3D Representative Volume Element Research Articles

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.

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.

A robust lattice Boltzmann scheme for high-throughput predicting effective thermal conductivity of reinforced composites

Accurately predicting effective thermal conductivity is of great importance for the design and performance evaluation of emerging composites. In this paper, an efficient and implementation-friendly lattice Boltzmann (LB) scheme for predicting the effective thermal conductivity of 3D complex structures is proposed. The key innovation is that the optimum convergence parameter of the 3D thermal LB method is found, which enables the LB equation to converge to steady heat conduction equation with the fastest speed and without losing any accuracy. To deal with the thermal contact resistance between different components, an interface treatment scheme is derived. In comparison with the existing schemes, the present scheme enjoys several hundred times higher computational efficiency. By virtue of this LB scheme, the effective thermal conductivity of the reinforced composites with different dimensional fillers are systematically calculated, and a comprehensive machine learning model is developed. This work provides a powerful numerical tool for high-throughput simulations of the 3D representative volume elements with high thermal conductivity ratios and large grid numbers. It may facilitate the application of data-driven techniques in study of the thermal transport properties of emerging composite materials and structures.

Evaluation of strain-sensitive behavior in elastomeric conductive nanocomposites containing carbon nanotubes-a finite element-percolation model approach

A finite element (FE)-percolation model approach is developed to predict the strain-sensitive response of the three-dimensional (3D) representative volume element (RVE) of carbon nanotube (CNT)-elastomeric nanocomposite. In the simulation model, CNTs are modeled as solid, impenetrable cylinders inside a cubic insulating matrix. FE simulation is performed to evaluate the structural response of the RVE under applied strain. The FE model updates the locations of the CNTs in the deformed RVE. The paths are found using a suitable 3D resistance network associated with different percolation paths involved in the critical distance criterion. The percolation model utilizes the paths found to identify the electrical circuit for predicting tunneling conductivity. The simulating algorithm is used to study the influence of tunneling barrier height, nanotube volume fraction, and geometrical aspects. The lowest critical distance criterion is achieved for higher volume fractions and the most heightened sensitivity is obtained for lower CNT aspect ratios.

Thermal expansion behavior and analysis of Al/AlN interpenetrating phase composites with different preform porosity

In this work, the coefficient of thermal expansion (CTE) of Al/AlN interpenetrating phase composites (IPCs) has been measured based on the length change from room temperature (RT) to 200 °C. 3D representative volume elements (RVEs) are created to model the microstructures of Al/AlN IPCs and the finite element models generated from RVEs are used to study thermal expansion behavior. CTE was predicted utilizing the finite element method (FEM) and thermo-elastic models of Kerner, Turner and Schapery, after which the results were compared with the experimental values. According to experimental results, a notable reduction in the CTE of IPCs is observed as preform porosity decreases. This shows that an AlN preform can effectively enhance dimensional stability. A comparative analysis of extant literature indicates that IPCs may attain a lower CTE compared to particle-reinforced composites. Experimental data align closely with analytical models. The FE simulation results demonstrate better consistency with experimental data only under conditions of high preform porosity, since residual thermal stresses and plastic deformation were not considered.

Incorporation of compaction effects in the automated generation of 3D woven composites representative volume elements by geometrical modelling

Advanced 3D woven composites have become an enabling technology in many industrial applications due to their proven benefits, particularly the improvement of the out-of-plane mechanical behavior with respect to other reinforcement schemes. The latter property has been shown to be strongly affected by the effects of compaction during manufacturing. The present study proposes an automated framework, based on heuristic procedures, for the generation of representative volume elements (RVEs) of 3D woven composites, allowing to include global and local geometrical features induced by transverse compaction, such as overall thickness reduction, changes in yarn cross-sections and consistent global/local fiber fractions. The methodology is illustrated for three types of reinforcement, namely a plain weave, an angular through-thickness interlock and a 3D orthogonal RVE. The resulting geometries generated by the proposed method compare favourably with typical observations from the literature in a quantitative manner. Finally, the proposed framework is integrated with a previously developed meshing strategy to allow damage studies for a selected architecture (plain weave) under torsional loading, presenting a complete computational chain by building cohesive zone finite element models from compacted RVEs. The torque-angle response curves obtained after the damage simulations show a decrease in stiffness and an increase of damage levels with compaction, which is in line with the expectations.

Multiscale homogenization of aluminum honeycomb structures: Thermal analysis with orthotropic representative volume element and finite element method

This study develops a thermal homogenization model for an aluminum honeycomb panel using the representative volume element (RVE) concept, considering the orthotropic nature of the structure. The RVE thermal homogenization method is a numerical approach for analyzing heterogeneous materials. It employs a constitutive model based on RVE performance to represent thermal behavior. Effective parameters are determined through averaging techniques, and the finite element method solves the thermal problem, accounting for structure topology and material behavior. The resulting heat conduction problem is solved using the finite element method (FEM) to evaluate the effective thermal characteristics. A 3D RVE is generated based on the honeycomb panel's geometry, evaluating thermal conductivity tensor and describing the medium's thermal performance. Numerical tests validate the model by comparing it with the real honeycomb structure under sinusoidal heat flux. Results show good correlation, with maximum temperatures of 1101.9 °C in the real structure and 1096.4 °C in the medium. The homogeneous medium is further used to investigate thermal performance under convective conditions with varying panel thicknesses, achieving over 77 °C temperature reduction with the thickest panel. Natural vibration behavior is considered, demonstrating strong correlation between modal responses and natural frequencies. This modeling approach efficiently analyzes thermal behavior in large honeycomb structures, reducing computational time significantly.

Global and Local Deformation Analysis of Mg-SiC Nanocomposites: Digital Image Correlation (DIC) and Representative Volume Element (RVE) Techniques

Improving the ductile deformation behavior of Mg-SiC nanocomposites without compromising strength is critical to enhancing their mechanical properties. Mg-SiC nanocomposites are produced through mechanical milling, cold isostatic pressing, sintering, and hot extrusion processes. This study investigates the uniaxial stress–strain response and deformation behavior of the Mg-SiC nanocomposite compared to pure Mg samples with and without the milling process. The deformation behavior was investigated by two-dimensional (2D) digital image correlation (DIC) at two macroscopic and microscopic scales, employing light micrographs and in situ loading samples, respectively, in the scanning electron microscope. Compared to the pure Mg samples, the mechanical test results demonstrated a significant improvement in strength (80 MPa) and fracture strain (23.5%) of the Mg-SiC nanocomposite. The three-dimensional (3D) representative volume element (RVE) model revealed the particle dispersion effect on the mechanical properties of the nanocomposite. The RVE results demonstrate ductile deformation behavior in the sample with homogenous dispersion of SiC particles compared with the heterogeneous dispersion of SiC particles in Mg-SiC nanocomposite. The results demonstrated a good agreement between DIC and RVE predictions for Mg-SiC nanocomposites across macro- and microscales.

Micromechanical characterization of Carbon/PEEK thermoplastic composite material in-situ consolidated by automated fiber placement: Stiffness prediction

Despite manufacturing challenges, Automated Fiber Placement (AFP) offers a viable alternative to conventional manufacturing methods, allowing for time and cost savings. Creating a Representative Volume Element (RVE) that realistically represents long-fiber-reinforced composites with high fiber volume fraction is a challenging task in modeling their response. The present research aims to predict effective stiffness properties of in-situ-consolidated Carbon/PEEK thermoplastic composite material by considering the effect of fiber volume fraction, void content, degree of crystallinity, and interlaminar resin pocket resulting from AFP in-situ consolidation manufacturing process. In this regard, two sets of samples were manufactured by AFP in-situ consolidation and autoclave re-consolidation methods. Both of them were evaluated by micrographic study and thermoanalytical Differential Scanning Calorimetry (DSC) technique to obtain inputs required for micromechanical analysis. The 2D RVEs on a micro-scale are developed to predict the transverse elastic modulus, out-of-plane Poisson's ratio and out-of-plane shear modulus of the composite material by applying Periodic Boundary Conditions (PBCs) and using Asymptotic Homogenization Theory (AHT). Results show that AFP in-situ consolidation may lead the transverse elastic and out-of-plane shear moduli of Carbon/PEEK thermoplastic composite material to be reduced by about 10 % and 20 %, respectively, compared to autoclave re-consolidation whereas the out-of-plane Poisson's ratio remains unchanged. The findings of the present work confirm that the mechanical performance of Carbon/PEEK thermoplastic composite material could be remarkably influenced by AFP in-situ consolidation manufacturing process, particularly in the transverse direction, which must be taken into account in finite element modeling, analyses, and design of AFP-manufactured composite laminates and structures.

Automatic generation of 3D micromechanical finite element model with periodic boundary conditions to predict elastic properties of bamboo fibre-reinforced composites

This study presents an automatic algorithm to generate a three-dimensional (3D) micromechanical finite element (FE) model to predict elastic behaviours of biocomposites reinforced with unidirectional (UD) continuous natural fibres such as bamboo fibres. The developed algorithm constructs a virtual FE framework by generating stochastic Representative Volume Elements (RVEs) of fibre-reinforced composites incorporating random fibre arrangement and random assignment of fibre radii. It also applies various loading scenarios and periodic boundary conditions to simulate elastic behaviours accurately. The algorithm generates 3D periodic RVEs by introducing boundary and corner fibres. All the 3D RVE models, representing different fibre-reinforced composites, various loading cases, and periodic boundary conditions, are automatically created using Python scripting with the Abaqus FE solver. The accuracy of the algorithm and virtual FE test model is validated through comparisons with analytical models and experimental results. The effects of different types of fibre radius assignment, fibre volume fraction, and fibre periodicity on the prediction of effective elastic properties are investigated. The study also establishes correlations between all elastic constants of bamboo fibre-reinforced composites and the fibre volume fraction.

A material–structure-wave integrated hydro-viscoelastic model for floating composite structure with generalized boundary

A floating viscoelastic composite structure with generalized elastic constraints, in which the material–structure-wave interaction induces energy dissipation, is analyzed with a novel cross-scale integrated hydro-viscoelastic model. A double-level three-dimensional (3D) representative volume element model coupling mesoscale reinforced particles to a macroscale composite structure is established to obtain the structure's viscoelastic dynamic equation. Therefore, a hydro-viscoelasticity analytical model for floating composite structures with arbitrary elastic constraints under wave action is developed in the context of potential flow theory. In the process of solving the velocity potential, the dispersion equation of the water covered by the composite structure is derived. The hydrodynamic and mechanical behaviors of the floating composite structure, including the reflection coefficient, transmission coefficient, dissipation coefficient, deflection, shear force, and bending moment, are comprehensively calculated, which depend on the cross-scale integrated effects of wave action, structural features, material characteristics, and constraint combinations. This material–structure-wave integrated model would be useful to elucidate the hydro-viscoelastic dissipation mechanism of marine structures.

A macroscopic viscoelastic viscoplastic constitutive model for porous polymers under multiaxial loading conditions

A macroscopic constitutive model, the Porous Eindhoven Glass Polymer (Porous EGP) model, is presented to describe the deformation behavior of cavitated rubber toughened polymers under multiaxial loading conditions. It is shown that the proposed macroscopic constitutive model is able to describe the non-linear pre-yield regime, strain rate dependence, post-yield behavior (strain softening and hardening) and void evolution for loading conditions ranging from shear to equi-triaxial (pure triaxial) tension and compression. The Porous EGP model is a combination of a well established non-linear viscoelastic viscoplastic model, the Eindhoven Glassy Polymer (EGP) model, and the modified Gurson model. The Gurson model is adopted to determine the equivalent stress and plastic rate of deformation tensor making it depending on the void volume fraction, deviatoric and hydrostatic stress. The macroscopic constitutive model is developed based on the response of realistic 3D representative volume elements (RVEs) containing randomly positioned mono-disperse inclusions. The constitutive behavior of the matrix phase in this full-field model is described by the EGP model, and the cavitated inclusions are idealized as voids. Their response is studied for a range of void volume fractions, multiaxial loading conditions, strain rates and thermodynamic states. The yield behavior of the heterogeneous material depends non-linearly on the macroscopic hydrostatic stress. This response is well captured with the proposed macroscopic constitutive model.

LCF life prediction of turbine disc alloy using crystal plasticity and 3D representative volume element containing twin boundaries

The traditional LCF life prediction method based on macroscopic behavior is difficult to reveal the microscopic fatigue failure mechanism. Therefore, the crystal plasticity finite element method and the representative volume elements considering the real microstructure were used to simulate the cyclic deformation of a nickel-based superalloy FGH4098, and a fatigue failure criterion is established to predict the LCF life. The influence of twin boundary on the prediction accuracy is particularly discussed. Meanwhile, the hotspots which are potential sites for fatigue crack initiation were analyzed. The results show that the consideration of twin boundary can improve the accuracy of life prediction, with a scatter factor of ±1.3 only.

Multiscale modeling of shape memory polymers foams nanocomposites

Shape memory polymer foams (SMPFs) are defined as lightweight cellular materials with the ability to recover their undeformed shape by applying an external stimulus like light, temperature, magnetic field, etc. Reinforcement of the material with nano-clay filler leads to a significant improvement in its physical properties. As a result, a wide range of applications is occupied by SMPFs, especially in industry and biomedical applications. Because of the heterogeneous nature of the SMPFs at different scale levels, modeling the material with one scale numerical model which able to capture all the effects of the lower scale material structure is really a complex task. Within this work, a full multiscale modeling approach is employed to investigate the thermomechanical response of the SMPFs. Furthermore, a combination of the 3D Representative Volume Element (RVE) and finite element method is used to explore the effects of the nano-filler weight fractions and the material's cellular structure at different length scales on the material dynamics. The multiscale modeling process gives great and promising results with good agreement with the experimental results. Moreover, the model shows relatively high sensitivity parameters that are initiated from the lower scale level.

Scripts to Insert Cohesive Elements at the Interfaces between Matrix and Precipitates with Irregular Shapes in Representative Volume Elements in ABAQUS

A MATLAB algorithm was developed to insert cohesive elements at the interfaces between the matrix and precipitates in two dimensional (2D) representative volume elements (RVEs) of metals. The RVEs were created using OOF2 and imported into the “Complete ABAQUS Environment” (CAE) interface. These RVEs are based on actual images of the metal at the microscale, where the precipitates have irregular shapes. The RVEs contain precipitates that are dispersed into matrix materials. Commercial finite element (FE) ABAQUS software does not provide the option to automatically generate cohesive elements at the interfaces. The presented algorithm enables the insertion of cohesive elements at the interfaces between the matrix and precipitate in a convenient manner. This algorithm enables the simulation of the fracture process, including initiation at the interfaces and propagation at microscale, for metals that contain precipitates and/or particles. This algorithm extends the simulation capabilities of the FE solver ABAQUS.

Study on the adverse effect of acid-corrosion on the dentin in terms of degradation of fracture resistance

Human dentin is known for its hierarchical structure through long-term evolution. Dental caries, embodied by dentin demineralization, is ascribed to a different reaction between peritubular dentin (PTD) and intertubular dentin (ITD) to acid dissolution. This study sheds light on the adverse effect of acid on dentin in terms of degradation of its fracture toughness (FT) due to the acid dissolution-induced corrosion of PTD. A scanning electronic microscope (SEM) is utilized to visualize the difference between normal and acid-treated dentin subjected to the same loading method in terms of crack propagation performance. 3D simulative representative volume elements (RVEs) are developed to analyze the effect of PTD missing on the performance of dentin fracture resistance (FR). The results indicate PTD plays a significant role in enhancing dentin FR capability and thus reveals the importance of structural integrity for dentin.

A representative volume element model to evaluate the effective properties of flexoelectric nanocomposite

In this paper, a computational homogenization approach is developed to investigate the effective material properties of flexoelectric nanocomposites. The analysis incorporates the isogeometric analysis (IGA) to solve an electromechanically coupled system using a 3D representative volume element (RVE) model with periodic boundary conditions. In particular, a micromechanical analysis is carried out to represent the microstructure of a heterogeneous domain composed of an elastic matrix and cylindrical flexoelectric fibers. The numerical simulations indicated that while the effective tensor of piezoelectricity is isotropic, the flexoelectricity tensor is transversely anisotropic concerning the geometry of the composite’s phases. Furthermore, the flexoelectricity coefficients, μ¯3113 and μ¯3333, which couple the polarization to the strain gradients with respect to the longitudinal axis, improved remarkably with increasing the inclusion’s volume fraction. The presented computational methodology and the findings of this study is expected to contribute valuably towards the design of flexoelectric nanostructures and devices.

Micromechanical analysis of age‐induced strength reduction in a multiaxially loaded short‐fiber reinforced thermoplastic

AbstractIn this study, we demonstrate that the strength of a short‐fiber reinforced polymer as measured in uniaxial tension is not a good indicator for its strength under multiaxial loading conditions. To illustrate this fact, the influence of physical aging on the strength of a 20 wt% short‐fiber reinforced polycarbonate is studied for a uniaxial and biaxial loading condition. Results demonstrate that aging strongly reduces the strength in multiaxial loading, whereas, it increases in uniaxial loading. To rationalize these observations, a micromechanical analysis of the local stress state is performed using three‐dimensional (3D) representative volume elements (RVE) in combination with a constitutive model that adequately describes the intrinsic deformation response of the matrix. RVE simulations demonstrate that biaxial loading results in higher local hydrostatic stresses and triaxiality than the uniaxial loadcase for the composite system considered, and aging results in a shift towards higher values. The high triaxiality, the magnitude of the hydrostatic stress, and the shift in hydrostatic stress upon aging, presents a clear rationalization why physical aging induces a strength reduction in biaxial loading and not in uniaxial loading. These results highlight that care should be taken when predicting strength under complex loading conditions with only uniaxial data available.

A Multiphysics-Multiscale Model for Particle–Binder Interactions in Electrode of Lithium-Ion Batteries

Understanding the electrochemical and mechanical degradations inside the electrodes of lithium-ion battery is crucial for the design of robust electrodes. A typical lithium-ion battery electrode consists of active particles enclosed with conductive binder and an electrolyte. During the charging and discharging process, these adjacent materials create a mechanical confinement which suppresses the expansion and contraction of the particles and affects overall performance. The electrochemical and mechanical response mutually affect each other. The particle level expansion/contraction alters the electrochemical response at the electrode level. In return, the electrode level kinetics affect the stress at the particle level. In this paper, we developed a multiphysics–multiscale model to analyze the electrochemical and mechanical responses at both the particle and cell level. The 1D Li-ion battery model is fully coupled with 2D representative volume element (RVE) model, where the particles are covered in binder layers and bridged through the binder. The simulation results show that when the binder constraint is incorporated, the particles achieve a lower surface state of charge during charging. Further, the cell charging time increases by 7.4% and the discharge capacity reduces by 1.4% for 1 C-rate charge/discharge. In addition, mechanical interaction creates inhomogeneous stress inside the particle, which results in particle fracture and particle–binder debonding. The developed model will provide insights into the mechanisms of battery degradation for improving the performance of Li-ion batteries.

Mechanical Characterization of MWCNT-Reinforced Cement Paste: Experimental and Multiscale Computational Investigation.

Computational approaches could provide a viable and cost-effective alternative to expensive experiments for accurately evaluating the nonlinear constitutive behavior of cementitious nanocomposite materials. In the present study, the mechanical properties of cement paste reinforced with multi-wall carbon nanotubes (MWCNTs) are examined experimentally and numerically. A multiscale computational approach is adopted in order to verify the experimental results. For this scope, a random sequential adsorption algorithm was developed to generate non-overlapping matrix-inclusion three-dimensional (3D) representative volume elements (RVEs), considering the inclusions as straight elements. Nonlinear finite element analyses (FEA) were performed, and the homogenized elastic and inelastic mechanical properties were computed. The use of a multiscale computational approach to accurately evaluate the nonlinear constitutive behavior of cementitious materials has rarely been explored before. For this purpose, the RVEs were analyzed both in pure tension and compression. Young's modulus as well compressive and tensile strength results were compared and eventually matched the experimental values. Moreover, the effect of MWCNTs on the nonlinear stress-strain behavior of reinforced cement paste was noted. Subsequently, three-point bending tests were conducted, and the stress-strain behavior was verified with FEA in the macro scale. The numerical modeling reveals a positive correlation between the concentration of MWCNTs and improved mechanical properties, assuming ideal dispersion. However, it also highlights the impact of practical limitations, such as imperfect dispersion and potential defects, which can deteriorate the mechanical properties that are observed in the experimental results. Among the different cases studied, that with a 0.1 wt% MWCNTs/CP composite demonstrated the closest agreement between the numerical model and the experimental measurements. The numerical model achieved the best accuracy in estimating the Young's modulus (underestimation of 13%), compressive strength (overestimation of 1%), and tensile strength (underestimation of 6%) compared to other cases. Overall, these numerical findings contribute significantly to understanding the mechanical behavior of the nanocomposite material and offer valuable guidance for optimizing cement-based composites for engineering applications.