% higher than those of bisphenol F type epoxy resin. The tensile strength of the silicon-containing epoxy resin at −180 °C is increased by 107.7% compared to that at room temperature, and the modulus at −180 °C is nearly twice that at room temperature. The carbon fiber reinforced silicon-containing epoxy resin composite is prepared by vacuum injection molding. The finite element model for the representative volume element of the composite unidirectional plate is established. The random sequence expansion method is used to randomly distribute the carbon fibers and simulate the thermal residual stress, the elastic performance, and the damage of the composite at cryogenic environments. Through comparison, it is found that the simulation results are in good agreement with the experimental results. The simulation reliability for cryogenic mechanical properties of carbon fiber reinforced resin matrix composites is verified. It is expected to provide a reference for the analysis and evaluation of cryogenic mechanical properties of composite tanks.

Failure analysis of unidirectional CFRP composites with the coupled effects of initial fibre waviness and voids under longitudinal compression

This research delves into the failure mechanisms exhibited by unidirectional Carbon Fiber Reinforced Polymer (CFRP) composites under longitudinal compression, while considering the interplay of three types of manufacturing-induced defects: initial waviness of fibres, void volume fraction, and void size. The study employs 3D high-fidelity intact representative volume element (RVE) models, incorporating the initial waviness of fibres and voids based on Micro-CT imaging. A novel algorithm is proposed to generate more accurate 3D void shapes, departing from conventional circular or triangular approximations. The results highlight the substantial influence of the initial waviness angle on the reduction of predicted compressive stiffness and strength. The volume and size of voids play a significant role in determining damage initiation within the composites. The failure mechanisms of the composite under the coupled effects of initial waviness of fibres and voids are discussed, exhibiting reasonable agreement with experimental observations.

Numerical Relaxation Analysis of Carbon Fiber Reinforced Polymers

AbstractCarbon fiber reinforced polymers are widely used to manufacture aerospace deployable structures. These structures are folded in launch configuration and then deployed in space for operational activities. Since the stowage of deployable structures in folded configuration occurs for long time, the understanding of the viscoelastic properties of the material is essential to predict the structural behavior during both the deployment phase and the operational life. In this work, numerical relaxation analysis is performed on the representative volume element (RVE) of a carbon fiber reinforced polymer using a homogenization approach at the microscale. This aims to predict the effects of matrix viscoelasticity on the structural performance of a deployable structure.

Effect of gravity number on soil contamination during dynamic adsorption of heavy metal ions: A lattice Boltzmann study

Contamination of soils and aquifers as a result of heavy metal ions adsorption is an extremely negative environmental phenomenon associated with natural or industrial disasters. This paper presents the first systematic study of the dynamic adsorption of heavy metal ions in soils during water-air immiscible displacement induced by pressure drop and gravitational force. This study addresses three objectives. The first purpose is to determine a representative elementary volume to estimate the adsorbed amount of heavy metal ions during two-phase flow with density contrast. The second objective is to study the effect of different balances between viscous and gravitational forces, described by the gravity number, on the adsorbed amount at drainage and imbibition regimes. And the final task is to identify the effect of the pore space heterogeneity on the adsorbed amount for various gravity numbers and wetting conditions. As samples of study, we examine two-dimensional granular digital images characteristic of soils. The lattice Boltzmann method, verified on the problem of capillary-gravitational equilibrium of a meniscus, was used as a research tool. It has been established that the scale of 4–5 mm is sufficient to be representative for estimating the adsorbed amount of heavy metal ions. An increase in gravity number promotes the destabilization of the interfacial front both in the drainage and imbibition regimes and results in suppression of the adsorbed amount. The effect of gravity number on the adsorbed amount is stronger in the drainage mode compared to the imbibition regime. It has been found that pore space heterogeneity is a factor negatively affecting the adsorbed amount of heavy metal ions. The strength of the heterogeneity effect is independent of wetting conditions and gravity numbers.

Mechanical behaviour of 3D printed carbon fibre reinforced composite metastructure with various filling rates

This paper evaluated the influence of filling rate and printing direction on the mechanical properties of composite metastructure via experimental and numerical approaches. A representative volume element (RVE) and finite element method were adopted to estimate the tensile and flexural properties and verify the applicability of these methods in the 3D printing of composite metastructure. Results showed that apparent tensile and flexural properties drop with decreasing filling rates. The tensile and flexural strength reached 70.7 MPa and 131.1 MPa for solid specimens. The bending test for samples with different printing directions showed that the printing direction of the core has no noticeable effect on flexural strength, but the +45°/-45° sample exhibited the highest modulus. The numerical estimation showed similar trend compared to experimental results for both tensile and flexural properties. Such an attempt indicates the feasibility of designing a composite metastructure with an optimum weight-strength relationship.

Optimisation of process-induced residual stresses in composite laminates by different genetic algorithm and finite element simulation coupling methods

To address the residual stress induced during the cure of fibre reinforced thermoset polymer composites, two different approaches were suggested for coupling a non-dominated sorting genetic algorithm (NSGA-II) with finite element (FE) simulations based on a viscoelastic constitutive law. These two approaches were proposed with consideration of different ways of integrating NSGA-II and the FE model. In Approach A, NSGA-II was performed based on results from a series of simulations under various combinations of cure variables. Alternatively, Approach B employed NSGA-II to iteratively update and optimise the cure profile for subsequent simulations. Results indicated that both approaches achieved simultaneous reductions in cure time and macroscale residual stress, with Approach B showing further improvements due to the direct coupling between the NSGA-II and simulations. Specifically, the maximum residual stress and cure time optimised by Approach A were reduced by 5%–9% and 22%–50% respectively, while those obtained by Approach B were reduced by 7%–10% and 32%–49% respectively, compared to those based on the manufacturer recommended cure profile. The evolution of stress in composites based on optimised cure profiles from these two approaches was also elucidated. Additionally, microscale modelling further revealed a 3%–5% reduction in the average residual stress within a representative volume element (RVE) model was also shown, depending upon the approach adopted. Ultimately, by combining a NSGA-II and FE simulations, the optimisation of cure time and residual stress at the macroscale and cure time together with a reduction of microscale stress could be realised.

Integrated model for simulating Coble creep deformation and void nucleation/growth in polycrystalline solids - Part I: Theoretical framework

This study proposes an integrated model for simulating Coble creep deformation and void nucleation/growth in a 3D polycrystalline solid. Part I of the paper provides a theoretical framework for the proposed model. A representative volume element approach is employed to predict the effects of 3D polycrystalline morphology. The model comprises two distinct but interconnected stages: deformation and void nucleation/growth. The deformation stage of the proposed model comprises two sub-models: grain boundary (GB) migration and GB diffusion. The void nucleation/growth stage is composed of three consecutive calculations: void nucleation, void growth, and postprocessing. The process simulated in the void nucleation/growth stage is driven by relative GB velocity of the respective GBFs and diffusional fluxes between adjacent GBFs, which are provided from the deformation stage. The void nucleation rate is quantified using the relative GB velocity, and the initial void size is determined based on the stability condition for void existence derived from Helmholtz free energy. The void growth rate is evaluated by the atomic diffusion on the GBF and the surface of each void.