Random Representative Volume Element Research Articles

Determination of effective properties of porous piezoelectric composite with partially randomly metalized pore boundaries using finite element method

In this study, we investigate the effective characteristics of a porous piezocomposite with randomly distributed pores of arbitrary size and with partly metalized pore boundaries. Using the ANSYS APDL finite element software, we created a novel random representative volume element (RVE), applied the finite element approach to solve boundary value problems of homogenization, and calculated equivalent properties using the Hill–Mandel principle. The results demonstrate that when large random RVE and an appropriate finite element mesh are used, the porous piezocomposite with randomly metalized porosity borders will have the same crystal symmetry as the piezoceramic matrix. Therefore, when there is a significant material contrast between the various phases, a large random RVE is preferred in the modeling of particulate-filled composites. Furthermore, when the areas of metalized surfaces increase, the performance of the investigated composite in transverse sensing and actuation applications improves.

Applying neural networks to analyse the properties and structure of composite materials

In this paper, we show how a simple convolutional neural network (CNN) can be trained to predict homogenised elastic properties of a composite material based on its representative volume element (RVE). We consider both 2D and 3D composites featuring two components with fixed isotropic elastic properties. The dataset used to train the neural network is obtained in two stages. The first stage is the generation of random RVEs and computation of their homogenised elastic properties using finite element analysis (FEA) with periodic boundary conditions (PBC) applied to them, and the second stage is the application of a data augmentation scheme to that dataset obtained in the first stage. For the 2D and 3D cases, we present two neural networks and show that they are able to estimate the values of homogenised elastic properties fairly accurately. At the same time, we confirm that the data generation stage is computationally very expensive and is a major challenge for machine learning based techniques in computational mechanics. Indeed, it is expensive even for “low resolution” RVEs such as those considered in our work, i.e. squares (2D case) or cubes (3D case) uniformly subdivided into 8x8 (2D case) or 8x8x8 (3D case) domains. We discuss the flaws and drawbacks as well as the possible developments and uses of this approach in multiscale modeling of composite materials.

Influence of the Geometric Parameters on the Fiber Stresses in Unidirectional Composites Subject to Transverse Loading

Abstract When a unidirectional (UD) composite is subjected to transverse loading, different fibers are not stressed equally. In this paper, realizations of virtual random representative volume element (RVE) and experimental SEM images are translated into finite element models and the average stresses in each fiber are determined. The average stress in individual fibers is correlated with various geometric parameters like nearest neighbor distance, the angle(s) between the nearest neighbor and local fiber volume fraction. A very loose correlation with significant outliers is observed. For the matrix, the region with the highest fiber content does not necessarily lead to the highest matrix stress. The fibers with highest average stresses and the regions with highest matrix stresses are difficult to determine and cannot be simply correlated with geometric parameters.

Investigation on carbon nanoparticle (CNP)-polymer sensors for fatigue monitoring of fiber-reinforced composites

Carbon nanoparticle (CNP)-polymer sensors are good candidates for monitoring structural damage. A combined numerical-analytical approach with considering the stiffness degradation of composite is proposed to calculate the resistance variations with the cyclic loads. The electro-mechanical behavior of the sensor can be simulated through the finite element analysis of a random representative volume element model and the equivalent resistance calculation of microcircuit. Then, taking the glass fiber-reinforced composite coated with the CNP-epoxy resin as example, its electro-mechanical behavior under tension-tension cyclic loading is investigated experimentally and numerically. Furthermore, by microscopic analysis, the fatigue damage monitoring mechanism of the sensor is revealed.

An incremental‐secant mean‐field homogenization model enhanced with a non‐associated pressure‐dependent plasticity model

AbstractThis article introduces a, possibly damage‐enhanced, pressure‐dependent‐based incremental‐secant mean‐field homogenization (MFH) scheme for two‐phase composites. The incremental‐secant formulation consists on a fictitious unloading of the material up to a stress‐free state, in which a residual stress is attained in its phases. Then the secant method is performed in order to compute the mean stress fields of each phase. One of the main advantages of this method is the natural isotropicity of the secant tensors that allows defining the linear‐comparison‐composite (LCC). In this work, we show that this isotropic nature is preserved for a non‐associated pressure dependent plastic flow, making possible the direct definition of the LCC. This model is thus able to represent the physics of real polymeric composites. The MFH scheme is then verified by testing its prediction capabilities in several cases, including cyclic and nonproportional loading involving perfectly elastic phases, elasto‐plastic and damage‐enhanced elasto‐plastic phases in random representative volume elements (RVE) of uni‐directional (UD) composites and of composites reinforced with spherical inclusions.

Comprehensive numerical characterization of a piezoelectric composite with hollow metallic inclusions using an adaptable random representative volume

This paper investigates a piezoelectric composite made up of a piezoceramic matrix with irregularly scattered random-sized hollow metal inclusions. This composite can be produced using a combination of porous ceramic fabrication methods and microcapsule transfer techniques that were previously utilized to deliver nanoparticle medicines in biomedical applications. The effective material characteristics were computed using a numerical homogenization methodology that included finite element analysis, random representative volume element, perfect contact between distinct phases, special linear boundary conditions, and the Hill–Mandel principle. To imitate the random distribution of inclusions inside a particle-filled composite, the relationship describing the inclusion’s volume fraction was adjusted by adding a regularity coefficient. Thus, a new representative volume was designed to study the effect of the non-uniform distribution of randomly sized inclusions on the effective coefficients of the composite. An analysis of the effective properties of this new composite system with metalized pores surfaces (SMPS) revealed the following features. Due to the presence of metallic impurities, the resulting electric induction field or mechanical stress field inside the piezoelectric phase is scattered, which raises the transverse piezoelectric moduli with the increase of the inclusion’s volume fraction. Also, the electrical permittivity coefficients increase steadily with the increase in the portion of the metallic impurities. According to the findings, the volume fraction of the inclusion can be considered the most critical parameter to modify the electromechanical characteristics of the SMPS. The effects of the regularity coefficient on the equivalent properties increase as the inclusion’s volume fraction increases. The effective dielectric constants decrease as the degree of regularity of the composite structure grows, increasing the effectiveness of the piezoelectric transducer in transverse energy harvesting and motor applications. The findings of the newly constructed representative volume were verified using a basic periodic unit-cell and a random representative volume based on the random sequential adsorption (RSA) method. The developed structure of the representative volume can be applied to simulate a wide range of composites in the form of solid particles. Piezoelectric transducers constructed from the proposed piezocomposite are predicted to function well in piezoelectric motors and transverse piezoelectric sensors.

Bounding transverse permeability of fibrous media: a statistical study from random representative volume elements with consideration of fluid slip

In this article, a statistical study on transverse permeability of random fibrous medium is performed. For that purpose, numerous random numerical microstructures are generated with constant or randomly varying fibre radii. Their statistical representativity with respect to experimental data is first briefly discussed. Flow simulations are then performed on these digital microstructures to retrieve their full transverse permeability tensor. The representative volume element (RVE) size is determined by studying convergence of permeability distribution when domain size increases. This allows to characterise the medium isotropy as well as the impact of geometrical randomness on permeability. The approach also integrates Gaussian process regression, that is a Bayesian machine-learning model, to consider variability within interpolation in the proposed permeability predictive model. In addition, this paper considers the impact of fluid slip at liquid/fibre interface on permeability for random fibrous media. An analytical expression is proposed to describe precisely the transition from a no-slip to a free-slip regime. This allows us to propose a probabilistic model that links permeability to both the fibre volume ratio and slip length. This finally yields two bounds for transverse permeability of fibrous media: a first related to statistical scattering and a second purely linked to fluid slip.

Prediction of the transverse elastic modulus of the unidirectional composites by an artificial neural network with fiber positions and volume fraction

This paper presents the development of artificial neural network (ANN) modeling for predicting the transverse elastic modulus of a unidirectional composite (E-glass/MY750) with fiber positions and volume fraction. For this prediction, random representative volume elements were generated according to the fiber volume fraction (). A training dataset consisting of input data ( and fiber locations) and output data (the effective elastic modulus), which were computed by the computational homogenization scheme (CHS), was used to train the ANN model to have proper weight and bias by back propagation. To demonstrate the performance of the proposed ANN model, prediction of the transverse elastic modulus of various test datasets whose transverse elastic moduli are known by CHS was conducted. The prediction accuracy was verified in terms of the mean squared error, correlation coefficient (R), and relative error. The prediction results showed excellent agreement with the test dataset and quickly predicted the transverse elastic modulus having random microstructures.

Random Fiber Array Generation Considering Actual Noncircular Fibers with a Particle-Shape Library

In this work, we generated a set of random representative volume elements (RVEs) of unidirectional composites considering actual noncircular cross-sections and positions of fibers with the aid of a shape-library approach. The cross-section of the noncircular carbon fiber was extracted from the M55J/M18 composite using image processing and a signed-distance-based mesh trimming scheme, and they were stored in a particle-shape library. The obtained noncircular fibers randomly chosen from the particle-shape library were applied to random fiber array generation algorithms to generate RVEs of various fiber volume fractions. To check the randomness of the proposed RVEs, we calculated spatial and physical metrics, and concluded that the proposed method is sufficiently random. Furthermore, to compare the effective elastic properties and the maximum von Mises stress in the matrix, it was applied to composite materials with different relative ratios of elastic moduli of M55J/M18 and T300/PR319. In the case of T300/PR319 having a high RRT (relative ratio of the transverse elastic moduli), simulation results were deviated up to about 5% in the effective elastic properties and 13% in the maximum von Mises stress in the matrix according to the fiber shapes.

Stress intensity factors and crack propagation of metal-ceramic random microstructures

This paper is concerned with the crack analysis of RVE (representative volume element) microstructures of metal-ceramic phase composite. The detailed random RVE microstructure models of metal-ceramic phase composite are generated by a mathematical RMDF (random morphology description functions) micro modeling technology. The dispersion pattern and scale of random microstructure models are controlled by the volume fractions V of base materials and the total number N of Gaussian functions. The stress intensity factors (SIF) and the crack propagation trajectories are evaluated by the interaction integral and predicted by Paris law. These crack characteristics are investigated with respect to the model scale N and the initial crack length, and also compared with those of homogenization models. Through the numerical results, it is observed that both SIFs and crack propagation trajectories are remarkably influenced by the crack length, the model scale N and the dispersion pattern of RVE microstructure.

Application of different plasticity models to PC/ABS blends within micromechanical approaches

AbstractRubber‐toughened thermoplastic polymers such as PC/ABS blends exhibit a non‐monotonic dependence of fracture toughness on composition, e.g. [6]. The key parameters determining the mechanical response of PC/ABS are the PC vs. ABS ratio and the rubber content in ABS. In this contribution, two micromechanical modeling approaches (single particle unit cell models, random representative volume elements) are considered to investigate this behavior. Thereby, different visco‐plasticity models are utilized to capture the specific deformation behavior of each phase. Computational studies of both micromechanical modeling approaches are compared to each other as well as to experimental data.

Efficient prediction of the electrical conductivity and percolation threshold of nanocomposite containing spherical particles with three-dimensional random representative volume elements by random filler removal

In this work, the effective electrical conductivity (EEC) and percolation threshold (PT) of a nanocomposite containing spherical particle fillers are predicted by computational homogenization schemes (CHS) with three-dimensional random representative volume elements (RVEs) by random filler removal (RFR). For this prediction, we prepare the RVE having the maximum filler volume fraction (Vf) of 52% with random particle fillers, also termed the master model, by the discrete element method (DEM), and the corresponding finite-element (FE) model is created. Then, 100 RVE samples for each Vf are derived by randomly replacing the material properties of several fillers by those of the matrix from the master model with diverse Vf from 5% to 50%. In addition, the interphase layer is employed by replacing some matrix elements with interphase elements according to the neighboring distance of the fillers.To demonstrate the performance of the proposed scheme, its randomness of RVEs is verified by spatial and physical metrics in terms of autocorrelation analysis, near-neighbor analysis, and directional conductivity ratio. The EEC prediction results with diverse Vf values are compared with those of an analytical model and test results. As a result, the PT at which EEC of the nanocomposites suddenly increases is successfully evaluated, and the effect of the void, interphase thickness, and conductivity, as well as the size of fillers on the EEC and PT is investigated through a sensitivity analysis.

Thermal conductivity of rubber composite materials with a hybrid AlN/carbon fiber filler

Composite materials with high thermal conductivity have the advantages of corrosion resistance, fatigue resistance, easy processing, and electrical insulation and hence are widely used in industries concerned with high heat dissipation, such as aviation, aerospace, and electronics. Adding with high thermal conductivity, such as carbon black, metal particles, carbon fiber, and carbon nanotubes, to rubber matrix materials is recognized as an efficient method to improve the thermal conductivity of the resulting composite materials. However, when single filler is used, the content of the often must be improved to obtain high thermal conductivity, which entails a complicated process and high production cost. In this study, a hybrid filler of spherical aluminum nitride (AlN) and carbon fiber is added to rubber matrix materials. These hybrid filler particles greatly influence the thermal conductivity of the composite materials. To explore the effects of the hybrid on the thermal conductivity of the composite materials, a three-dimensional random representative volume element (RVE) model filled with both spherical AlN and carbon fiber was developed using a random sequential addition method and homogenization theory. The size of the RVE model was 40 μm×40 μm×40 μm. To prevent the formation of larger fillers by the aggregation of small fillers, a lower volume fraction of filler was investigated in this study. ANSYS software was used to simulate the influence of the space distribution, volume ratio, and filling fraction of the two on the thermal conductivity of the composite material with hybrid fillers. A steady-state heat conduction model was adopted, and a temperature gradient from 20 to 40°C was applied in the X , Y , and Z directions. The results showed that the thermal conductivity was different in the three directions due to the difference in the orientation of the carbon fibers. It can be seen from the temperature distribution clouds that there are many thermal network paths in the direction of higher thermal conductivity. The average thermal conductivity in all directions could macroscopically characterize the thermal conductivity of the composite materials. Carbon fiber plays a dominant role in the thermal conductivity of the composite material, and the thermal conductivity increases linearly with the ratio of the fillers. When the volume fraction of the carbon fibers is constant, the thermal conductivity of the composite material increases slowly with the increase in the AlN fraction. In comparison, when the volume fraction of AlN is constant, the thermal conductivity of the composite material increases rapidly with the increase of in the carbon fiber fraction. Because of enhanced synergistic effects between the in the matrix, a lower filling fraction of carbon fibers could be used to obtain higher thermal conductivity when designing the structure of composite materials. The results of this study provide a theoretical basis for the preparation of composite materials with high thermal conductivity.

A micromechanical study of stress concentrations in composites

Random and periodic representations of composite microstructures are inherently different both in terms of the resultant range of stresses that each phase carries as well as the total load over the entire volume comprising both matrix and fiber phases. In this study, an algorithm was developed to generate random representative volume elements (RVE) with varying volume fractions and minimum distances between fibers. The random microstructures were analyzed using finite element models (FEM) and the results compared to those for periodic microstructured RVEs in terms of the range of stress values, maximum stress, and homogenized stiffness values. Using a large number of random RVE analyses, a meaningful estimation for range and average maximum stress in the matrix phase was achieved. Results show that random microstructures exhibit a much larger range of stress values than periodic microstructures, resulting in an uneven distribution of load and distinct areas of high and low stress concentration in the matrix. It is shown that the maximum stress in the matrix phase, often responsible for failure initiation, is largely dependent on the random morphology, minimum distances between fibers, and volume fraction. Moreover, it is shown that the predicted overall load-carrying capacity of the matrix changes depending on the use of random or periodic microstructures.

Stochastic Numerical Simulation for the Evaluation of Mechanical Properties of Filled Polymer Composites

Reinforced polymeric composites are profoundly used in variety of applications due to its high strength to weight ratio and ease of fabrication. The wide spread application of reinforced polymeric materials in the electronic industries have created a great demand in fabricating a kind of reinforced polymeric system, which is light but has better mechanical strength and good thermal properties. Especially glass microsphere filled epoxy resin composites is used as a potting compound in electronic and aviation industries. Therefore knowledge of the fundamental thermal and mechanical properties of these systems is highly essential in the formulation of advanced electronic potting compounds. In this work, the effective mechancial properties of glass microsphere filled epoxy system is investigated numerically by stochastic simulation. Numerical simulation software ANSYS is used to characterise the microstructure of the filled epoxy system. MATLAB code has been developed to model the randomness of the particle. The geometric model generated from the MATLAb code is given as an input to ANSYS. Random particle Representative Volume Element (RVE) model is used to evaluate the mechanical properties at various loading fractions. The effect of particle size on mechanical properties of glass microsphere filled epoxy composite is studied. Further the random RVE modeling scheme is compared with single RVE modeling scheme and its significance is reported. The numerically predicted values of effective modulus is then compared with the analytical models and with the literature experimental data. Also the significance of the analytical model on the determination of properties is reported. Then, the effect of interface on the mechanical characterisation by stochastic model is analysed and the debonding of the particle is also simulated.DOI: http://dx.doi.org/10.5755/j01.ms.23.1.14217

Micromechanical Modeling of Fiber-Reinforced Composites with Statistically Equivalent Random Fiber Distribution.

Modeling the random fiber distribution of a fiber-reinforced composite is of great importance for studying the progressive failure behavior of the material on the micro scale. In this paper, we develop a new algorithm for generating random representative volume elements (RVEs) with statistical equivalent fiber distribution against the actual material microstructure. The realistic statistical data is utilized as inputs of the new method, which is archived through implementation of the probability equations. Extensive statistical analysis is conducted to examine the capability of the proposed method and to compare it with existing methods. It is found that the proposed method presents a good match with experimental results in all aspects including the nearest neighbor distance, nearest neighbor orientation, Ripley’s K function, and the radial distribution function. Finite element analysis is presented to predict the effective elastic properties of a carbon/epoxy composite, to validate the generated random representative volume elements, and to provide insights of the effect of fiber distribution on the elastic properties. The present algorithm is shown to be highly accurate and can be used to generate statistically equivalent RVEs for not only fiber-reinforced composites but also other materials such as foam materials and particle-reinforced composites.

Computational modeling of the effect of equiaxed heterogeneous microstructures on strength and ductility of dual phase steels

In this study, a code was developed to create virtual random representative volume elements (RVEs) depicting the actual and highly equiaxed heterogeneous microstructure of ferrite–martensite dual phase (DP) steels. Within this approach it was possible to perform a parametric study of the effects of DP microstructure (e.g., volume fraction, size, and distribution of the martensite; grain size and boundaries of the ferrite; martensite–ferrite interphase) and mechanical properties of the ferrite and martensite phases on the overall stress–strain behavior. A finite strain elastic–viscoplastic constitutive model has been used in conducting these microstructural-based simulations. It is shown that plastic strain localization in the form of localized narrow bands significantly control the ductility and ultimate fracture of DP steels. It was also noticed that by adding viscosity into the material property, the ductility increased significantly without compromising the strength of DP steels. It is shown that by decreasing the size of martensite phase and considering the ferrite–martensite interphase the overall response yields a simultaneous increase in strength and ductility.

A unified level set based methodology for fast generation of complex microstructural multi-phase RVEs

In the frame of the multi-scale computational analysis of complex materials, the generation of Representative Volume Elements (RVE) is often a crucial step. Various microstructure generation tools may be used, depending on the material to be considered, such as Discrete Element Methods (DEM), Random Sequential Addition (RSA) based methods for particulate media requiring important computation times; or Voronoï tessellation methods for polycrystalline materials. Besides being material specific, some of these methods may become unaffordable when considering complex microstructures, large inclusions numbers or high volume fractions. The present contribution presents a unified level set based methodology for complex, periodic (or not) and random RVE generations. The presented methodology allows RVE generation for particulate granular media, polycrystalline aggregates with large size distribution and arbitrary shapes, as well as for complex three-phase or poly-phase microstructures. A level set controlled Random Sequential Addition algorithm is used for particle distribution generation, allowing increasing the RSA algorithm efficiency, generating large and dense populations of arbitrary shaped inclusions with precise control on neighboring distances. Starting from this, several methods are presented to add specific realistic features to the generated RVEs. Modifications and densifications allow the distribution pattern to fit observed real samples or to present a specific spatial organization. The addition of one (or more) phase(s) obtained from the growth of the initial inclusions allows reproducing some typical microstructural patterns such as grain bridging in clayey soils, interfacial transition zones in concrete or hydrated gel in cement paste. The versatility of the proposed RVE generation method is illustrated by means of various examples, reproducing realistic microstructural arrangements of clayey soils, irregular masonry and polycrystalline aggregates with bimodal size distributions.

Simulation of Two‐Phase Steels based on Statistically Similar Representative Volume Elements

AbstractAn increasing number of engineering structures in the fields of light weight constructions or automotive applications makes use of advanced high‐strength steels. To optimize the overall mechanical behavior computer simulations taking into account the micro‐heterogeneity of these materials have been becoming the major tool. Direct micro‐macro‐transition procedures, also known as the FE2‐method, provide a suitable numerical framework. The main problem of these methods applied to large random microstructures turns out to be the high computational cost with respect to both, the amount of memory and the computation time. In this context the definition of a representative volume element (RVE) plays an important role. Therefore, we focus on the construction of statistically similar RVEs (SSRVEs), which are characterized by a much less complexity than usual random RVEs and which represent still the mechanical response of the real material. For the construction of these SSRVEs we select several statistical measures of the microstructure of a two‐phase steel and assume them to be as similar as possible to the ones computed for the SSRVE. These measures are included in a least‐square functional, which has to be minimized. The accuracy of this method is presented by some representative numerical simulations, where the response of the real microstructure of the considered two‐phase steel and the SSRVEs is compared to each other. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Stochastic laminate analogy for simulating the variability in modulus of discontinuous composite materials

Abstract Recent composite technology research and development efforts have focused on discontinuous carbon fiber/epoxy molding systems derived from chopped aerospace-grade unidirectional tape prepreg. Although the average elastic modulus of this material has been shown to be as high as that of the continuous tape quasi-isotropic benchmark, experimental measurement by means of strain gage or extensometer has shown variation as high as 20%. Digital Image Correlation can be used successfully to obtain a full-field strain measurement, and it shows that a highly non-uniform strain distribution exists on the surface of the specimen, with distinct peaks and valleys. This pattern of alternating regions of high and low strain gradients, and which exhibit a characteristic shape and size, can be described in terms of Random Representative Volume Element (RRVE). The RRVE proposed here exhibits random elastic properties, which are assigned based on stochastic distributions. This approach leads to the analysis method proposed here, which is designed to compensate for the fact that traditional methods cannot capture the experimentally observed variation in modulus within a specimen and among different specimens. The method utilizes a randomization process to generate statistical distributions of fractions and orientations of chips within the RRVE, and then applies Classical Laminated Plate Theory to an equivalent quasi-isotropic tape laminate to calculate its average elastic properties. Validation of this method is shown as it applies to a finite element model that discretizes the structure in multiple RRVEs, whose properties are generated independently of the neighboring ones, and then are solved simultaneously. The approach generates accurate predictions of the strain distribution on the surface of the specimen.