Arrangement Of Inclusions Research Articles

Hardening Parameter Homogenization for J2 Flow with Isotropic Hardening of Steel Fiber-Reinforced Concrete Composites

Numerical modeling of the stress–strain state of composite materials such as fiber-reinforced concrete is a considerable computational challenge. Even if a computational grid with the resolution of all inclusions is built, it will take a great amount of time for the most powerful clusters to calculate the deformations of one concrete block with ideal parallelization. To solve this problem, the method of numerical homogenization is actively used. However, when plastic deformations are taken into account, the numerical homogenization becomes much more complicated due to nonlinearity. In this work, the description of the anisotropic nature of the hardening of the composite material and the numerical homogenization for the J2 flow with isotropic hardening is proposed. Here, the deformation of a composite material with a periodic arrangement of inclusions in the form of fibers is considered as a model problem. In this case, the assumption is made that inclusions have pure elastic properties. Numerical homogenization of the elasticity and plasticity parameters is performed on the representative element. The novelty of the work is related to the attempt at hardening parameter homogenization. The calculated effective parameters are used to solve the problem on a coarse mesh. The accuracy of using the computational algorithm is checked on model problems in comparison with the hardening parameters of the base material. The finite element implementation is built using the FEniCS computing platform and the fenics-solid library.

Analysis on the Dynamic Wave Attenuation Properties of Metaconcrete Considering a Quasi-Random Arrangement of Inclusions

The mitigation properties of metaconcrete cast with two types of resonant inclusions are assessed through wave transmission tests. Three cylindric metaconcrete specimens of regular size (20 cm height, 10 cm diameter), containing an equal number of different type of inclusions disposed in a semi-regular lattice, are tested in the longitudinal direction within the sonic range of frequencies. Inclusions, bi-material spheres consisting of a heavy core coated with a soft material, are characterized by a resonant behavior, evaluated numerically with a finite element modal analysis of a unit metaconcrete cell. Each metaconcrete specimen contains six layers consisting of six engineered aggregates of different type. Inclusions are disposed by rotating each layer with respect to the adjacent ones, as so as to create a pseudo-random arrangement. Specimens are excited by a sinusoidal signal of linearly growing frequency, sweeping a range centered at the translational eigenfrequency of the resonant inclusion. A standard plain concrete specimen is used as reference to define a transmissibility coefficient, that facilitates the quantification of the attenuation properties. With respect to plain concrete, all metaconcrete specimens show a marked (up to 80–90%) attenuation of the transmitted signal in proximity of the numerically estimated eigenfrequency of the inclusion. The intensity of the attenuation is weakly dependent on the type of the inclusion, while the frequency where the attenuation is observed depends markedly on the inclusion type. As a very positive quality in the view of practical applications, experimental results confirm that the attenuation effectiveness of metaconcrete is not related to the ordered microstructural arrangement.

A fast multipole BEM with higher-order elements for 3-D composite materials

The present work is to develop the FMBEM with quadratic elements to the analysis of 3-D linear elastic structures containing subdomains. To the numerical integration, an adaptive method with subdivision of elements is applied. The BEM formulation for perfectly bonded subdomains, in which interface traction forces are eliminated from the system of equations is implemented. The method is applied to problems of solids with spherical inclusions: a single inclusion, two interacting inclusions, many regularly distributed inclusions and randomly distributed inclusions. Different values of volume fraction of inclusions, up to 0.5 for the cubic arrangement of inclusions, and contrast in elastic properties between the matrix and inclusions, up to 1000 for the ratio of Young’s moduli of the constituents, are considered. Stresses or effective elastic constants are computed. The results are compared to analytical models and a good agreement is observed. The proposed method shows a perspective of modelling 3-D composites efficiently.

Experimental Investigation and Numerical Modelling on Strength and Fracture Behaviors of Sandstone with Weak Distributed Inclusions

In the diagenetic process of sedimentary rocks, inclusions widely exist in geological rock mass due to the intrusion of different lithologic rocks. In this paper, uniaxial compression experiments were performed on the sandstone specimens with weak inclusions of different distribution. The influence of inclusion arrangement on the strength and failure mode of the complex was analyzed. Due to the difference of lithology between inclusions and matrix, the mechanical behavior of specimens is different from that of homogeneous materials. Based on the laboratory experiments, the deformation and failure process of the composite model is further analyzed from the perspective of crack field and displacement field evolution by using the particle flow code. Indeed, the interaction mechanism and progressive nonlinear fracture behaviors between inclusions were discussed through the process of stress accumulation and transfer between the matrix and inclusions. The results show that the arrangement of inclusions can significantly affects the mechanical behaviors of composite specimens. In particular, due to the evolution process of the concentrated stress between the inclusions and matrix, the penetrating surface between inclusions and macroscopic fracture surface of specimens were successively formed, which resulted in the failure of the composite specimens showing the progressive nonlinear fracture characteristic. Furthermore, the interaction mechanism and progressive nonlinear fracture behaviors between inclusions are discussed through the process of stress accumulation and transfer between the matrix and inclusions.

Transport under advective trapping

Abstract

Induced anisotropy in composite materials with reconfigurable microstructure: Effective medium model with movable percolation threshold

In composite materials, with field-dependent restructuring of the filler material (changes in the mutual arrangement of inclusions), the presence of an external magnetic field induces anisotropy of the dielectric properties, even if the composite is isotropic in the absence of an external field. A modified effective medium approximation is proposed for the calculation of the components of effective permittivity within a class of composites with reconfigurable microstructure, where both phases (the filler and the matrix) are isotropic and the inclusions have spherical shape. The effective physical properties are calculated in the parallel and perpendicular directions to an applied field. The appearance of the anisotropy of the permittivity is simulated by the introduction of two not-equal, possibly variable (field-dependent) percolation thresholds. The implications, of the proposed theoretical approach, are demonstrated for the case of the dielectric properties of magnetoactive elastomers (MAEs). In MAEs with soft polymer matrices, the mutual arrangement of micrometer-sized magnetic inclusions can significantly change in an applied magnetic field. A reasonable agreement between theory and experiment at a measurement frequency of 1 kHz is found, and is improved in comparison to the previous models. The components of the effective permittivity tensor, characterizing the dielectric properties along the direction of the applied magnetic field and in the orthogonal direction, grow with an increasing field. This growth is more pronounced for the permittivity component in the field direction. The possible extensions of the theoretical model and future directions of research are discussed. The presented theoretical approach can be useful for the application-driven development of a number of smart materials, in particular electro- and magnetorheological gels, elastomers and fluids.

Polarization Control with Helical Metasurfaces

The ability to fully control the polarization of light using chiral metadevices has drawn considerable attention in various applications of integrated photonics, communication systems, and life sciences. In this work, we propose a comprehensive approach for the design of metasurfaces with desired polarization properties for reflected and transmitted waves based on the proper spatial arrangement of chiral inclusions in the unit cell. Polarization conversion is achieved by engineering induced electric and magnetic dipole moments of the metasurface inclusions. We show that under a proper arrangement, the same inclusion can be used as a building block of metasurfaces with drastically different wave-transformation functionalities. The horizontally and vertically oriented metallic helices were used as simplest chiral inclusions, which can be manufactured by the established 3D fabrication techniques from THz up to the visible spectral range. The proposed metadevices provide a deep understanding of the light–matter interaction for polarization conversions with helix-based structures and opens the way to new possibilities of electromagnetic polarization control with advanced chiral metadevices in communication and imaging systems.

Acoustic response for nonlinear, coupled multiscale model containing subwavelength designed microstructure instabilities.

Nonperiodic arrangements of inclusions with incremental linear negative stiffness embedded within a host material offer the ability to achieve unique and useful material properties on the macroscale. In an effort to study such types of inclusions, the present paper develops a time-domain model to capture the nonlinear dynamic response of a heterogeneous medium containing a dilute concentration of subwavelength nonlinear inclusions embedded in a lossy, nearly incompressible medium. Each length scale is modeled via a modified Rayleigh-Plesset equation, which differs from the standard form used in bubble dynamics by accounting for inertial and viscoelastic effects of the oscillating spherical element and includes constitutive equations formulated with incremental deformations. The two length scales are coupled through the constitutive relations and viscoelastic loss for the effective medium, both dependent on the inclusion and matrix properties. The model is then applied to an example nonlinear inclusion with incremental negative linear stiffness stemming from microscale elastic instabilities embedded in a lossy, nearly incompressible host medium. The macroscopic damping performance is shown to be tunable via an externally applied hydrostatic pressure with the example system displaying over two orders of magnitude change in energy dissipation due to changes in prestrain. The numerical results for radial oscillations versus time, frequency spectra, and energy dissipation obtained from the coupled dynamic model captures the expected response for quasistatic and dynamic regimes for an example buckling inclusion for both constrained and unconstrained negative stiffness inclusions.

A computationally efficient approach for predicting toughness enhancement in ceramic composites with tailored inclusion arrangements

Advanced manufacturing techniques such as extrusion-based methods have enabled the fabrication of ceramic composites with ordered inclusion phases (i.e. the size and position of the inclusion can be precisely controlled) to improve their overall strength and toughness. Conventional theories, simulation approaches, and experimental methods for analyzing fracture in composites with randomly dispersed inclusion phases (resulting in homogeneous, isotropic effective properties) become inadequate at understanding and designing composites with ordered inclusions for enhancing effective properties such as toughness. In addition, existing methods for analyzing fracture in composites can be computationally expensive and pose challenges in accurately capturing experimentally observed fracture growth. For example, extended finite element and phase-field methods are computationally expensive in evaluating the large design space of possible inclusion arrangements enabled by the new manufacturing techniques. In this work, a closed-form analytical model for the mixed-mode stress intensity factor in a composite with selected inclusion arrangements is presented, which expedites the analysis for various composite designs. Moreover, the fracture initiation calculation is adapted to approximate crack propagation with computational efficiency. The accuracy of this model for predicting fracture initiation is validated by linear elastic fracture mechanics analysis using the finite element method. The prediction of fracture propagation is validated using a phase-field model, as well as a 4-point bending experiment. Finally, the model is applied to analyze three different composite inclusion arrangements to study the effect of various material combinations and geometries on the overall toughness of the composite; a complete sampling of (and optimization) over the entire design space, however, is beyond the scope of this work. The relative increase in crack length (compared to a homogeneous material) is used as a metric to compare the relative toughness of three different composite designs. Within these designs, using the fast-running approximate method, the effect of the ratio of inclusion radius to inclusion spacing, and the elastic mismatch on the resulting crack length are compared to determine the composite arrangements that result in the greatest toughness enhancement for selected material properties. In particular, a multi-phase cubic array resulted in the greatest toughness enhancement of the designs considered.

Exclusión en el Golfo de México: una visión desde los pescadores sobre la industria petrolera en Tabasco

En las aguas someras de Tabasco se establecieron reglas para impedir la pesca alrededor de plataformas petroleras y de buques. En el artículo se analiza la percepción de exclusión de los pescadores frente a la petrolización en su espacio marino. Para conocer la visión de los pescadores, se realizaron tres talleres considerando la elaboración de mapas participativos sobre sus áreas de pesca y la actividad petrolera, y las tensiones entre ellos y los “otros”. La injusticia espacial aparece en la activa exclusión de los pescadores del espacio alrededor de plataformas petroleras, pero también —pasivamente— por la contaminación, la inseguridad y, más aún, por una frustrante idea de futuro. El artículo demuestra que estas exclusiones iniciaron con un arreglo aceptable de inclusión de pescadores, hasta construir un cerco para incrementar la extracción ante el agotamiento del sistema de extracción petrolera pública en México.Ideas destacadas: artículo de investigación sobre la exclusión pesquera en México a favor de las plataformas petroleras. Los pescadores perciben: 1) exclusión activa (legal y policíaca), mas no eficaz, y 2) exclusión pasiva (contaminación, inseguridad o falta de recursos pesqueros); lo cual conforma injusticia espacial. Para reducirla se requieren arreglos aceptables de inclusión, una oportunidad esperada con el gobierno de izquierda.

Petrology and U–Pb zircon age of the Variscan porphyroclastic Rand Granite at the southeastern margin of the Central Schwarzwald Gneiss Complex (Germany)

The Variscan Rand Granite as defined in this paper is a deformed I-type biotite granite that intruded along the southern-to-southeastern margin of the Central Schwarzwald Gneiss Complex. Former K-feldspar megacrysts (now porphyroclasts) of this K–Mg-rich alkali-calcic granite frequently show zonal crystallographic arrangement of mineral inclusions and are enclosed in a matrix of plagioclase, K-feldspar, quartz, biotite, apatite, zircon, and magnetite. Minor sphene and allanite are mostly altered. K-feldspar is orthoclase with perthitic exsolutions. Myrmekite is common and typically replaces marginal K-feldspar. Both feldspars show cataclastic and incipient ductile deformation that took place within the stability field of biotite (≥ 400 °C) as proven by grey varieties of Rand Granite with stable biotite. At most places, however, the Rand Granite shows a reddish colour, caused by late-stage chloritization of biotite and formation of hematite within K-feldspar. Furthermore, plagioclase became partially altered to sericite. This hydrothermal alteration took place at temperatures below the stability of biotite (< 400 °C). In situ ion probe U–Pb dating on zircon gave a concordant age of 330.9 ± 4.8 Ma (2σ), interpreted as the intrusion age of the Rand Granite. A large number of younger concordant to slightly discordant zircon ages between 309 and 90 Ma are interpreted to be due to episodic Pb loss during hydrothermal alteration. The Rand Granite apparently does not contain zircon domains older than the intrusion age and, furthermore, shows relatively high Zr contents (247–358 µg/g). These characteristics suggest high magma temperatures of at least 850–900 °C. The granitic magma most probably resulted from remelting of K-rich mafic to intermediate rocks in the middle crust at H2O-undersaturated conditions. Low Sr/Y ratios suggest a garnet-free residuum, which is only possible at pressures below ~ 0.9 GPa.

Flexural wave scattering by varying-thickness annular inclusions on infinite thin plates

This paper proposes a semi-analytical method for flexural wave scattering by cylindrical annular inclusions of varying thickness on an infinite thin plate. The thickness of inclusions is assumed to vary in arbitrary power form along the radial direction. In the numerical method, analytically linear relationships between expansion coefficients of exciting and scattered fields around each inclusion are firstly derived by means of closed form solutions of a hypergeometric governing equation of varying-thickness thin plates, and boundary conditions at the interface between different media. Then, linear algebraic equations containing only expansion coefficients of exciting fields are set up with the aid of foregoing linear relations. Expansion coefficients of exciting fields are finally solved by a numerical collocation method. Numerical examples of single and multiple scattering are designed to demonstrate the applicability of the method. The results of single scattering show the change of thickness variations allows tuning local resonances of inclusions to specified frequencies. Furthermore, displacement amplitude spectra of flexural waves for multiple scattering have captured the details of stop band formation of square and hexagonal arrangements of varying-thickness inclusions. It is also demonstrated that stop bands of flexural wave propagation can be controlled by changing stiffness gradients of varying-thickness inclusions.

Calculation of band structures of a phononic crystal within a waveguide in 3D with cubic inclusions using a Periodic Green’s Function Method

The Phononic Crystals have generated a growing scientific interest as a means to control the dispersion of waves in various technological applications such as telecommunications. In particular, Phononic Crystal Waveguides are composed of periodic distributions of dispersers immersed in a propagation medium and, designed by an arrangement with dimensions and periods comparable to the wavelength. These crystals have properties that give them the ability to guide acoustic waves efficiently. In this paper, we present a numerical Boundary Element Method, which requires the use of a Periodic Green’s Function. This method allows to calculate the band structure of phononic crystals in two- and three-dimensions. In particular, the band structure is calculated for a waveguide formed by two flat, and parallel plates that involve a two-dimensional periodic arrangement of cubic inclusions. All surfaces involved are considered acoustic hard surfaces. The system considered, in addition to being a waveguide is in itself a phononic crystal, so that this type of systems present an alternative to manufacture to phononic crystal that can act as a phononic crystal and as an acoustic waveguide. These properties present some interest from a technological point of view.

Tunable microstructure transformations and auxetic behavior in 3D-printed multiphase composites: The role of inclusion distribution

We experimentally and numerically investigate instability-induced pattern transformations and switchable auxetic behavior in multiphase composites consisted of circular voids and stiff inclusions periodically distributed in a soft elastomer. We specifically focus on the role of inclusion distribution on the behavior of the soft transformative composites. The inclusions are distributed in either square or triangular periodic configurations, while the voids are distributed in the triangular periodic array – the configurations enabling cooperative buckling induced transformations of the unit cells. Through the survey of microstructure parameter, we show that tailored positioning of the stiff inclusions can be exploited to expand the set of admissible switchable patterns in multiphase composites. Thus, extreme values of negative Poisson's ratio can be attained through applied strains; moreover, the onset of instabilities, and the corresponding switches to extremely soft behavior are shown to be controlled by the inclusion arrangements and volume fractions. Furthermore, the dependence of the microstructure buckling and post-buckling behavior on loading direction is investigated, and the composite anisotropic properties depending on the microstructure parameters are discussed.

Modeling of the Flows of Admixtures in a Random Layered Strip with Probable Arrangement of Inclusions Near the Boundaries of the Body

We study the random flow of admixtures in a two-phase stochastically inhomogeneous strip with the most probable arrangement of inclusions in the vicinity of the surfaces of the body. A mathematical model is formulated for the function of diffusion flow with nonzero constant initial concentration. A random diffusion flow is represented in the form of a Neumann series. The procedure of averaging of the random mass flow over the ensemble of phase configurations with arcsine distribution function is performed. The influence of the characteristics of the medium on the distribution of mass flow is analyzed. It is shown that if the diffusion coefficient of admixtures in the inclusion is higher than for the matrix, then the increase in the characteristic thickness of the layers causes a decrease in the value of the diffusion flow, whereas the mass flow in the entire body increases with the volume fraction of the inclusions.

Understanding the effect of deoxidation regime on the formation and arrangement of sulphide inclusions and on mechanical properties in steel

Understanding the effect of deoxidation regime on the formation and arrangement of sulphide inclusions and on mechanical properties in steel

Cr-spinel assemblage from the Upper Triassic gritstones of the northeastern Siberian Platform

An assemblage of Cr-spinels widespread in Carnian (Upper Triassic) diamondiferous deposits in the northeastern Siberian Platform is studied. Analysis of their morphology and chemical composition has revealed two dominant varieties of Cr-spinels and has demonstrated certain regularities in their distribution in the study area. Correlations have been established between the areal distribution of the recognized types of Cr-spinels and diamond varieties typical of kimberlite sources and between the distribution of Cr-spinels and rounded diamond dodecahedrons. The phase and chemical compositions of polyphase inclusions in the Cr-spinels are studied. The spatial arrangement of inclusions along the crystal growth zones indicates their primary genesis and trapping from the melt during crystallization. Compositional features of some minerals in the inclusions—SiO2 impurity in apatite and high CaO contents (0.2-0.8 wt.%) in olivines—point to a nonkimberlite source of these Cr-spinels. The presence of K- and Na-containing phases and calcite in the inclusions indicates saturation of the initial melt with alkalies, Ca, and CO2. The data obtained suggest that the numerous Late Vendian diatremes in K-rich alkaline basites of the Olenek Uplift area are the source of the dominant Cr-spinel variety.

Particle arrangement effects on the stress intensity in composite material

Motivated by recent advances in material design methods that allow for the controlled engineering of microstructure, we study how the degree of spatial ordering of the inclusions within a particle composite will affect the stress intensity factor associated with an existing crack. By exploring statistically representative sets of random inclusions using linear elastic fracture mechanics expressions, trends of the particle arrangement effect on the stress intensity factor are observed. We find that ordered, random, and clumped inclusion arrangements show an increasing effect on toughness, in that order. These results are verified using finite element analysis. To quantify the observed trend in material behavior with the spatial order of inclusions we consider two metrics of order: the bond-orientational order parameter, Q, and the translational order parameter, T. Finite element models of particle composites with increasing degrees of order reveal that the increasing effect on toughness can be captured and that T is more closely correlated to the effect on the stress intensity factor. We also find that the correlation between the stress intensity factor and particle arrangement is sensitive to the nearest-neighbor distance in Q, revealing that a quantifier approaching a global measure of order is more representative depending on the inclusion volume fraction. The results of this work can improve our understanding of how the stress intensity factor in particle composites explicitly varies with inclusion arrangement. It also provides key insights to develop formulations to engineer random composite microstructures for improved material fracture integrity and to identify issues in quality control of manufacturing methods involving particle distribution.

New algorithms for virtual reconstruction of heterogeneous microstructures

A new set of algorithms is introduced for the virtual reconstruction of heterogeneous material microstructures, in which morphologies of embedded particles/fibers are explicitly represented. As a pre-processing phase, a shape library containing morphologies of heterogeneities, parameterized in terms of Non-Uniform Rational B-Splines (NURBS), is extracted from digital data such as micro-computed tomography images. Two packing algorithms are then introduced to reconstruct an initial (raw) periodic microstructure: In the first approach, a set of hierarchical bounding boxes approximating particle shapes are employed to check for overlap. The second approach, which is specialized for fibrous microstructures, uses the NURBS representation of fiber centerlines during the packing process. An optimization phase is applied to build the final microstructural model, relying either on the Genetic Algorithm to selectively eliminate some of the inclusions or their sequential relocation within the raw microstructure. The objective functions of this optimization phase are designed to replicate the target statistical microstructural descriptors such as the volume fraction, size distribution, and spatial arrangement of inclusions. Several example problems are presented to show the application of these algorithms for synthesizing various heterogeneous microstructures, as well as their finite element modeling and simulation.

Deep Cement Mixed Walls with Steel Inclusions for Excavation Support

Deep cement mixed (DCM) walls are widely used in supporting excavations in many parts of the world. In this paper, a case study of an excavation supported by a DCM wall with steel inclusions is analysed using a three-dimensional finite element model and based on the coupled theory of nonlinear porous media. The DCM wall is constructed with wide flange steel inclusions. The stress–strain behaviour of the DCM wall section is simulated using an extended version of the Mohr–Coulomb model, which considers the strain-softening behaviour of DCM columns beyond yield. The computed lateral deformations are compared with the field measurements to validate the numerical modelling procedure. Using the same case study, the internal stability of the wall against bending and shear failure modes is investigated. In addition, the lateral pressure distribution along the wall length is investigated because in practice design is carried out considering a uniform pressure distribution assuming rigid wall movements. A parametric study was carried out to investigate the viability of DCM walls in supporting excavations by varying the spacing between steel inclusions, wall thickness and initial lateral earth pressure. Based on the results of the parametric study, guidelines are proposed to select the most efficient geometric arrangement of steel inclusions within DCM walls.