Volume Element Research Articles

Stochastic mesoscale characterization of ablative materials for atmospheric entry

This study addresses the estimation of material properties at a mesoscopic level using the PuMA software from an uncertainty quantification perspective. Stochastic simulation with PuMA is primarily related to the random distribution of fibers, which is an intrinsic source of uncertainty. Additionally, the selection of certain physical parameters, such as the fiber's thermal conductivity, introduces further uncertainties. The first contribution of this study is to propose a low-cost surrogate-based methodology with an unequal allocation scheme, applied for the first time to the stochastic mesoscale characterization of ablative materials. The second contribution is a study on uncertainty propagation and sensitivity analysis of material properties, providing a systematic assessment of the choice of voxel resolution for both the fibers and the domain. Specifically, the convergence of quantities of interest can be monitored, thus identifying the minimal reference elementary volume.

Strength response investigation of defective C/C composite materials based on the Weibull model

In this study, the issue of random fiber strength resulting from initial fiber defects and matrix pore defects in the strength response of C/C composite materials is addressed. A method for generating random numbers following the Weibull distribution is proposed and an improved random sequence adsorption (RSA) algorithm is employed to describe pore defects in the matrix, ultimately leading to the development of a representative volume element (RVE) model for C/C composite materials. The influence of fiber strength distribution and pore defects on the mechanical properties of unidirectional C/C (UD-C/C) composite materials is analyzed. This study offers a new approach to investigate the mechanical behavior of C/C composite materials, taking into account both fiber initial defects and pore defects.

Design methodology of functionally graded cellular materials: Manipulating design parameters of triply periodic minimal surfaces through three-dimensional density distributions

Functionally Graded Cellular Materials (FGCM) with variable volume fractions have demonstrated significant advantages, including weight reduction, improved stiffness, and enhanced load distribution, when compared to uniform density counterparts. Their design is often characterized by the application of a density distribution to locally modify Representative Volume Elements (RVEs). Current studies have explored the application of Triply Periodic Minimal Surfaces (TPMS) topologies, given their capability to create seamless and interconnected structures, thus avoiding stress concentration issues commonly encountered in traditional lattice configurations. Consequently, this paper introduces a design methodology tailored to TPMS-based FGCM allowing for independent or simultaneous adjustments of RVE thickness and size. Models for predicting relative density as a function of the RVE design parameters of Primitive and Gyroid topologies are presented and discussed. These models are employed to adapt the topologies to three-dimensional density distributions. The proposed method is implemented as a set of design tools and is illustrated for the studied TPMS topologies.

A periodic micromechanical model for the rate- and temperature-dependent behavior of unidirectional carbon fiber-reinforced PVDF

The rate- and temperature-dependent mechanical behavior of unidirectional carbon fiber-reinforced polyvinylidene fluoride (PVDF) is investigated through uniaxial tension and compression experiments under various off-axis loading conditions. To improve the understanding of the behavior of the composite, a 3D micromechanical model is developed. Microscopic analyses are used to characterize the geometrical properties of the UD composite at the fiber length-scale. These properties are used to construct a periodic 3D representative volume element (RVE). In combination with periodic boundary conditions, uniaxial macroscopic deformation (in any possible direction) is applied to the RVE to accurately and efficiently model off-axis loading. The rate- and temperature-dependent behavior of the PVDF matrix is accurately described using an elasto-viscoplastic constitutive model. The finite element simulations of uniaxial tension and compression tests are compared to the experimental data and the micromechanical response is analyzed. The micromechanical model accurately describes the rate-dependent macroscopic behavior of unidirectional carbon fiber-reinforced PVDF for various off-axis loading directions at different temperatures. Analysis of the local matrix response in the RVE reveals the influence of the matrix on the macroscopic behavior of the composite.

Experimental and numerical study of the thermomechanical properties of flexible self-reinforced polyimide composite membrane

Polyimide membranes are favored in the aerospace field for their excellent comprehensive properties, but new application requirements demand higher strength, modulus and thermal expansion properties. Here, self-reinforced polyimide composite membranes (SRPICM) with varying fiber tow arrangement densities were fabricated by unidirectional reinforcement of polyimide fiber tows to enhance the thermomechanical properties of the membranes while maintaining the characteristics of low thickness and flexibility. A micro-scale representative volume element model with interface, and a macro-scale model containing cracks were developed based on the membranes' morphology to investigate the tensile and thermal expansion behavior of SRPICM. Experimental and numerical analyses demonstrated that fiber tows significantly improved the longitudinal tensile properties of SRPICM, with maximum increases in modulus and strength to 34.02 GPa and 1.26 GPa, respectively, over 13 times those of pure PI membranes. Further, the test results, combined with the two-scale finite element model revealed the evolution of longitudinal and transverse tensile deformation and thermal expansion behavior of SRPICM. The validity of the two-scale model was confirmed by experimental results, attributed to the practical consideration of interfacial bonding, prefabricated cracks and thermal residual stress effects during initial modeling. Notably, SRPICM with 10 fiber tows/20 mm arrangement density exhibited excellent longitudinal tensile properties (modulus and strength of 14.01 GPa and 470.89 MPa, respectively) and a longitudinal thermal expansion close to zero (0.03 μm/m°C), making it an ideal material for aerospace applications.

Meso-scale finite element modelling of biaxial non-crimp-fabric composites under compression

Non-crimp-fabric (NCF) reinforced composites have been receiving attention in the composite market due to their cost-effectiveness and excellent mechanical performance. However, compared to traditional unidirectional laminates (UD), NCF composites have different mechanical behaviours due to their heterogeneous internal structures. The influence of the internal structure of biaxial NCF composites on compressive behaviour was therefore investigated in this study. The representative volume element (RVE) method was adopted to establish finite element (FE) models for biaxial NCF composites at the micro- and meso‑scale. Micro-scale models developed at fibre/matrix level could provide homogenised compressive properties of 0° and 90° tows, while meso‑scale repeated unit cell (RUC) models developed at tow/resin-rich area level could predict homogenised compressive behaviours of biaxial NCF composites. Finally, the homogenised meso‑RUC results were employed in the macro-scale FE model to validate the test result. The novelty lies in developing RUC models to comprehensively investigate key parameters at the micro- and meso‑scale controlling the overall compressive strength, including matrix strength, layup sequence, tow waviness, tow placement, interfacial strength, and out-of-plane shear stress. Another novelty is to explain the differences in compressive strengths between the RUC model and the test result. These models form a multiscale framework for biaxial NCF composites, which could contribute to an analysis tool for NCF material design. The FE results by this multiscale framework indicated that the misaligned resin-rich areas could contribute to the higher compressive strength. Increasing tow waviness could change the failure mode from fibre crushing to fibre kinking failure, while matrix properties, interfacial strength, and fibre waviness were the key factors influencing compressive strength. The conclusion can further guide the development of NCF composites with optimal compressive strength.

Permeability of porous membrane polymers modified by supercritical carbon dioxide

An approach to predict the gas permeability of membrane polymers after supercritical CO2 treatment is proposed. The approach is based on the connection of the temperatures of secondary relaxation transitions with the effective sizes of mobile free volume elements in the polymers. The correlation between permeability of nitrogen and effective sizes of mobile holes for a set of polymers is established. The effect of supercritical CO2 on the nitrogen permeability of polycarbonate, polysulfone, polyvinylbutyral is analyzed by FTIR spectroscopy of low-molecular weight conformationally-inhomogeneous compounds introduced in the polymers. Membranes were exposed at 40 MPa and 333 K for 4 h through static treatment and dynamic treatment separately. For polyvinylbutyral, the nitrogen permeability did not change after supercritical CO2 modification while for polysulphone, the effective volume of mobile holes increased, but the nitrogen permeability decreased. For polycarbonate after supercritical CO2, the effective volume of mobile holes and the nitrogen permeability increased.

Investigation on thermal conductivities of plain-woven carbon/phenolic and silica/phenolic composites at high temperature: Theoretical prediction and experiment

Phenolic resin-based ablation materials have found widespread applications in the aerospace industry. The prediction of their thermal conductivity is of paramount importance for the optimization and evaluation for thermal protection systems. However, there is rarely reported thermal conductivity performance of phenolic composites during ablation processes. Therefore, this investigation theoretically predicts the dynamic response of thermal conductivity at high temperatures for plain-woven carbon/phenolic and high silica/phenolic composites. By combining the progressive cubic ablation model with existing composite material property formulas, a multiscale prediction model for effective thermal conductivity is developed. The thermal performance of the resin matrix, reinforcing fibers, yarns, and overall fabric composites is calculated. Additionally, mesoscale representative volume elements are implemented to investigate the overall heat transfer characteristics of carbon/phenolic and high-silica/phenolic composites, including temperature and heat flux distributions. Moreover, both composites thermal conductivities are measured in the range from 298 K to 473 K. The proposed prediction model demonstrates good reliability, with average deviations of 3.76 % and 7.36 % compared to finite element analysis results and experimental data, respectively.

Solute transport in unsaturated porous media with spatially correlated disorder

Solute transport in unsaturated porous media is of interest in many engineering and environmental applications. The interplay between small-scale, local forces and the porous microstructure exerts a strong control on the transport of fluids and solutes at the larger, macroscopic scales. Heterogeneity in pore geometry is intrinsic to natural materials across a large range of scales. This multiscale nature, and the intricate links between two-phase flow and solute transport, remain far from well understood, by and large. Here, we use high-resolution direct simulation to quantify solute mixing and dispersion behavior within correlated porous media during drainage under an unfavorable viscosity ratio. Through analysis of flow and transport at multiple realizations, we find that increasing spatial correlations in pore sizes increase the size of the required Representative Elementary Volume (REV). We show that increasing the correlation length enhances solute dispersivity through its impact on the spatial distribution of low-velocity (diffusion-dominated) and high-velocity (advection-dominated) regions. Fluid saturation is shown to directly affect diffusive mass flux among high- and low-velocity zones. Another indirect effect of correlated heterogeneity on solute transport is through its control of the drainage patterns via repeated alteration in the connectivity of flowing pathways. Our findings improve quantitative understanding of solute mixing and dispersion under two-phase conditions, highly relevant to some of our most urgent environmental problems.

A statistical volume element-based procedure for the prediction of the mechanical and electrical response of an epoxy-PZT self-sensing layer for application in composite laminates

Structural Health Monitoring (SHM) techniques are being developed to continuously oversee defects in composite structures. Within this context, research is focusing on the development of new types of sensors with high sensitivity and proper integration in the laminate.In this work, the mechanical and electrical properties of a recently developed piezoelectric composite material made of a Lead Zirconate Titanate (PZT) powder embedded in an epoxy matrix are evaluated with finite element simulations of plane strain Statistical Volume Elements (SVEs). The homogenized properties are then implemented in a second finite element model of a composite specimen with the embedded self-sensing material and loaded in compression. The electrical sensitivity is evaluated as a function of the distance between the signal electrodes.The results show that the finite element models with the homogenized properties have decreasing sensitivity with increasing electrodes distance, in agreement with the experimental results from another work, in which Glass Fiber Reinforced Polymer (GFRP) laminates with the embedded piezoelectric composite are loaded in compression and tested for output signal.

Spatiotemporally nonlocal homogenization method for viscoelastic porous metamaterial structures

The underlying size-dependent mechanism of viscoelastic porous metamaterial structures is still unclear, and the solution to their response using the high-fidelity numerical method is time-consuming, even prohibitive. This paper explores how the size-dependent effect of metamaterial structures emerges from the underlying nonlocal interactions in metamaterial microstructures, and then develops an accurate but efficient homogenization method for analyzing their size-dependent and time-dependent mechanical behaviors of viscoelastic porous metamaterial structures. By accounting for the nonlocal interaction between different representative volume elements and the history-dependent effect, a spatiotemporally nonlocal discrete element model is developed to analyze the mechanical behavior of viscoelastic porous metamaterial structures. With the help of the spatiotemporally nonlocal discrete element model, a spatiotemporally nonlocal homogenization method is proposed to accurately yet efficiently assess the size-dependent mechanical behavior of the porous metamaterial structure. The remarkable potential of the spatiotemporally nonlocal homogenization method is illustrated by simulating the stress relaxation of a viscoelastic porous metamaterial structure under axial strain. Results indicate that the size-dependent phenomenon can be significant, and the spatiotemporally nonlocal homogenization model can efficiently capture the size-dependent relaxation stress evaluated by the high-fidelity finite element model without loss of accuracy.

Study on material behaviours of additively manufactured high-impact polystyrene using artificial neural networks

AbstractFused Filament Fabrication (FFF), a process parameters-dependent manufacturing method, currently dominates the additive manufacturing (AM) sector because of its prominent ability to produce parts with intricate profiles, customise products, and minimise waste. Though the effects of FFF process parameters were investigated experimentally, recent research highlighted the importance of developing numerical modelling and computational methods on optimising the FFF printing process and FFF-printed materials. This study aims to investigate the tensile strength (TS) of FFF-printed high-impact polystyrene (HIPS) via devising a systematic testing and analysis framework, which combines experimental testing, representative volume element (RVE)-finite element method (FEM), rule of mixture (ROM), and artificial neural networks (ANN). HIPS samples are fabricated using FFF considering the variations of infill density, layer thickness, nozzle temperature, raster angle, and build orientation, and tested with standard tensile testing. The rule of mixtures (ROM) and its modified version (MROM) are employed to calculate the TS of longitudinally and transversely built samples at various infill densities, respectively, while an ANN model is constructed to investigate the effect of material anisotropy precisely. The optimal ANN architecture is built with five hidden layers with the number of neurons in each layer as 44, 82, 169, 362, and 50. Although both MROM and ANN perform well on the validation set, ANN exhibits superior accuracy with only a maximum error of 0.13% for training set and 11% for validation set. The combination of the RVE-FEM, MROM, and ANN approaches can significantly improve the FFF printing process of polymers for optimisation.

Understanding plasticity in multiphase quenching & partitioning steels: Insights from crystal plasticity with stress state-dependent martensitic transformation

This study develops a novel crystal plasticity (CP) model incorporating deformation-induced martensitic transformation (DIMT) and transformation-induced plasticity (TRIP) effect to predict the complex interplay between microstructural evolution and mechanical behavior in a third-generation advanced high-strength steel QP980. This model introduces phenomenological theory of martensite crystallography (PTMC) based TRIP theory and DIMT kinetics grounded on nucleation-controlled phenomenon. Notably, the DIMT model is improved by utilizing a geometric approach for calculating shear band intersections. A virtual multiphase representative volume element (RVE) based on the Voronoi tessellation is generated for the QP980 steel, which comprises ferrite, martensite, and retained austenite (RA). The study highlights how phase transformation affects mechanical properties, notably the strengthening from transformed martensite and the mechanical alterations in RA due to the TRIP effect. The DIMT kinetics dependent on stress states such as uniaxial tension (UT), uniaxial compression (UC), plane strain tension (PST), and equi-biaxial tension (EBT) are analyzed using the developed model. The role of microstructural surroundings on martensitic transformation is also examined. Furthermore, analysis under biaxial loading angles using the model reveals an asymmetric yield surface, with more pronounced changes in yield stress in the tensile region due to accelerated transformation behaviors, as opposed to the more gradual transformations in the compressive region. This study provides valuable insights into the deformation mechanisms of the third-generation advanced high-strength steels including relationship between plastic anisotropy, transformation kinetics, and microstructural evolution.

Mechanical Properties and Constitutive Model for Artificially Structured Soils under Undrained Conditions

Triaxial tests are performed for remolded, artificially isotropic, and anisotropic structured samples under undrained conditions at confining pressures of 25, 100, and 200 kPa. Based on these test results, a binary-medium constitutive model is formulated based on homogenization theory and a breakage mechanism to describe the behaviors of structured soils. In this model, the binary-medium material is idealized as a representative volume element (RVE) composed of bonded elements, whose mechanical behaviors are expressed by the linearly elastic model, and frictional elements, whose mechanical behaviors are described by the double-yield surfaces constitutive model. The parameters of the bonded and frictional elements are determined from the test results of structured and remolded samples, respectively. The expressions for the breakage ratio and local stress coefficient matrix are introduced, and their parameters are provided. The computed results are compared with the test results, demonstrating that the model can reflect the main deformation features of structured soil relatively well, including the influence of anisotropy, gradual damage to particle bonding, and pore development.

Study on the Properties and Fatigue Characteristics of Glass Fiber Composites Due to Porosity

A study was conducted on the changes in mechanical properties and fatigue failure characteristics due to voids, one of the fabrication defects in composite materials. This study was primarily based on glass fiber fabrics applied to wind turbine blades and their material properties were predicted through micro and meso modeling of composite materials by simulating random defects including voids. As the wind turbine blades become larger, various defects develop. The fundamental changes in the materials’ properties due to voids were predicted through homogenization methods and Representative Volume Element (RVE), and the failure properties were obtained through progressive failure analysis by applying virtual coupons according to ASTM D3090 and ASTM D6641. The progressive failure was identified using the Matzenmiller–Lubliner–Taylor (MLT) failure condition, and the fatigue failure characteristics were assessed through the Tsai–Hill 3D load.

Multiscale modeling and thermal conductivity evaluation of nano-reinforced composite materials with pore defect

The performance of resin-based composite materials often exhibits diversity due to the designability of various components. Thermal conductivity, an important thermal parameter of the composite, plays a significant role in thermal-chemical reactions, thermal stress analysis, temperature conduction, etc. However, it is relatively difficult to experimentally explore the thermal conduction mechanism of hybrid composite materials, mainly due to the relatively difficult control of various components. Therefore, this paper proposes a sequentially coupled cross-scale numerical method to characterize the thermal conductivity of nano-reinforced composite materials with pores by a multiscale periodic Representative Volume Element model generated by an improved Random Sequential Absorption algorithm. Firstly, periodic temperature boundary conditions are described, and the thermal conductivity performances of nano-reinforced matrix and composite with pores are investigated based on the finite element homogenization theory. Then, the proposed modes are validated and grid sensitivity analysis is conducted, indicating that the optimal grid sizes for the RVE models are 1.9 nm for the nano-reinforced matrix and 0.14 μm for the composite with pores based on a comprehensive comparison of four pore characterization methods, respectively. Furthermore, the study explored the effect of multiple parameters including nanoparticle content, pore content, and pore shape on thermal conductivity. Numerical findings reveal that the thermal conductivity of the nanocomposite matrix exhibits a linear increase with higher particle content. Specifically, compared to 0 % particle content, the thermal conductivity rises by 141.92 % at 12 % particle content. While the composite material's transverse thermal conductivity is sensitive to porosity content, it is less influenced by pore shape. The method proposed in this paper provides an effective approach for studying the thermal conduction of nano-reinforced composite materials with pores, and the research findings also offer theoretical guidance for process engineers.

Thermal modeling of porous medium integrated in PCM and its application in passive thermal management of electric vehicle battery pack

The integration of a composite of porous medium with phase change material (PCM) offers significant advantages in thermal management systems, enhancing heat transfer efficiency and addressing various thermal regulation challenges. This approach utilizes the PCM's latent heat absorption and the enhanced thermal conductivity provided by the porous medium, resulting in optimized system performance. Its applicability spans across electronics cooling and building insulation systems. However, predicting the thermal behavior of this composite material is challenging, necessitating computational tools to anticipate its response under different conditions and evaluate its influence on cooling strategies. The objective of this study is to create a computational tool specifically tailored to evaluate constitutive parameters of this composite material, thereby providing a comprehensive description of its thermal behavior. To achieve this goal, the multiscale homogenization principle is employed to assess the composite's effective thermophysical material properties using the representative volume element approach. The repeating unit cell of the aluminum lattice is incorporated into the PCM to define a representative volume element. The finite element method (FEM) is utilized to solve the three-dimensional homogenization problem, yielding an orthotropic effective thermal conductivity due to the inherent symmetry of the repeating material cell. Moreover, the study leverages the apparent heat capacity method to effectively manage the phase transitions within the PCM domain, utilizing smooth and temperature-dependent functions to accurately describe the thermophysical properties of the PCM. Integrating the composite into battery pack thermal management, this study thoroughly examines thermal dynamics by comparing outcomes with and without PCM integration. The transient thermal problem is accurately tackled using the FEM, employing the evaluated effective constitutive parameters of the homogenized composite to minimize computational effort. The results indicate a notable decline in the highest temperatures of the battery pack, leading to a reduction of about 14 °C at the specific moment when the phase change material fully transitions into its liquid form. The obtained results emphasize the effectiveness and practical feasibility of the proposed thermal management strategy. The modeling approach presented provides a robust tool with significant efficiency in reducing computational time for analyzing the thermal behavior of large models, as the utilization of the homogenization technique notably decreases the computational time.

Dual-phase polycrystalline crystal plasticity model revealing the relationship between microstructural characteristics and mechanical properties in additively manufactured maraging steel

To elucidate the relationship between microstructural characteristics and mechanical properties in additively manufactured (AM) maraging steel, this study introduces a computational approach that addresses two fundamental challenges. Firstly, it addresses the creation of representative volume elements (RVEs) that mimic the observed microstructural complexities, such as meltpool boundaries, prior austenite grains, packets and blocks of lath martensite. This is accomplished through the application of Potts Monte-Carlo methods and grain segmentation techniques in accordance with the Kurdjumov–Sachs orientation relationship. Secondly, this study develops a comprehensive crystal plasticity (CP) model encompassing both bcc and fcc plasticity. Inspired by atomistic and discrete dislocation dynamics studies, the proposed CP model incorporates characteristics intrinsic to bcc plasticity, including non-Schmid effects, dislocation and precipitate strengthening, and Hall–Petch type strengthening of elongated martensitic blocks. Utilizing the created RVEs and the proposed CP framework, finite element simulations are conducted based on an update-Lagrangian formulation. The purpose of this study is to investigate the deformation behavior, texture evolution, tension–compression asymmetry, and evolution in dislocation density in RVEs representative of as-built and heat-treated samples of maraging steel. This computational approach and its findings deepen our understanding of the intricate interplay between microstructural characteristics and mechanical properties in maraging steel and also provide valuable guidelines for refining its additive manufacturing and heat treatment processes.

CNN-based prediction of microstructure-derived random property fields of composite materials

The simulation of random spatial variation in the mechanical properties of composite materials using random fields derived from their microstructure can be computationally demanding, since it often requires numerical homogenization of a large number of stochastic volume elements (SVEs). These SVEs are usually extracted from an initial image of the composite microstructure by using a moving window technique and their homogenized properties constitute the discrete data points of the random field at the centroid of each SVE. By replacing the expensive and highly repetitive homogenization procedure with a convolutional neural network (CNN), it is possible to perform nearly instant computations of random property fields. In this work, a CNN is proposed, that takes as input an SVE image and returns its apparent mechanical properties, and can therefore be applied along with the moving window technique. Training is performed on randomly generated SVEs with varying volume fractions and inclusion positions, which are representative of the SVEs obtained during processing of the initial large composite image. It is shown that the proposed CNN can accurately predict the mechanical properties of SVEs and it is subsequently applied for the prediction of random property fields derived from computer simulated and real microstructure images. Results show that, with the proposed methodology, it is possible to make accurate predictions of random fields within a few seconds, a procedure which could potentially require hours of computation time with the finite element based approach.

A binary-medium-based constitutive model for rocks under cyclic loading

The present study extends the existing three-scale constitutive model to investigate the mechanical response of mudstone under cyclic loading conditions. The research framework encompasses macro, meso, and micro scales, with the mudstone sample treated as a macro Representative Volume Element (RVE) at the macroscale, bonded and frictional elements with distinct mesostructures at the mesoscale, and three-phase composites with varying micro-component contents at the microscale. The transitions at micro, meso, and macro scales are realized through various homogenization methods and the refined binary medium framework.To enhance the model’s predictive capabilities under cyclic loading, isotropic and kinematic hardening effects are introduced to capture the elastoplastic behavior of the frictional elements. To further enhance the model’s numerical stability and convergence, the fixed-point iteration method is introduced to leverage the relationships among macroscopic strain, and the strains of the bonded and frictional elements within the binary-medium framework. Model verification against experimental data enables the prediction of stress and deformation patterns in mudstone samples subjected to cyclic loading, with a notable reduction in model parameters. The model’s enhanced capabilities in capturing material behavior and numerical stability make it a valuable tool for analyzing the response of mudstone structures to cyclic loading scenarios.