Analysis Of Heterogeneous Materials Research Articles

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.

Determination of representative volume element size for a magnetorheological elastomer

Smart composite materials have been an active field of research in the last few decades. Magnetorheological elastomers (MREs) are examples of such smart composites and they show a coupling between magnetism and elasticity. MREs are heterogeneous materials and they consist of magnetic particles and a silicone-based elastomer. To describe and predict the behaviour of the macroscopic continuum accurately, microstructural information needs to be taken into account in the analysis of heterogeneous materials. Therefore, a combined approach called multi-scale analysis is used to consider various scales of observation simultaneously. The concept of Representative Volume Element (RVE) is typically employed by multi-scale approaches to describe the micro scale, and thus the size of RVE becomes a model parameter in such techniques. This has motivated the determination of the RVE size and the derivation of magnetoelastic constitutive relations in terms of the RVE sizes in our paper. The finite element method and a statistical analysis based on the coefficient of variation have been used to determine the RVE size of MREs. The results show that it is possible to determine a lower bound of the RVE size for an MRE. Furthermore, a parametric study has been conducted to examine the sensitivity of the RVE size on the different material properties of the constituents. It was found that the RVE size is primarily set by the contrast of the different material properties, i.e. the stiffness, permeability and magnetoelastic coupling coefficients.

Tunable X-ray dark-field imaging for sub-resolution feature size quantification in porous media

X-ray computed micro-tomography typically involves a trade-off between sample size and resolution, complicating the study at a micrometer scale of representative volumes of materials with broad feature size distributions (e.g. natural stones). X-ray dark-field tomography exploits scattering to probe sub-resolution features, promising to overcome this trade-off. In this work, we present a quantification method for sub-resolution feature sizes using dark-field tomograms obtained by tuning the autocorrelation length of a Talbot grating interferometer. Alumina particles with different nominal pore sizes (50 nm and 150 nm) were mixed and imaged at the TOMCAT beamline of the SLS synchrotron (PSI) at eighteen correlation lengths, covering the pore size range. The different particles cannot be distinguished by traditional absorption µCT due to their very similar density and the pores being unresolved at typical image resolutions. Nevertheless, by exploiting the scattering behavior of the samples, the proposed analysis method allowed to quantify the nominal pore sizes of individual particles. The robustness of this quantification was proven by reproducing the experiment with solid samples of alumina, and alumina particles that were kept separated. Our findings demonstrate the possibility to calibrate dark-field image analysis to quantify sub-resolution feature sizes, allowing multi-scale analyses of heterogeneous materials without subsampling.

NovADEC: Novel Approach for Determination of the Elemental Content of organic matter

ABSTRACT Organic matter (OM) significantly influences the physico-chemico-biological properties of geomaterials (viz., soils, sediments, municipal solid waste) and hence its accurate determination has profuse applications in agriculture, environmental and geotechnical engineering fields. OM mainly consists of carbon, hydrogen, nitrogen, and oxygen, collectively known as elemental content (EC), and these elements can be determined to estimate OM and its variation in several processes, including decomposition under the actions of thermal and biological activities. Usually, EC is determined by employing an elemental analyser, wherein the sample is exposed to an elevated temperature for the conversion of the elements to their respective gases (viz., CO2, H2O, N2, and NyOx) followed by detection of these gases to quantify the percentage of C, H, N, and O. However, this technique has limitations, including time-consuming process, expertise required for instrument operation, issues related to sample preparation and analysis of heterogeneous materials and the destruction of the analysed specimen. These provided the impetus for the development and validation of a Novel Approach for Determination of the Elemental Content, NovADEC, which employs Fourier-transform infrared (FTIR) spectroscopy and multiple regression analysis (viz., partial least-squares regression), as presented in the present manuscript. To develop NovADEC, five samples of different natures, including geomaterials and two standard materials (viz., cellulose and its derivative), with volatile solids ranging between 13% and 85% have been considered. Further, to create a wide range in ECs, sub-samples were thermally treated at furnace temperatures ranging between 150°C and 700°C. These sub-samples were subsequently analysed by employing elemental analyser and FTIR-spectroscopy techniques. A critical synthesis of the results demonstrates that the NovADEC predictive model facilitates a quick determination of the OM of geomaterials.

Fast and In-Situ Identification of Archaeometallurgical Collections in the Museum of Malaga Using Laser-Induced Breakdown Spectroscopy and a New Mathematical Algorithm

This paper reports the use of an advanced statistical algorithm for the recognition and classification of a set of 30 archaeological metallic objects from the Museum of Malaga. In-situ laser-induced breakdown spectrometry (LIBS) analysis was performed using a portable analyzer. The coordinate-obtaining method provided the statistical weights of each element in the sample. A comparative study between the coordinate-obtaining method and the linear correlation method is also discussed in order to corroborate the applicability of the proposed approach to the field of cultural heritage. The possibility of fast identification based on the simultaneous comparison of all the spectra in the reference LIBS library while allowing the analysis of heterogeneous materials is the main advantage of the method. In addition, statistical analysis (Euclidean distance analysis and binary diagrams) suggested that differentiating between archaeological sites is feasible.

A data-driven analysis on bridging techniques for heterogeneous materials and structures

A bridging technique based on Lagrange multipliers, namely the Arlequin method, is widely used for coupling multi-scale models. However, the definition of the following key parameters is still unclear: the energy partition functions, the characteristic length of the coupling operator and the size of the coupling zone. This work aims to investigate the influences of these factors on the coupling accuracy by conducting global sensitivity analysis on different multi-scale models. To this end, a data-driven model that approximates the input/output behavior of the numerical model is built by using the Sparse Polynomial Chaos Expansion (SPCE) methodology. Then, Sobol’ indices that quantify the sensitivity of the input factors are calculated analytically from the data-driven model with a negligible additional computational cost. Interaction effects among different parameters are also captured. Using this approach, several benchmark tests, including a coarse-fine bar model, a particle-continuum model and a 2D-1D sandwich model, are considered to explore the optimal settings of the coupling factors, which hopefully help for the multi-scale analysis of heterogeneous materials and structures.

Stochastic stress analysis of heterogeneous material considering random location variation of inclusion with an improved mesh superposition method

Stochastic stress analysis of heterogeneous material considering random location variation of inclusion with an improved mesh superposition method

A parallel and efficient multi-split XFEM for 3-D analysis of heterogeneous materials

We propose a parallel and computationally efficient multi-split XFEM approach for 3-D analysis of heterogeneous materials. In this approach, multiple discontinuities (pores and reinforcement particles) may intersect any given element (we call those elements multi-split elements). These discontinuities are modeled by imposing additional degrees of freedom at the nodes. The main advantage of the proposed scheme is that the mesh size remains independent of the relative distance among the heterogeneities/discontinuities. The pores and reinforcement particles are assumed to be spherical. The simulations are performed for uniform and non-uniform heterogeneity distribution. The Young’s modulus of the heterogeneous material is evaluated for different amount of pores and reinforcement particles. To demonstrate the computational efficiency of the multi-split XFEM, elastic damage analysis is performed for the unit cell with 5% pores and 5% reinforcement particles under uniaxial tensile loading. These simulations show that the Young’s modulus decreases linearly with the increase in the volume fraction of the pores and increases linearly with the increase in volume fraction of reinforcement particles. The multi-split XFEM is found to be at least 1.8 times computationally efficient than standard XFEM and at least 6.7 times computationally efficient than FEM.

An efficient multiscale stochastic stress analysis of heterogeneous materials considering quasi-periodicity of material properties in microstructure

An efficient multiscale stochastic stress analysis of heterogeneous materials considering quasi-periodicity of material properties in microstructure

A 3-D Interface-Enriched Generalized FEM for Electromagnetic Problems With Nonconformal Discretizations

An interface-enriched generalized finite-element method (IGFEM) is introduced for efficient 3-D electromagnetic analysis of heterogeneous materials. Without using meshes that conform to the material microstructures, which greatly lessens the burden of mesh generation, the method assigns generalized degrees of freedom (DOFs) at material interfaces to capture the discontinuities of the field and its derivatives. The generalized DOFs are supported by enriched vector basis functions (VBFs), which are constructed through a linear combination of the VBFs from the subelements. Several verification examples are provided to show that the IGFEM is not sensitive to the quality of the subelements and maintains the same level of solution accuracy and computational complexity as the standard finite-element method (FEM) based on conformal meshes. The potential of the proposed IGFEM is demonstrated by simulating some engineering problems with complex, periodic internal structures, including composite materials with randomly distributed spherical particles and ellipsoidal inclusions and microvascular channels.

Multilevel Adaptive Algorithm for Multiscale Analysis of Heterogeneous Materials

AbstractA multilevel adaptive FEM is proposed for multiscale mechanical analysis of heterogeneous materials. The algorithm is developed based on the extended multiscale FEM (EMSFEM), which has been proven to be an efficient method for multiscale mechanical analysis. A residual force-based error estimate is introduced, which is able to detect both global and local errors economically. The concept of microscopic numerical base function (NBF) is introduced, which can be used to refine the local results at the regions with a high-stress gradient level by level. Two efficient methods for updating the microscopic NBFs were developed, i.e., the hierarchical NBFs scheme and the residual force NBFs scheme. A hierarchical linear solver is designed to solve the multilevel equation system in each iteration step. In the algorithm, the calculations at the current iteration step take full advantage of the results of previous iteration steps, which is helpful to save computational resources. The numerical examples demons...

Enrichment based multiscale modeling for thermo‐stress analysis of heterogeneous material

SUMMARYThis paper details a novel new multiscale technique for modeling heterogeneous materials undergoing substantial thermal stresses. The technique is based on an enriched partition of unity approach that incorporates the thermal effects occurring on the microstructure into the global model. We demonstrate the effectiveness of this technique by implementing it into both the standard finite element method and the octree partition of unity method (OctPUM). The results demonstrate that the technique has uniquely improved accuracy over the homogenization method conditional to the method into which it is implemented in. The multiscale technique, when implemented into either the standard finite element method or OctPUM, increases the accuracy of the strain energy calculation. When the multiscale technique is implemented into OctPUM, it also is able to capture the unique stress fields on the microstructure of the model. Published 2012. This article is a US Government work and is in the public domain in the USA.

Multiscale Modelling Strategies for Heterogeneous Materials

This paper considers modelling strategies for the multiscale analysis of heterogeneous materials. Initial focus is on computational homogenization (e.g. [1-4]) which represents a powerful, albeit computationally intensive, technique for capturing the influence of an evolving microstrucuture on the overall macroscopic behaviour. First-order homogenization assumes that the representative volume element (RVE) is infinitely small compared to the macroscopic characteristic length scale and that there is clear separation of scales. Second-order schemes [2,4,5] are subsequently discussed as a possible solution. This approach introduces a material length scale into the macroscopic constitutive model and potentially enables geometric size effects to be captured. However, the size of the RVE now becomes an important parameter for the macroscopic response and there is no clear way of determining this length scale. Second-order computational homogenization is demonstrated in the context of an indentation problem. In situations where the RVE cannot be defined and there is no clear separation of scales, computational homogenization is not applicable and full resolution of the microstructure may be necessary. This paper summarises an efficient solution strategy for such situations following the work of Miehe and Bayreuther [6], with particular focus on fracturing heterogeneous materials, which utilises a geometric multi-grid preconditioner and the scale transition methodology from computational homogenization. This solution strategy is coupled with the use of the hybrid-Trefftz stress elements for modelling cohesive cracking [7]. The resulting modelling approach is demonstrated with the analysis of concrete dog-bone specimens where the different phases of matrix, aggregate and interfacial transition zone are explicitly modelled. Such an approach is still computationally intensive and so this paper also presents a novel hybrid multiscale approach that avoids the need for the finite element mesh to fully resolve all heterogeneities [8]. Classical micromechanics is utilised to enhance the approximation space in order to capture the effect of microstructural inclusions. In comparison to where the finite element mesh fully resolves the microstructure, this novel approach significantly reduces the number of degrees of freedom required while still accurately capturing the influence of the inclusions.

Nuclear magnetic resonance relaxation and diffusion in the presence of internal gradients: The effect of magnetic field strength

It is known that internal magnetic field gradients in porous materials, caused by susceptibility differences at the solid-fluid interfaces, alter the observed effective Nuclear Magnetic Resonance transverse relaxation times T2,eff. The internal gradients scale with the strength of the static background magnetic field B0. Here, we acquire data at various magnitudes of B0 to observe the influence of internal gradients on T2-T2 exchange measurements; the theory discussed and observations made are applicable to any T2-T2 analysis of heterogeneous materials. At high magnetic field strengths, it is possible to observe diffusive exchange between regions of local internal gradient extrema within individual pores. Therefore, the observed exchange pathways are not associated with pore-to-pore exchange. Understanding the significance of internal gradients in transverse relaxation measurements is critical to interpreting these results. We present the example of water in porous sandstone rock and offer a guideline to determine whether an observed T2,eff relaxation time distribution reflects the pore size distribution for a given susceptibility contrast (magnetic field strength) and spin echo separation. More generally, we confirm that for porous materials T1 provides a better indication of the pore size distribution than T2,eff at high magnetic field strengths (B0>1 T), and demonstrate the data analysis necessary to validate pore size interpretations of T2,eff measurements.

Simulated optimisation of disordered structures with negative Poisson’s ratios

Two-dimensional regular theoretical units that give a negative Poisson’s ratio (NPR) are well documented and well understood. Predicted mechanical properties resulting from these models are reasonably accurate in two dimensions but fall down when used for heterogeneous real-world materials. Manufacturing processes are seldom perfect and some measure of heterogeneity is therefore required to account for the deviations from the regular unit cells in this real-life situation. Analysis of heterogeneous materials in three dimensions is a formidable problem; we must first understand heterogeneity in two dimensions. This paper approaches the problem of finding a link between heterogeneous networks and its material properties from a new angle. Existing optimisation tools are used to create random two-dimensional topologies that display NPR, and the disorder in the structure and its relationship with NPR is investigated.

Thermo-Mechanical Analysis of Alumina-Zirconia Composites by a Hybrid Finite Element Method

In the present work a hybrid finite element method, based on the Voronoi Cell method, is proposed for the thermo-mechanical analysis of heterogeneous materials containing cracks. The proposed method uses two hybrid elements to model the second phase heterogeneities of the material and the crack tips. The method was used to analyze alumina-zirconia ceramic materials; specifically, effective elastic moduli, thermal expansion coefficients and stress intensity factors were calculated. The effects due to zirconia t → m phase transformation and thermal stresses, which develop during the cooling stage of sintering, were also taken into account in calculating the stress intensity factor.

Evaluation of effective electromagnetic properties in heterogeneous media

This paper presents the application of a homogenisation technique, based on the multi-scale expansion theory, to the analysis of heterogeneous materials constituted of magnetic inclusions dispersed in a dielectric lattice. The role of the shape and dimensions of the inclusions is analysed with reference to the effective electromagnetic properties and energy losses. The investigation is extended to the influence of flux waveforms with harmonic distortion, focusing the attention on the energy loss dependency on the harmonic content.

Parametric variational principle based elastic-plastic analysis of heterogeneous materials with Voronoi finite element method

The Voronoi cell finite element method (VCFEM) is adopted to overcome the limitations of the classic displacement based finite element method in the numerical simulation of heterogeneous materials. The parametric variational principle and quadratic programming method are developed for elastic-plastic Voronoi finite element analysis of two-dimensional problems. Finite element formulations are derived and a standard quadratic programming model is deduced from the elastic-plastic equations. Influence of microscopic heterogeneities on the overall mechanical response of heterogeneous materials is studied in detail. The overall properties of heterogeneous materials depend mostly on the size, shape and distribution of the material phases of the microstructure. Numerical examples are presented to demonstrate the validity and effectiveness of the method developed.

Statistically Equivalent Representative Volume Elements for Unidirectional Composite Microstructures: Part I - Without Damage

The representative volume element (RVE) of a material microstructure plays an important role in the analysis of heterogeneous materials, such as composites. Effective material properties in a composite material depend on the microstructural concentration and dispersion of different phases in the RVE. In this study, a combination of statistical and computational tools are proposed for identifying the statistically equivalent RVE (SERVE) for an elastic composite with nonuniform dispersion of inclusions. Numerical tests are conducted with various statistical functions of geometry, stresses, and strains to examine the validity of potential alternative definitions of the SERVE. In the first of this two-part article, methods are addressed for undamaged composite microstructures with continuous interfaces between the fiber and the matrix. The sequel article deals with the evolution of SERVE caused by damage due to interfacial debonding.

Modelling error estimation and adaptive modelling of perforated materials

AbstractTraditional computational analyses of perforated materials, much like traditional computational analyses of heterogeneous materials, involve the use of homogenization, using either the assumption of periodicity or the assumption of statistical homogeneity. Recently, Oden and Vemaganti (Journal of Computational Physics 2000; 164:22–47) have proposed a goal‐oriented approach to the modelling of heterogeneous multi‐phase linearly elastic materials that does not rely on such idealized situations. In this approach, the mathematical model is adaptively selected based on estimates of the modelling error: the error resulting from the smearing out of rapidly varying material moduli. The approach is said to be goal‐oriented because the adaptive process is driven by local estimates of modelling error in quantities of interest to the analyst, instead of global estimates. We extend this goal‐oriented adaptive approach to the case of perforated domains composed of linearly elastic materials. Toward this end, new global and local bounds on modelling errors resulting from homogenization of perforated materials are developed. A representative numerical experiment is presented. Copyright © 2004 John Wiley & Sons, Ltd.