Meso-scale Representative Volume Element Research Articles

A scale-span method to characterize the mechanical property of BCF/PEEK considering uncertain structural characteristics

The focus of this study is exploring a scale-span characterization method to predict the mechanical properties of Braided Carbon Fiber Reinforced Poly Ether Ether Ketone (BCF/PEEK) considering structural uncertainty. Firstly, a complicated micro-scale Representative Volume Element (RVE) model that considers the random position and size of fiber was established via the developed Python script. Analogously, a mathematical expression adopted by the trust region algorithm was proposed to accurately describe the detailed cross-sectional shapes and fluctuation amplitude characteristics of BCF/PEEK for the sake of establishing the precision meso-scale RVE model. Then, the corresponding elastic properties that consider fiber volume fraction and fiber distribution location were characterized via the span-scale characterization method. Meanwhile, the influence of fiber bundle fluctuation amplitude and fiber volume fraction on the mechanical properties was investigated as well. In addition, the mechanical properties of BCF/PEEK with the change of the braid angle between warp and weft yarn were predicted via the established meso-scale RVE model. Finally, a series of experiments have been carried out. The maximum and minimum absolute prediction deviation of all elastic property parameters were only 4.07 % and 1.41 %, respectively, which verified the proposed scale-span characterization method can predict the mechanical properties of composites well.

A novel multiscale prediction strategy for simulating the progressive damage behavior of plain-woven bamboo fabrics reinforced epoxy resin composites

This study proposed a novel multiscale prediction strategy, including mesoscale and macroscale damage evolution modeling, to investigate the effective properties and progressive damage failure behavior of plain-woven reinforced composites (PWRCs) under various external loads (tension, compression). A high-precision mesoscale representative volume element (RVE) that could accurately describe the local mechanical behavior of PWRCs was developed by combining experimental characterization (scanning electron microscope and X-ray computed tomography) and numerical simulation. To solve the problem of inaccurate prediction results caused by multiscale characteristics and complex stress changes in the damaged area of PWRCs, the strain-based 3D Hashin failure criterion and the multiscale damage models were used to predict the damage initiation and evolution of mesoscale reinforcement (bamboo fiber yarn bundle) and macroscale composites, respectively. Considering the damage evolution law of isotropic materials, a damage model based on the Von Mises criterion was used to characterize the damage initiation and evolution of mesoscale matrix epoxy resin (EP) under external loading. The effective properties and mechanical behavior of the PWRCs were transferred from mesoscale to macroscale through the progressive homogenization method. The bilinear constitutive relationship of the mixed-mode cohesive element was used to characterize the interlaminar failure of the PWRCs. Finally, the corresponding mechanical characterization (tension, compression) of the PWRCs was carried out. Moreover, the experimental results were highly consistent with the simulation results, verifying the reliability of the novel multiscale prediction strategy in investigating the mechanical response of the PWRCs at multiple scales and revealing the damage mechanism of the PWRCs.

A mesoscale computational approach to predict ABD matrix of thin woven composites

The ABD matrix is a fundamental method to characterize the overall stiffness behavior of laminated composite structures. Although classical laminate theory has been widely used, it has limitations in predicting the ABD matrix for woven composites. To address this issue, this paper presents a mesoscale homogenization approach aimed at computing the ABD matrix for thin woven composites accurately. The mesoscale representative volume element (RVE) of the woven composite is generated using TexGen and imposed with periodic boundary conditions to enforce the Kirchhoff thin plate assumption. The ABD matrix is computed by conducting six separate finite element simulations, each representing one simple in-plane or out-of-plane deformation in a specified direction. Moreover, to facilitate the implementation of the method, an open-source plugin tool was developed within ABAQUS CAE, automating the ABD matrix calculation for various types of woven composites including 2D weave, 3D weave, and multiaxial. The accuracy of the proposed method was validated through benchmark calculations against existing literature results.

Effect of void defects on mechanical behavior and failure features of C/C honeycomb structure

The combination of honeycomb structure and carbon/carbon (C/C) composites offers unique high load-bearing and light-weight advantages in satellite-bearing platforms. However, the defects generated by the imperfect preparation process are inevitable. This paper employs the chemical vapor infiltration (CVI) technique to fabricate novel C/C honeycomb structures and considers the presence of internal void defects. Based on micro-computerized tomography (μ-CT) images, the void distribution and porosity as well as the micro-structure characteristics are acquired. Meso-scale representative volume element (RVE) models is established to predict the performance of honeycomb wall material. A secondary development of ABAQUS is performed to establish a model of honeycomb structure containing void defects. Multi-scale models are developed for investigating the mechanical performance of the C/C honeycomb structure. Experimental methods and finite element simulations are utilized to examine the effects of porosity and different weave structures on the compression and shear properties, as well as damage modes of C/C honeycomb structures in detail. The results demonstrate that the presence of low porosity ρ = 1 % severely diminishes the load-bearing capacity of the honeycomb and affects its damage pattern. Twill-2 weave C/C honeycomb inherits the advanced performance of the composites and exhibits superior comprehensive properties compared to plain weave and twill-1 weave honeycomb structures.

Mechanical Characterization of Multifunctional Metal-Coated Polymer Lattice Structures.

Metal-coated lattice structures hold significant promise for customizing mechanical properties in diverse industrial applications, including the mechanical arms of unmanned aerial vehicles. However, their intricate geometries pose computational challenges, resulting in time-intensive and costly numerical evaluations. This study introduces a parameterization-based multiscale method to analyze body-centered cubic lattice structures with metal coatings. We establish the validity and precision of our proposed method with a comparative analysis of numerical results at the Representative Volume Element (RVE) scale and experimental findings, specifically addressing both elastic tensile and bending stiffness. Furthermore, we showcase the method's accuracy in interpreting the bending stiffness of coated lattice structures using a homogenized material-based solid model, underscoring its effectiveness in predicting the elastic properties of such structures. In exploring the mechanical characterization of coated lattice structures, we unveil positive correlations between elastic tensile stiffness and both coating thickness and strut diameter. Additionally, the metal coating significantly enhances the structural elastic bending stiffness multiple times over. The diverse failure patterns observed in coated lattices under tensile and bending loads primarily stem from varied loading-induced stress states rather than external factors. This work not only mitigates computational challenges but also successfully bridges the gap between mesoscale RVE mechanical properties and those at the global structural scale.

Prediction and adjustment of elastic properties in three‐dimensional orthogonal woven composites through dual‐scale modeling

AbstractThree‐dimensional (3D) orthogonal woven composites can overcome the drawback of weak interlaminar strengths in traditional laminated composites and exhibit excellent resistance to out‐of‐plane impact, however, the significant difference in properties in the in‐plane orthogonal direction will limit the potential range of application thereof. Predicting elastic properties and exploring methods of adjustment are therefore of paramount importance. Using computed tomography (CT) scanning to obtain detailed parameter models, a corresponding dual‐scale model of microscopic representative volume element (RVE) and mesoscopic RVE was established, and the accuracy of the model was experimentally validated, which can predict the elastic properties of materials. In addition, the influences of the yarn fiber volume fraction and weaving distance on elastic properties were evaluated using the elastic modulus visualization method, and a formula integrating these two factors is provided for adjustment of the in‐plane orthogonal Young's modulus.Highlights Experimentally validated microscale and mesoscale RVE models were established. The influences of factors on elastic properties were visualized. The relationship between Young's modulus and influencing factors was derived. A reliable strategy for adjusting the in‐plane Young's modulus was proposed.

Mesoscale analysis of aging mechanical behaviors of 3D woven composites

3D orthogonal woven composites (3DOWCs) are inevitably subjected to the severe cyclic hygrothermal aging environment in the application of supersonic aircraft structures and their durability should be proven. However, most current works relating to the hygrothermal aging of 3DOWCs rely on the experimental methods which are of high cost. To address this issue, a matrix-yarn mesoscale model of 3DOWCs was established to investigate the cyclic hygrothermal aging mechanical behaviors in this paper. High-fidelity mesoscale representative volume element (RVE) was constructed with realistic geometric configuration of the reinforcement. Only the aging properties of pure resin were needed in the mesoscale model. The aging properties of fiber yarns were calculated with Chamis formulas accounting for resin aging. Tension-compression asymmetry behavior of resin matrix was accounted in the constitutive model. The damage initiation and propagation of resin matrix, yarn and cohesive interface were modeled by the progressive 3D damage model. The mechanical properties of 3DOWCs before and after aging were predicted by the mesoscale model and validated with experiment. This work can provide effective tool for the design of 3DOWCs applied in harsh environments.

Experimental and numerical investigation on tension–tension fatigue behavior of three-dimensional five-directional hybrid braided composites

This paper presents an experimental and numerical investigation on tension–tension fatigue behavior of hybrid carbon/glass three-dimensional five-directional (3D5D) braided composites. Fatigue tests were carried out under the stress ratio of 0.1. The experimental results show that the fatigue strength significantly decreases as the fatigue life increases and the stiffness gradually decreases as the loading cycles increase. The fatigue life at the stress level within 35 %–50 % ultimate tensile strength (UTS) is within 4 × 103–6 × 105 cycles. The stiffness degradation before failure increases from 39 % to 58 % as the fatigue stress decreases from 50 % UTS to 35 % UTS. Under tension–tension fatigue loading, matrix cracking inside the yarns and interfacial debonding between the yarns and the matrix firstly occur and propagate, then matrix cracking appears in the resin-rich regions and numerous fiber breakage happens until final failure. The fatigue performance and damage mechanisms of braided composites are affected by fiber hybrid mode and braiding methods. Additionally, a mesoscale representative volume element (RVE) model with periodic boundary conditions and a progressive fatigue damage model was developed for the 3D5D hybrid braided composites. The numerical simulation results of fatigue life, stiffness degradation and damage progression have good agreement with experiments, demonstrating the validity of the developed model.

Research into the thermal expansion behavior of spread tow woven pierced carbon/carbon composites at high temperature

Textile-reinforced carbon/carbon composites are frequently used for thermal safety due to their superb thermophysical properties. The coefficient of thermal expansion (CTE) is a fundamental performance metric of spread tow woven pierced carbon/carbon composites (STWPs). The multiscale representative volume element (RVE) models constructed as part of this work were used for investigating the CTEs of STWPs at high temperature. The temperature displacement coupling analysis step was established to predict the CTEs of STWPs considering the high-temperature environment. In addition, periodic displacement boundary conditions were adopted as node constraints with the spatial periodicity of RVE models. The influences of pore positions and configurations on the CTEs of the matrix were considered through two different matrix RVE model. The CTEs of the spread tow (ST) and fiber rod were computed using two microscale RVE models with an unequal fiber volume fraction. A novel modeling strategy for the mesoscale RVE model was put forth in order to calculate the CTEs of the STWPs due to the remarkable lightness and thinness of the ST. Only 9.64% and 7.92% errors in the in-plane and out-of-plane directions were found when the experimental findings were compared to those predicted by numerical models, demonstrating the accuracy and effectiveness of the multiscale RVE models. Moreover, the impacts of areal density of ST woven fabric on the CTEs of STWPs were discussed. The fundings demonstrated that the in-plane and out-of-plane CTEs both decreased as the areal density increased.

Statistical field theory for nonlinear elasticity of polymer networks with excluded volume interactions.

Polymer networks formed by cross linking flexible polymer chains are ubiquitous in many natural and synthetic soft-matter systems. Current micromechanics models generally do not account for excluded volume interactions except, for instance, through imposing a phenomenological incompressibility constraint at the continuum scale. This work aims to examine the role of excluded volume interactions on the mechanical response. The approach is based on the framework of the self-consistent statistical field theory of polymers, which provides an efficient mesoscale approach that enables the accounting of excluded volume effects without the expense of large-scale molecular modeling. A mesoscale representative volume element is populated with multiple interacting chains, and the macroscale nonlinear elastic deformation is imposed by mapping the end-to-end vectors of the chains by this deformation. In the absence of excluded volume interactions, it recovers the closed-form results of the classical theory of rubber elasticity. With excluded volume interactions, the model is solved numerically in three dimensions using a finite element method to obtain the energy, stresses, and linearized moduli under imposed macroscale deformation. Highlights of the numerical study include: (i) the linearized Poisson's ratio is very close to the incompressible limit without a phenomenological imposition of incompressibility; (ii) despite the harmonic Gaussian chain as a starting point, there is an emergent strain-softening and strain-stiffening response that is characteristic of real polymer networks, driven by the interplay between the entropy and the excluded volume interactions; and (iii) the emergence of a deformation-sensitive localization instability at large excluded volumes.

Study on impact resistance and parameter optimization of patch‐repaired plain woven composite based on multi‐scale analysis

AbstractPatch‐repaired plain woven composite structures were exposed to internal damage caused by impact during service, which reduced mechanical properties. A multi‐scale modeling strategy was proposed to study the impact resistance characteristics of patch‐repaired plain woven carbon‐fiber‐reinforced‐polymer (CFRP) laminates. The micro representative volume element (RVE) was extracted from the yarn; a local homogenization method was used to obtain the equivalent cross‐ply laminate (ECPL) cells corresponding to the mesoscale RVE. The finite element model (FEM) of patch‐repaired plain woven laminate was established by extending the ECPL cells. The FEM was checked by the low‐velocity impact (LVI) tests, and the impact parameter errors were within 10%. Furthermore, impact resistance of repaired specimens under different impact conditions (e.g., the impact energy was 3 ~ 20 J) was studied. Finally, patch parameters (patch thickness, patch size, off‐axis angle) of the repaired specimen were optimized by multi‐objective optimization based on the surrogate model and response surface method (RSM). After multi‐objective function optimization, the optimal patch parameter configuration (the thickness of the patch was 0.87 mm, the diameter was 66 mm, and the off‐axis angle was 44.2°) reduced the absorbed energy value of the repaired specimen from 4.9089 to 4.1640 J, and the delamination area of the repaired specimen from 605 to 280 mm2. All the results provide a reference for patch repair of plain woven composites.

Multiscale Finite-Element Analysis of Damage Behavior of Curved Ramp Bridge Deck Pavement Considering Tire–Bridge Interaction Effect

The present study developed a three-dimensional (3D) multiscale modeling approach to investigate the mesoscale damage behavior of curved ramp bridge deck pavement subjected to tire loading. First, a full-scale tire–bridge interaction finite element (FE) model was established to solve the macroscopic response of deck pavement during vehicle turning. Subsequently, the 3D mesostructure of the asphalt concrete layer was reconstructed from X-ray computer tomography (CT) images through a digital image processing (DIP) technology. Finally, a homogenization method was adopted to link the mechanical properties of deck pavement at two different scales, and a mapping procedure was employed to transfer the boundary displacements from macroscale pavement target element to the mesoscale representative volume element (RVE) model. Also, the bilinear cohesive elements were applied to simulate damage initiation in the RVEs. The results showed that smaller curvature radius and higher travel speed can promote unbalanced stress and local damage of the outer loading zone. From the mesoscale viewpoint, reducing curvature radius or increasing travel speed could result in crack direction shifts and increase the irregularity of microcrack distribution. In addition, transverse microcracks are commonly found in the center of the tire load, while longitudinal microcracks are distributed on the deck pavement surface around the tire edges and the dual-tire clearance center.

A dynamic FEM-DEM multiscale modeling approach for concrete structures

The dynamic behavior of concrete is strain-rate-dependent, which affects the failure modes of structures. In this study, a multiscale modeling approach is developed for concrete structures under dynamic loading, which couples the macroscale finite element method (FEM) and the mesoscale discrete element method (DEM). The dynamic response of structures is analyzed using the macroscale FEM, and a representative volume element (RVE), composed of aggregate, mortar, and interface, is simulated using the mesoscale DEM to capture the strain rate effects of concrete. By fully taking the advantages of macroscale and mesoscale simulations, it is no longer essential to use complex constitutive laws or input rate-dependent parameters for the macroscale FEM modeling because the concrete fracture can be explicitly illustrated through the breaking process of the mesoscale RVE. This approach is applied to concrete beams and the Koyna dam to verify its applicability. These practical comparisons demonstrate that the seismic tensile strength increases with the strain rates under seismic loading and that the actual repeated crack-closure process of concrete is adequately simulated by the proposed method.

Postbuckling response of unitized stiffened textile composite panels: Computational modeling

A computational investigation of unitized stiffened textile composite panels that are manufactured from triaxially braided textile composites and loaded in axial compression into the postbuckling regime is presented. The stiffened panels are unitized because the textile nature of the constituent material, in conjunction with an alternative stiffener design, form a near-net shape one-piece stiffened panel structure where the textile laminae that form the skin section of the panel are also used, without discontinuity of material, to form the stiffener. A multiscale computational model is presented where the architecture-dependent behavior of a discretely modeled mesoscale representative volume element is passed up to the orthotropic homogenized macroscale stiffened panel shell model. The mesoscale model is automatically executed based on input from the macroscale shell model. Progressive damage initiation and propagation is accomplished by implementing a crack band model in the macroscale model to simulate a material softening behavior. The experimental results are compared to the computational multiscale framework analysis results where a mesoscale triaxially braided textile composite architecture-based model serves as the damage initiation criterion for a smeared progressive damage crack band model in the orthotropic homogenized stiffened panel macroscale shell model.

An integrated computational materials engineering framework to analyze the failure behaviors of carbon fiber reinforced polymer composites for lightweight vehicle applications

A bottom-up multi-scale modeling approach is used to develop an Integrated Computational Materials Engineering (ICME) framework for carbon fiber reinforced polymer (CFRP) composites, which has the potential to reduce development to deployment lead time for structural applications in lightweight vehicles. In this work, we develop and integrate computational models comprising of four size scales to fully describe and characterize three types of CFRP composites. In detail, the properties of the interphase region are determined by an analytical gradient model and molecular dynamics analysis at the nano-scale, which is then incorporated into micro-scale unidirectional (UD) representative volume element (RVE) models to characterize the failure strengths and envelopes of UD CFRP composites. Then, the results are leveraged to propose an elasto-plastic-damage constitutive law for UD composites to study the fiber tows of woven composites as well as the chips of sheet molding compound (SMC) composites. Subsequently, the failure mechanisms and failure strengths of woven and SMC composites are predicted by the meso-scale RVE models. Finally, building upon the models and results from lower scales, we show that a homogenized macro-scale model can capture the mechanical performance of a hat-section-shaped part under four-point bending. Along with the model integration, we will also demonstrate that the computational results are in good agreement with experiments conducted at different scales. The present study illustrates the potential and significance of integrated multi-scale computational modeling tools that can virtually evaluate the performance of CFRP composites and provide design guidance for CFRP composites used in structural applications.

FE$$^2$$ investigation of aggregate characteristics effect on fracture properties of concrete

The relation between aggregate characteristics and fracture properties of concrete mixtures is investigated numerically. A homogenization-based multiscale approach is introduced based on objective failure zone averaging for heterogeneous meso-structure, and traction–separation law of fracture process zone (FPZ) instead of phenomenological constitutive model for macro-structure. A rate-dependent anisotropic damage-plastic formulation is employed to reproduce degradation process in the fine-scale from diffuse damage to localized bands, and extended finite element method (X-FEM) is utilized to resemble the localized region as a macro-crack within the coarse-scale. Different aggregate types are used to randomly generate meso-scale representative volume element (RVE) for concrete mixtures, and effect of size and shape of aggregates on mechanical characteristics, and sources of diversity in fracture properties of concrete are addressed.

Three-scale asymptotic homogenization of short fiber reinforced additively manufactured polymer composites

In this research, prediction of mechanical properties of short fiber-reinforced composites manufactured with the help of fused filament fabrication (FFF) process is investigated. Three-scale formulation of asymptotic homogenization is employed to upscale the properties from microscale to mesoscale and from mesoscale to macroscale. Since generating microscale representative volume element (RVE) infused with short fibers requires sophisticated modeling tools, the algorithm for the microscale RVE generation is presented and discussed. Homogenization was performed for microscale RVEs with random and aligned (fibers aligned with the beads on mesoscale) fiber orientations, and for mesoscale RVEs with unidirectional and 0/90 layup formation. Tensile tests were performed for different short carbon fiber concentrations 5, 7.5 and 10% (by volume) to validate predicted homogenized properties. Moreover, to analyze the morphology of 3D printed specimens, microstructural analysis using SEM was performed on all the printed specimens. Surface morphology helped to gain more insight into the bead structure and fiber distribution. It was concluded that Young's modulus prediction using random fiber orientation has low relative errors tested in bead direction. Overall, this study has unique contribution to mechanical property prediction for FFF-made short fiber-reinforced composite parts.

A multi-scale stochastic model for damage analysis and performance dispersion study of a 2.5D fiber-reinforced ceramic matrix composites

This paper presents a stochastic approach to study the damage evolution and performance dispersion of a 2.5D woven fiber-reinforced ceramic matrix composite in a multi-scale framework. The mechanical behavior of the composite depends on the constituent properties, fiber volume fraction, weave architecture and loading conditions. The dispersion behavior of the material was investigated with: i) a full-thickness meso-scale representative volume element (RVE) model which is established based on the weave architecture of the material, and ii) the Monte-Carlo method to obtain the effective mechanical properties of the material which are influenced by the dispersion in its constituents. The simulations reveal the damage initiation and propagation process of the material at micro/meso-scale. The results show that there are significant relationships between the constituent properties and the effective mechanical properties; the effective properties of material can be predicted with small errors, which would guide the design and optimization of composite materials.

Refine reconstruction and verification of meso-scale modeling of three-dimensional five-directional braided composites from X-ray computed tomography data

This paper proposes a statistical approach to generate the refine meso-scale representative volume element of three-dimensional (3D) five-directional braided composites considering the fabric compaction and the axial yarn torsion. The method firstly extracts the regions of interest to obtain the reference model (R-model) from the X-ray computed tomography (Micro-CT) data. Then, the geometric parameters of the collected yarns of R-model are statistically analyzed based on the scanning tomograms. Consequently, the meso-scale statistical model (S-model) are reconstructed after being fitted with the appropriate function. Moreover, for the validation of S-model, the traditional ideal model (I-model) and the experimental tests are considered. The results show that the proposed S-model is capable of accurately presenting the effects of the fabric compaction and yarn torsion on the mechanical behaviors of 3D braided composites, validated by the elastic constants and the damaged modes.

Hybrid woven carbon-Dyneema composites under drop-weight and steel ball impact

In this study, the impact behavior and damage mechanism of novel carbon-Dyneema hybrid fabric reinforced plastic composites are investigated using drop-weight and steel ball impact tests. The force-displacement response, energy absorption and damage mechanisms of the hybrid composite were analyzed and compared with those of woven carbon laminates. The experimental results suggest that the impact resistance of the hybrid composites has been improved when benchmarked with carbon fiber composites. The Dyneema fibers suppress the splitting of bottom surfaces during impact but are susceptible to buckling due to the low compressive strength of Dyneema fibers. A multi-scale approach is proposed for modelling impact damage of hybrid woven composite accounting for the interweave patterns. A meso-scale representative volume element of the interwoven hybrid structure is analyzed and discretized into several sub-sections, each regarded as a type of laminate. Then, a macro-scale impact model is established based on the homogenized effective properties of the sub-sections using continuum shell elements. The failure of the material is modelled using energy-based continuum damage mechanics. Overall, the numerical simulations show good agreement with experimental data in terms of impact force history and damage features, providing insight into the impact damage behavior of hybrid composites.