Analysis Of Representative Volume Element Research Articles

Size effects of voids on the mechanical properties of 3D printed parts

AbstractAlthough the effects of additive manufacturing process parameters on the mechanical properties of 3D printed parts have been numerically investigated in the literature, less attention has been paid on the size effects of voids between deposited filaments. This study fills this gap by developing a methodology based on a combined finite element (FE) and design of experiment (DoE) technique. The development of FE methodology is based on micro-mechanical analysis of representative volume element (RVE) of 3D printed parts to predict the effective orthotropic properties. To account for the size effects of inter-bead voids, the RVE includes contribution of the multiple parameters of layer heights, layer widths and overlapping regions. To study the main and interaction effects of the above input parameters on the stiffness properties of 3D printed parts, a structured approach based on full factorial design is used. Although the size effects of voids on the constituents of elastic moduli of RVE were investigated, the main focus in the present work is to develop a regression model to predict the stiffness properties. The FE stress analysis of the RVE conducted in this study provides an insight about the potential failure modes such as delamination and filament debonding that may occur in load bearing 3D printed parts. For a case study, the results of FE-based homogenization technique in terms of stiffness properties are validated against the experimental data via three-point bending and Iosipescu shear tests which were conducted in conjunction with digital image correlation technique. The combined numerical and statistical approach proposed in this study provides a swift iterative design of 3D printed parts prior to the time-consuming computation modelling, contributing to reduce the number of tests and manufacturing costs.

A multiscale hydro-elastoplastic model for large floating structures in two-dimension

A novel fluid–structural model was presented considering hydro-elastoplastic behavior, which coupled multiple hydro-structural-material scales. A large floating sandwich structure (LFSS) comprising upper and lower high-strength panels and a low-weight core was considered as an illustration. The mesoscale characteristics of materials and elastoplastic parameters of the low-weight perforated components were coupled by utilizing the representative volume element (RVE) method. Through the parameterized relations from RVE analysis, the flexure dynamics model for the floating sandwich structure with an equivalent homogenized core was deduced. With the flexure dynamic equation, yield criterion, and potential flow model, a multiscale hydro-elastoplasticity theoretical model was established, which combined the wave action, hierarchical component, material configuration, and structural behavior. The dynamic responses of the large floating structure under fluid–structure interaction were calculated, and the internal deformation (i.e., core strain) was set as the determining variable for the plastic region. The initially intact floating structure became hinged multi-modules after plastic cracking, and the high-strength layers at the cracking positions behaved as flexible hinges, which was defined as a hydro-elastoplastic process. The elastoplastic state evolutions of the LFSSs with different structural parameters and material configurations were solved for practical optimization. The results indicated that the multiscale coupled calculation model can provide great scientific guidance for designing large floating structures.

Investigation of the effects of volume fraction, aspect ratio and type of fibres on the mechanical properties of short fibre reinforced 3D printed composite materials

AbstractMechanical behaviour of 3D-printed composite parts is affected by the volume fraction, aspect ratio and type of fibre reinforcement. Although in the literature experimental approaches have been used to characterise the effects of the above factors on the mechanical properties of 3D printed parts, time and cost of the manufacturing process as well as the uncertainty associated with a large number of experimental techniques are the key issues. This study aims to address these challenges by developing a methodology based on a multi-scale Finite Element (FE) analysis of representative volume element (RVE) of 3D printed composite parts to predict the effective orthotropic properties. To account for the effects of fibre features, RVEs were modelled considering variables of volume fraction, aspect ratios and type of short fibres. To study the main and interaction effects of the above variables on the mechanical properties of 3D printed composite parts, a structured approach based on the Design of Experiments is used. The FE stress analysis of the RVE provides an understanding about the potential failure modes such as interfacial debonding between fibres and matrix, interlayer and intralayer delamination that may occur in load-bearing 3D printed composite parts. The FE computed mechanical properties are validated against experimental data through a series of mechanical testing of flexure, Iosipescu, and short beam shear which were conducted in conjunction with the Digital Image Correlation technique. As a result, certainty is obtained in using the proposed approach for a fast iterative design of 3D printed composite parts prior to industrial applications.

Scanning Electron Microscopy Analysis of Kenaf Coir Epoxy Reinforced Carbon Nanotubes Nanoparticles Hybrid Composite

Ecological awareness and sustainable development have attracted researchers’ focus on composites developed using natural fibers. Consequently, natural fiber polymer composites are flattering and increasingly prominent for use and research. Fiber-reinforced composites inhibit considerable benefits, in conjunction with high strength and lesser weight, simpler fabrication, biodegradability, lesser cost of production, and so on. Natural fiber offers good properties, but it requires proper matrix interface bonding along with effective synergy amongst each matrix-fibre combination. In the case of the hybrid composite proposed in this research, analytical modeling has been carried out and compared with the previous literature, in our previously published research [Parashar, S. and Chawla, V., 2022. Kenaf-coir based hybrid nanocomposite: AN analytical and representative volume element analysis. Engineering Solid Mechanics, 11(1), pp.103–118]. The present paper investigates the composite proposed in the research for scanning electron microscopy examinations, using an S3400M Scanning Electron Microscope. Each of the specimens has been cut to the necessary dimensions for SEM examination. The micrographs have been created with a high voltage of 20 kV. The broken surface of the tensile specimens of the composite samples was investigated using SEM. According to the findings of SEM and analytical modeling it has been observed that, combining nanoparticles of CNT as filler and kenaf-coir as fiber reinforcement results in a composite material with good interfacial adhesion betwixt matrix and fibers, high strength, and mechanical capabilities, to make hybrid composites for various industrial and automotive applications compared to composite present in the previous literature. The hybridization effect has also been evaluated for the composite, which depicts the higher tensile failure strain of the proposed hybrid composite.

Analysis of the Effect of Hybridization of Coconut Shell Particles on Kenaf-Coir Based Epoxy Hybrid Composites

These days manufacturing and automobile industries need structures and materials that are good in strength, higher in toughness, low in weight as well as, are more sustainable in comparison to the presently used materials. Innovative materials like hybrid composite materials are gaining a lot of attention in industrial sector. Recent research work depicts that fiber-reinforced hybrid composite can be utilized in several application areas due to their good mechanical and physical characteristics like, high strength, low weight, and higher opposition to corrosion. In this paper, the combined effect of kenaf fibers and coconut shell nanoparticles on coir fibre reinforced epoxy composites has been investigated. Three different combinations of samples with varying content of coconut shell particles as 0, 3, 5 wt% respectively and kenaf fibres as 5, 4, 0 wt% respectively, along with coconut fibers and epoxy matrix, have been used in the research. Results have been calculated for the three samples using six different analytical models. The results are analyzed using Representative Volume Element (RVE) analysis. The mechanical characteristics like Poisson’s ratio, transverse modulus, longitudinal modulus, are evaluated. The outcomes of analytical modelling are in harmony with the results obtained from the RVE analysis. The outcomes of the research show that the hybridization of various fibres in the composite is among the most potent ways to augment the attributes of composite laminates. The incorporation of coconut shell nanoparticles has also seen to increase the elastic properties of the coir kenaf epoxy hybrid nanocomposite.

Kenaf-Coir based hybrid nano-composite: an analytical and representative volume element analysis

The increasing demand for good and improved polymeric composites has led to a surge in the number of researches on hybrid composites, strengthened and enforced with the natural fibres. This paper mainly analyses and presents the attributes of hybrid composites made from natural fibres and carbon nano-tube (CNT) nanoparticles. A novel hybrid composite considered in this research includes kenaf and coir fibres with CNT nanoparticles embedded in an epoxy matrix. The proposed hybrid nanocomposite’s elastic features are calculated by using different analytical models like Chamis, Mori-Tanaka, Nielson elastic models etc and also with the help of Representative Volume Element Analysis (RVE). The content of fibre volume is varied in four different samples and it is found that upon varying the content of fibre volume, the mechanical properties like longitudinal modulus and transverse modulus got affected. The results evaluated from different analytical models are observed to be in good agreement with each other and also with the results of RVE analysis.

Modeling elastic properties of biocomposites using various analytical models and ansys material designer

A major focus of emerging research is the design and development of new materials for future industries in order to replace older ones in an environment-friendly way. Composite material is one of them, especially biocomposites. Over the past few decades, there is a lot of advancement in developing composite materials. We can see the applications of composite materials are increasing day by day in aerospace, automotive, medical, and construction field. Generally, the properties of unidirectional composites are evaluated by analytical methods or by Finite element Method. We present here a study of the properties of unidirectional biocomposite by using Ansys Material Designer and compare them with analytical methods including Rule of mixtures (ROM), Modified Rule of mixtures (MROM), Halpin-Tsai, Chamis, and Elasticity Approach models. The use of finite element analysis requires rigorous analysis of representative volume element (RVE), results strongly depend on the loading and boundary conditions we applied. So it is a cumbersome task to find out the elastic constants of composites. Hence, we used Ansys material designer, which is the easiest and quickest way of modeling composites. It is also possible to model various RVEs like square, hexagonal, and diamond. The results obtained by analytical methods and Ansys material designer are compared through graphs and the explanation is provided for each deviation in the properties. The results show great accuracy as compared with analytical methods. Only the Transverse elastic modulus (E22) and in-plane shear modulus (G12) show slight variation in properties. As we got accurate results, we also proposed properties for Random unidirectional, Woven, and Chopped fiber composites also by using Ansys material designer.

Prediction of thermal and thermo‐mechanical behavior of nano‐zirconia reinforced aluminium matrix composites

AbstractAluminium bequeaths the same benefits to medical industry as it does to other industries: it is incredibly lightweight and possesses superior strength‐to‐weight ratio. This study‘s aim is to investigate the thermal and thermomechanical behaviour of aluminium 6061 alloy reinforced with nano zirconia (0 wt. % to 15 wt. %; in 5 % steps) for medical applications. The effect of nano zirconia loading on thermal conductivity and thermo‐mechanical (thermo‐gravimetric analysis and dynamic mechanical analysis) have been systematically investigated. The thermal conductivity (128 W/m⋅K to 79 W/m⋅K) decreases with the increasing of nano zirconia particles reinforcement. The storage modulus increases with the nano zirconia particles (64 GPa to 172 GPa), whereas loss modulus indicates an increasing trend concerning the increasing temperature. The thermogravimetric analysis and differential thermal analysis result shows that composites’ decomposition temperature improved with the weight percentage of nano zirconia particles. Furthermore, representative volume element analysis is conducted to evaluate the thermal conductivity and results indicates good agreement with the experimental results within a deviation of ∼5 %.

A frictional cohesive zone model for characterizing transverse compression responses of unidirectional fiber-reinforced polymer composites

The Coulomb friction law is incorporated into the traction separation law, so a friction cohesive zone model (FCZM) combining sliding friction, interfacial debonding, and the coupling of the debonding and friction is developed. The proposed interface model is used to describe the interfacial mechanical responses of fiber/resin composite. To verify this model, the finite element model of microdroplet is built, then the calculated results of the finite element model are compared with the microdroplet test. To analyze the effect of interface friction on the macroscopic strength and stiffness of unidirectional composites, the FCZM is applied to representative volume element (RVE), and the mechanical behaviors of composites is simulated by finite element analysis of RVE, then the results are compared with the test in reference [1, 2]. It is found that the interfacial debonding is accelerated and the macroscopic strength is reduced due to the friction.

Experimental and Digimat-FE Based Representative Volume Element Analysis of Dye-Mixed Colored Resin and Carbon Fiber.

Recently, the automobile industry has demanded weight reduction, so research on materials is being actively conducted. Among this research, carbon fiber-reinforced composite materials are being studied a lot in the automobile industry due to their excellent mechanical properties, chemical resistance, and heat resistance. However, carbon fiber-reinforced composite materials have disadvantages, in that they are not free from color selection, and have weak interfacial bonding strength. In this study, a colored epoxy resin was prepared by mixing epoxy—which is a thermosetting resin according to the pigment concentration (0.1, 0.3, 0.5, 1.0 wt%)—and curing shrinkage. Thermal expansion characteristics were analyzed and the concentration of 0.5 wt% pigment showed the lowest shrinkage and thermal expansion characteristics. In addition, to measure the interfacial shear strength (IFSS) of the carbon fiber and the colored epoxy resin, the IFSS was obtained by performing a microdroplet debonding test, and the strength of the pigment concentration of 0.5 wt% was reduced to a relatively low level. Through these experiments, it was determined that an epoxy resin in which 0.5 wt% pigment is mixed is the optimal condition. Finally, using the composite material modeling software (Digimat 2020.0), the representative volume element (RVE) of the meso-scale was set, and interfacial properties of carbon fibers and colored epoxy resins were analyzed by interworking with general-purpose finite element analysis software (Abaqus CAE).

Multiscale modelling framework for elasticity of ultra high strength concrete using nano/microscale characterization and finite element representative volume element analysis

Ultra-High Strength Concrete (UHSC) (greater than 100 MPa) is a mechanically superior material compared with the Normal Strength Concrete (NSC) due to its inherent performance characteristics. Improved modulus of elasticity is one of the key target characteristics in the development of UHSC. Macroscopic response of UHSC is a result of a multitude of phases in different spatial length scales such as mesoscale, microscale, nanoscale etc. and investigating these spatial scales can yield a better understanding about contribution of each heterogenous phases to the macroscopic behaviour of UHSC. In this paper, a new multiscale modelling method including procedures to obtain micro/nano scale properties is proposed to predict the macroscopic elastic modulus using nanoindentation experiments, hydration simulations, Scanning Electron Microscopy (SEM) and Finite Element Representative Volume Element (FE-RVE) modelling.Characterization of nanomechanical properties of the cementitious composite was carried out using nanoindentation, microstructural characterization was performed using scanning electron microscopy, and hydration simulation of the cementitious paste was carried out using Virtual Cement and Concrete Testing Laboratory (VCCTL) software. A five-level multiscale framework is proposed for UHSC and results from these experimental testing and simulations were used as inputs in the proposed framework.A novel algorithm which can model any volume fraction of different phases was developed to generate geometries for RVEs to be used in FE-RVE simulations. Upscaling of elastic modulus using FE-RVE was found to be very accurate, and this method can generate detailed variation of microfields inside the RVE. A parametric study was carried out on how varying inhomogeneities in the RVE, boundary conditions, and the shape of the inhomogeneities would affect the homogenized elastic modulus.Continuum micromechanics models such as Mori-Tanaka method and Self Consistent Scheme were used for the analytical homogenization at each scale for comparison with FE-RVE method. The results of the proposed FE-RVE analysis, the Mean Field Homogenization (MFH) method, and experiment were compared and found to be a very good fit.

A representative volume element network (RVE-net) for accelerating RVE analysis, microscale material identification, and defect characterization

Representative volume element (RVE)-based analysis plays a central role in understanding the response of heterogeneous materials to properties and geometry of the constituents. However, the accuracy of RVE analysis on real-life materials requires extra effort on the identification of material constituents and characterization of imperfections (e.g., voids and cracks) introduced in the fabrication process. For these reasons, together with the multiscale and spatially varying nature of heterogeneities, analysis of heterogeneous materials can be prohibitively time-consuming. In this work, a fully convolutional network (FCN)-based framework called RVE-net is proposed to take advantage of the state-of-art use of FCNs in image segmentation and feedforward neural networks in universal approximation to accelerate multiscale analysis, identify microscale material properties, and automatically characterize defects in materials. In contrast with standard numerical methods (e.g., the finite element method), which depend heavily on domain discretization and local interpolations, the RVE-net takes microstructure images — parameterized by a coupled Heaviside and level-set field representation — and loading conditions as inputs. The aim is to directly learn the nonlinear interaction between the microstructures and their local responses in a hierarchical manner. This avoids burdensome discretization and interpolations, makes it possible to transfer the learned structure-response from one microstructure to another, and thus significantly accelerates the modeling of heterogeneous materials. Several numerical examples are performed to examine the performance of the proposed RVE-net. It is demonstrated that the RVE-net can leverage the power of graphics processing units (GPUs) in RVE analysis, inverse derivation of material constituents, and characterization of defects.

Novel Discrete Multiscale Model (DM) for non-linear analysis in composite materials

In recent years, the study of the behavior of materials at the microscopic level has increased significantly in terms of design of high-performance materials. Despite recent advances in high-performance computers, the application of multiscale numerical methods to simulate large structures still requires prohibitive computational costs. The purpose of this work is to provide a procedure capable to predict the nonlinear mechanical response of composite materials under monotonic incremental load to reduce the computational cost required for the numerical analysis of complex structures. The solution of the macroscopic problem through the first order multiscale method (FE2) will be replaced by a Discrete Multiscale Model (DM) characteristic of the Representative Volume Element (RVE). Through the definitions of an equivalent damage parameter (deq), function of the global stress at the microscale, a series of virtual tests in deformation control will be carried out, storing the stress-strain state reached by certain levels of deq in a Database. Analyzing the evolution of the fracture in the composite materials can be observed as the non-linear regime is reached only in some elements of the structure. Therefore, a procedure, the Discrete Multiscale Threshold Surface (DMTS), in which the RVE analysis is used to obtain the surface at which the damage begins (deq>0) is proposed. This law allows to know if for a certain stress-strain state the material has damaged, without needing to solve the micro-model. Once the damage is initiated, it is proposed to generate an RVE only at the integration points that have been damaged. This work will demonstrate how the FE2 method can be replaced by a Discrete Multiscale Model, representative of the composite material, obtaining significant computational improvements.

A crystal plasticity model for porous HCP crystals in titanium alloys under multiaxial loading conditions

In this paper, an efficient and effective crystal plasticity model is proposed for porous HCP crystals subject to a variety of multiaxial loading conditions. These conditions include (i) uniaxial, biaxial, and triaxial, (ii) tension and compression, (iii) low and high triaxiality, and (iv) axisymmetric and non-axisymmetric loadings. The framework is based on a combination of variational homogenization, phenomenological extensions, and assumptions motivated by observations from the high-fidelity micromechanical analysis. A novel penalty-free algorithm is employed to reach and maintain a specified stress state while performing representative volume element (RVE)-based crystal plasticity finite element (CPFE) analysis with porosity. The RVE studies demonstrate that the initial porosity, crystallographic orientation, and stress states have a significant effect on the homogenized mechanical responses of microscopically porous RVEs. The proposed porous crystal plasticity model is developed and calibrated using a database generated from the results of micromechanical RVE analysis. The calibrated porous model is reasonably effective in predicting the response of porous crystalline RVEs.

Mechanical modeling of a stitched sandwich thermal protection structure with ceramic-fiber-reinforced SiO2 aerogel as core layer

Ceramic-fiber-reinforced SiO2 aerogel (CFRSA) composite was used as core layer to prepare a stitched sandwich thermal protection structure (SSTPS). Mechanical properties of the SSTPS were experimentally investigated and compared with that of CFRSA, including flatwise tension, flatwise compression, edgewise compression and shear. Research results showed that the SSTPS can greatly improve the mechanical properties of CFRSA. To further understand the non-linear, tension-compression asymmetric and transversely isotropic properties of the SSTPS, inner configurations were investigated by X-ray computed tomography and scanning electron microscopy. Mechanical models were established to predict the overall properties of the SSTPS through performance of each component, including theoretical model and finite element analysis (FEA) model. Mixed series-parallel spring models were constructed to theoretically predict the effective elasticity modulus of the SSTPS. Representative volume element (RVE) was selected for FEA modeling of the SSTPS, which can not only predict the equivalent elastic modulus of SSTPS, but also predict the nonlinear flatwise compression behavior. In order to verify whether the mechanical properties of large area SSTPS under complex stress can be represented by the properties of uniform materials through RVE analysis, four-point bending test and FEA modeling were carried out on a large scale SSTPS specimen. Results showed that when analyzing the macro bending behavior of large area SSTPS, the method of equivalent SSTPS to uniform material were of relatively high accuracy and efficiency.

Micromechanical Modeling of Anisotropy and Strain Rate Dependence of Short-Fiber-Reinforced Thermoplastics

The anisotropy and strain rate dependence of the mechanical response of short-fiber-reinforced thermoplastics was studied using a straightforward micromechanical finite element analysis of representative volume elements (RVEs). RVEs are created based on the fiber orientation tensor, which quantifies the processing-induced fiber orientation distribution. The matrix is described by a strain rate-dependent constitutive model (the Eindhoven glassy polymer (EGP) model), which accurately captures the intrinsic response of amorphous polymers. The micromechanical results indicate that the influence of strain rate and that of the loading direction on the yield stress are multiplicatively decouplable, which confirms previous experimental observations. Moreover, it is demonstrated that the yield stress, to a good approximation, can be directly linked to the fiber orientation in the direction of loading. This leads to a new relation that uniquely links the rate dependence of the yield stress to the fiber orientation in loading direction.

The Strength and Delamination of Graphene/Cu Composites with Different Cu Thicknesses

This study analyzed the mechanical and fracture behavior of graphene/copper (Cu) composites with different Cu thicknesses by using molecular dynamics (MD) and representative volume element (RVE) analysis. Three graphene/Cu composite analytical models were classified as 4.8, 9.8, and 14.3 nm according to Cu thicknesses. Using MD analysis, zigzag-, armchair-, and z (thickness)-direction tensile analyses were performed for each model to analyze the effect of Cu thickness variation on graphene/Cu composite strength and delamination fracture. In the RVE analysis, the mechanical characteristics of the interface between graphene and Cu were evaluated by setting the volume fraction to 1.39, 2.04, and 4.16% of the graphene/Cu composite model, classified according to the Cu thickness. From their obtained results, whether the graphene bond is maintained has the greatest effect on the strength of graphene/Cu composites, regardless of the Cu thickness. Additionally, graphene/Cu composites are more vulnerable to armchair direction tensile forces with fracture strengths of 14.7, 8.9, and 8.2 GPa depending on the Cu thickness. The results of this study will contribute to the development of guidelines and performance evaluation standards for graphene/Cu composites.

Total finite element tearing and interconnection method for computationally efficient micromechanical analysis

Micromechanical analysis of a representative volume element (RVE) is commonly performed to estimate the material’s effective/homogenized properties in a multiscale analysis of deformation of materials. Typically numerical analysis techniques such as the finite element (FE) method are used for such an analysis. A highly refined FE mesh is required to capture microstructure features accurately for the analysis of RVE. However, this increases the number of degrees of freedom and affects computational time adversely. In this contribution a total finite element tearing and interconnection (TFETI) domain decomposition method based approach is presented for a computationally efficient micromechanical analysis. Two critical aspects of the micromechanical analysis, namely, a) computationally efficient solution of the boundary value problem and b) ease of computation of effective properties, are addressed in this work. This work focuses on the displacement driven micromechanical analysis where the boundary conditions are available in terms of displacements over the entire boundary. Two types of displacement boundary conditions, viz uniform or proportional displacements and periodic displacements corresponding to the state of uniaxial extension and simple shear are considered. The performance of the adapted TFETI with commonly used preconditioners, namely Dirichlet and lumped, for such displacement driven analysis is investigated. An efficient algorithm that exploits the structure of the TFETI method is proposed to calculate the effective properties. The proposed method’s efficacy is demonstrated by analyzing some representative model problems of composite materials. It is observed that the method’s performance depends on various problem parameters such as volume fraction, the shape of inclusion, the distance between the inclusions, and the contrast between the material properties of matrix and inclusion. The performance also depends on the numerical method parameters, such as the number of subdomains, shape of subdomains, and preconditioners. Therefore, a systematic study is carried out to study the influence of these parameters on the method’s performance.

Multiscale Modelling Framework for Elasticity Homogenization of Ultra High Strength Concrete Using Nano/Microscale Characterization and Finite Element Representative Volume Element Analysis

Multiscale Modelling Framework for Elasticity Homogenization of Ultra High Strength Concrete Using Nano/Microscale Characterization and Finite Element Representative Volume Element Analysis

Micromechanics based analytical model for estimation of stress distribution and failure initiation in constituents of UDFRP composites subjected to transverse loading

When a Unidirectional fiber reinforced polymer (UDFRP) composite is subjected to transverse loading, there is spatial variation of stresses in the constituents. The failure in matrix initiates at the location of maximum stress. Stress distribution and failure initiation in constituents of UDFRP composites is usually studied through finite element (FE) analysis of representative volume element (RVE) which is computationally expensive and time consuming. The present study proposes an analytical model through which stress variation and failure initiation in the constituents of UDFRP composite can be obtained in simple and reliable way and it can be readily used in designing. For this model, RVE is idealized in the form of springs arranged in parallel and series. These springs represent the stiffness of constituents (fiber and matrix). The results of analytical model are compared with FE simulations and good agreement is observed. Influence of fiber volume fraction on failure initiation of UDFRP composites is also studied through FE analysis of RVE and analytical model.