Showing papers on "Representative elementary volume published in 2020"

Determination of metamaterial parameters by means of a homogenization approach based on asymptotic analysis

Abstract: By using modern additive manufacturing techniques, a structure at the millimeter length scale (macroscale) can be produced showing a lattice substructure of micrometer dimensions (microscale). Such a system is called a metamaterial at the macroscale, because its mechanical characteristics deviate from the characteristics at the microscale. Consequently, a metamaterial is modeled by using additional parameters. These we intend to determine. A homogenization approach based on asymptotic analysis establishes a connection between these different characteristics at micro- and macroscales. A linear elastic first-order theory at the microscale is related to a linear elastic second-order theory at the macroscale. Small strains (and, correspondingly, small gradients) are assumed at both scales. A relation for the parameters at the macroscale is derived by using the equivalence of energy at macro- and microscales within a so-called representative volume element (RVE). The determination of the parameters becomes possible by solving a boundary value problem within the framework of the finite element method. The proposed approach guarantees that the additional parameters vanish if the material is purely homogeneous; in other words, it is fully compatible with conventional homogenization schemes based on spatial averaging techniques. Moreover, the proposed approach is reliable, because it ensures that the obtained additional parameters are insensitive to choices of the RVE consisting of a repetition of smaller RVEs depending upon the intrinsic size of the structure.

Finite element analysis of natural fibers composites: A review

Abstract: Abstract Natural fiber composites (NFCs) also termed as biocomposites offer an alternative to the existing synthetic fiber composites, due to their advantages such as abundance in nature, relatively low cost, lightweight, high strength-to-weight ratio, and most importantly their environmental aspects such as biodegradability, renewability, recyclability, and sustainability. Researchers are investigating in depth the properties of NFC to identify their reliability and accessibility for being involved in aircrafts, automotive, marine, sports’ equipment, and other engineering fields. Modeling and simulation (M&S) of NFCs is a valuable method that contributes in enhancing the design and performance of natural fibers composite. Recently many researchers have applied finite element analysis to analyze NFCs’ characteristics. This article aims to present a comprehensive review on recent developments in M&S of NFCs through classifying the research according to the analysis type, NFC type, model type, simulation platform and parameters, and research outcomes, shedding the light on the main applicable theories and methods in this area, aiming to let more experts know the current research status and also provide some guidance for relevant researches.

Piezoresistive response of graphene rubber composites considering the tunneling effect

Abstract: The piezoresistive behavior of graphene conductive polymer composites is vital for the performance of smart-sensing materials. In this paper, a numerical method for predicting the piezoresistive properties of graphene rubber composites is established in which user subroutines include the quantum tunneling effect. A representative volume element (RVE) with randomly distributed graphene was constructed, taking into account the large deformation characteristics of the rubber matrix, which accurately predicted the conductivity, the percolation value, and the mechanical properties of the graphene rubber composites. Additionally, the strain sensing behavior of graphene rubber composites was calculated, which was in good agreement with the experimental results. The effects of the curved and crumpled graphene configuration, tunneling effect, and nanoparticle distribution on the piezoresistive response are discussed. These results play an essential role in evaluating and designing advanced smart rubber composites.

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

Abstract: 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.

Experimental and numerical study on HDPE/SWCNT nanocomposite elastic properties considering the processing techniques effect

Abstract: The aim of this study is to evaluate the elastic properties of high-density polyethylene (HDPE) using single-walled carbon nanotubes (SWCNTs) reinforcements with experimental and Finite element method (FEM) considering two different processing techniques effect. SWCNT nanoparticles were used to strengthen the HDPE matrix at the weight fractions (wt%) of 0, 0.2, 0.4, 0.6, 0.8, and 1 and the resulting nanocomposites were processed using injection and compression moulding. From each processing method, the HDPE/SWCNTs nanocomposites tensile test specimen were prepared and tested for the elastic properties. Experimental results showed that the addition of SWCNT nanoparticles for each weight fractions and both processing methods enhanced the elastic properties of HDPE. Finally, the numerical simulations were conducted using FEM for the prediction of the elastic modulus of HDPE/SWCNT nanocomposites for both processing methods. Whereby the representative volume element (RVE) model was presented with an interfacial phase region separating the load transfer between the SWCNT and HDPE with the properties obtained from the atomic modelling results. The numerical FEM elastic modulus results were found to correlate with the experimental results.

Effect of 3D Representative Volume Element (RVE) Thickness on Stress and Strain Partitioning in Crystal Plasticity Simulations of Multi-Phase Materials

Abstract: Crystal plasticity simulations help to understand the local deformation behavior of multi-phase materials based on the microstructural attributes. The results of such simulations are mainly dependent on the Representative Volume Element (RVE) size and composition. The effect of RVE thickness on the changing global and local stress and strain is analyzed in this work for a test case of dual-phase steels in order to identify the minimal RVE thickness for obtaining consistent results. 100×100×100 voxel representative volume elements are constructed by varying grain size and random orientation distribution in DREAM-3D. The constructed RVEs are sliced in depth up to 1, 5, 10, 15, 20, 25, 30, 40, and 50 layers to construct different geometries with increasing thickness. Crystal plasticity model parameters for ferrite and martensite are taken from already published data and assigned to respective phases. Although the global stress/strain behavior of different RVEs is similar (<5% divergence), the local stress/strain partitioning in RVEs with varying thickness and grain size shows a considerable variation when statistically compared. It is concluded that two-dimensional (2D) RVEs can be used for crystal plasticity simulations when global deformation behavior is of interest. Whereas, it is necessary to consider three-dimensional (3D) RVEs, which have a specific thickness and number of grains for determining stabilized and more accurate local deformation behavior. This estimation will help researchers in optimizing the computation time for accurate mesoscale simulations.

High fidelity simulation of the mechanical behavior of closed-cell polyurethane foams

Abstract: The mechanical behavior of closed-cell foams in compression is analyzed by means of the finite element simulation of a representative volume element of the microstructure. The digital model of the foam includes the most relevant details of the microstructure (relative density, cell size distribution and shape, fraction of mass in the struts and cell walls and strut shape), while the numerical simulation takes into account the influence of the gas pressure in the cells and of the contact between cell walls and struts during crushing. The model was validated by comparison with experimental results on isotropic and anisotropic polyurethane foams and it was able to reproduce accurately the initial stiffness, the plateau stress and the hardening region until full densification in isotropic and anisotropic foams. Moreover, it also provided good estimations of the energy dissipated and of the elastic energy stored in the foam as a function of the applied strain. Based on the simulation results, a simple analytical model was proposed to predict the mechanical behavior of closed-cell foams taking into the effect of the microstructure and of the gas pressure. An example of application of the simulation tool is presented to design foams with an optimum microstructure from the viewpoint of energy absorption for packaging.

Experimental and numerical approach to study mechanical and fracture properties of high-density polyethylene carbon nanotubes composite

Abstract: This work investigates the elasto-plastic and fracture properties of high-density polyethylene (HDPE) carbon nanotubes (CNTs) composite using a multi-scale finite element (MSFE) approach. The composites consist of CNTs, which are randomly embedded within the HDPE matrix throughout the volume. CNT reinforcement is numerically modelled by considering elastic properties while the elasto-plastic constitutive law is used for the matrix (HDPE) composition. Elastic properties of composites are estimated at meso-scale by numerical modelling of a representative volume element (RVE). Hollomon’s (power-hardening law) model has been employed to get the plastic properties of the polymer composite. Equivalent consecutive properties are predicted at meso-scale, further, these properties have been used at macro-scale simulation for fracture analysis. A detailed study of stress intensity factors has been presented for the different volume fraction of CNTs in the composite composition. The presented numerical results are supported by experimental investigations.

Micromechanical prediction of elastic-plastic behavior of a short fiber or particle reinforced composite

Abstract: Homogenized stresses of the fiber and matrix in a representative volume element (RVE) of a short-fiber or particle reinforced composite are calculated by extended Bridging Model. A matrix plasticity induced nonlinear deformation is predicted. All of the formulae are analytical and in closed-form, and only the original fiber and matrix properties are required. The homogenized stresses of the matrix must be converted into true values before used to determine an effective property of the composite. The true stress under a longitudinal tension is defined and evaluated in the first time. A geometric model is proposed to determine the matrix-to-fiber length ratio in the RVE. The effect of fiber orientations is considered in obtaining the composite properties from the RVEs. The predicted nonlinear responses are verified against the available experimental data of different fiber contents and fiber aspect ratios, showing that the true stress concept is critical for a reasonable prediction.

Computational micromechanics-based prediction of the failure of unidirectional composite lamina subjected to transverse and in-plane shear stress states:

Abstract: This paper presents a micromechanics-based 3D finite element model for predicting the damage initiation, propagation, and failure strength of TC33/Epoxy carbon fiber reinforced polymer (CFRP) unidi...

Effective strain gradient continuum model of metamaterials and size effects analysis

Abstract: In this paper, a strain gradient continuum model for a metamaterial with a periodic lattice substructure is considered. A second gradient constitutive law is postulated at the macroscopic level. The effective classical and strain gradient stiffness tensors are obtained based on asymptotic homogenization techniques using the equivalence of energy at the macro- and microscales within a so-called representative volume element. Numerical studies by means of finite element analysis were performed to investigate the effects of changing volume ratio and characteristic length for a single unit cell of the metamaterial as well as changing properties of the underlying material. It is also shown that the size effects occurring in a cantilever beam made of a periodic metamaterial can be captured with appropriate accuracy by using the identified effective stiffness tensors.

X-ray Micro-Computed Tomography of Polymer Electrolyte Fuel Cells: What is the Representative Elementary Area?

Abstract: With the growing use of X-ray computed tomography (X-ray CT) datasets for modelling of transport properties, comes the need to define the representative elementary volume (REV) if considering three dimensions or the representative elementary area (REA) if considering two dimensions. The resolution used for imaging must be suited to the features of interest in the sample and the region-of-interest must be sufficiently large to capture key information. Polymer electrolyte fuel cells have a hierarchical structure, with materials spanning multiple length scales. The work presented here examines the nature of the REA throughout a 25 cm2 membrane electrode assembly (MEA), focusing specifically on the micron length scale. Studies were carried out to investigate key structural (volume fraction, layer and penetration thickness, pore diameters) and transport (effective diffusivity) properties. Furthermore, the limiting current density of the nine regions was modelled. Stochastic heterogeneity throughout the sample results in local variations throughout. Finally, effects of resolution were probed by imaging using a range of optical magnifications (4× and 20×). The correlated and competing effects of voxel resolution and sampling size were found to cause difficulties where loss of clarity in the boundaries between phases occurs with larger imaging volumes.