Homogenization Procedure Research Articles

Micromechanics modelling of cement stabilised rammed earth

Rammed earth (RE) is a generic term for a number of construction materials that contain stabilised or non-stabilised earthen materials. RE materials are heterogeneous and their bulk performance depends on their mineralogical composition, physical texture, water content and mode of preparation. This category of building materials has recently been the subject of extensive studies, given the increasing interest in sustainable construction. This trend has highlighted not only the potential of RE, but also the lack of standards and guidelines that can promote its adoption by architects and builders. Predictive modelling techniques that faithfully forecast the mechanical behaviour of RE are also scarce. This study introduces a micromechanics approach and proposes a multi-scaling model to predict the mechanical behaviour of cement stabilised rammed earth (CSRE) in linear elasticity. The RE heterogeneity is addressed hierarchically at different scales separated by the sizes of their representative volume elements (RVE). Homogenisation procedures are applied to predict the material properties at each scale and investigate the overall macroscopic behaviour of earthen mixtures. The Mori-Tanaka homogenisation scheme is used to predict the linear elastic behaviour of CSRE by treating it as a porous composite. The theoretical results obtained by the application of various micro-mechanics-based models (Reuss-Voigt, Hashin-Strickman, Mori-Tanaka and Self-consistency) are assessed by comparison with the experimental data. The Mori-Tanaka homogenisation scheme proved to predict the material's macroscopic linear elastic behaviour fairly accurately while taking into account local heterogeneities.

Magnetically induced topological transitions of hyperbolic dispersion in biaxial gyrotropic media

Magnetically induced topological transitions of isofrequency surfaces of bulk waves propagating through an unbounded biaxial gyrotropic medium are studied. The medium is constructed from a two-component superlattice composed of magnetized ferrite and semiconductor layers. To derive the constitutive parameters of the gyrotropic medium, a homogenization procedure from the effective medium theory is applied. The study is carried out in the frequency range near the frequency of ferromagnetic resonance, where the magnetic subsystem possesses the properties of natural hyperbolic dispersion. The topological transitions from an open type-I hyperboloid to several intricate hyperbolic-like forms are demonstrated for the extraordinary waves. We reveal how realistic material losses change the form of isofrequency surfaces characterizing hyperbolic dispersion. The obtained results broaden our knowledge on the possible topologies of isofrequency surfaces that can appear in gyrotropic media influenced by an external static magnetic field.

A FEM Multiscale Homogenization Procedure using Nanoindentation for High Performance Concrete

This paper aims to develop a numerical multiscale homogenization method for prediction of elasto-viscoplastic properties of a high performance concrete (HPC). The homogenization procedure is separated into two-levels according to the microstructure of the HPC: the mortar or matrix level and the concrete level. The elasto-viscoplastic behavior of individual microstructural phases of the matrix are identified from nanoindentation data using an inverse identification method. The micromechanical results are then used as input parameters for numerical elasto-viscoplastic homogenization at microscale. The mortar level is analyzed with numerical homogenization by using the finite element simulation to predict the overall elasto-viscoplastic properties of HPC. The results are compared with macroscopic experimental and analytical results from the literature showing a good agreement.

Efficiency of Faith and Secular Based Microfinance Institutions

This paper represents numerical illustration with real data from three major continental regions Asia, Africa, and South America (Latin America & Caribbean). The financial and social data was obtained legally for each institution from the above regions and the aim is to examine the efficiencies with intermediate approach non-parametric two-stage data envelopment analysis (DEA) is implemented followed by Tobit regression random effect model. Here the faith and secular firms were identified and filtered later through smoothed homogeneous bootstrapped procedure the efficiencies are estimated with suitable inputs and outputs. The principles of respective religions are provided to show the differences. The efficiency of each financial institution is different socially and financially according to the geographical locations. The regression results are obtained by the censored model from a minimum value to the maximum value of the dependent variable.

Free vibration analysis of functionally graded hybrid matrix/fiber nanocomposite conical shells using multiscale method

This study is dedicated to propose a numerical solution for free vibration analysis of nanocomposite conical shells. The First-order Shear Deformation Theory (FSDT) is used to achieve the governing equations. Then, an efficient numerical method, namely the Generalized Differential Quadrature Method (GDQM), is employed to solve the Donnell-type governing differential equations. The effects of the nanofillers aggregation are investigated throughout this research. It is considered that a single conical shell is composed of a variety of the constituent material. This type of material includes three phases: polymer matrix, macro-scale fibers and nano-scale Carbon Nano Tubes (CNTs). Two well-known approaches, namely Han and Chamis, are employed for the homogenization procedure to obtain the equivalent material properties. It is worth mentioning that the power pattern is employed for the functionally distribution of CNTs within the polymer matrix. Furthermore, the effects of different boundary conditions, geometric and material properties on the dimensionless frequency parameter of the multiscale nanocomposite conical shells are considered. Afterward, a parametric study is implemented to determine the deep influences of the volume fraction of the nanofillers throughout the inclusion on the vibrational behaviors of conical shells. It is found out that increasing the agglomeration parameter increases the frequency parameter of the conical structures. Moreover, increasing the power exponent of the volume fraction of FG-CNT material deals decrease of the frequency parameter of conical shells. Comparing the obtained results with the outputs of some well-known benchmarks proves the correctness, accuracy and high capability of the proposed formulation.

A three-scale micro-mechanical model for elastic–plastic damage modeling of shale rocks

This paper is devoted to study the elastic–plastic damage behavior of heterogeneous shale rocks. The representative microstructure of this kind of rocks is first studied in order to define the representative elementary volume for the implementation of homogenization procedure. Three relevant material scales are considered. Inter-particle pores are distributed at the nanoscopic scale. Fine grains of calcite and kerogen are immersed at the microscopic scale. Large grains of minerals are embedded at the mesoscopic scale. Effective elastic properties of shale rocks are first determined by using a three-step linear homogenization procedure. The plastic damage behavior is estimated by developing a three-step nonlinear homogenization method. The effective plastic behavior of porous clay matrix with nanoscopic pores is described by an analytical model. The effects of small and large grains of various mineral inclusions are investigated by using a two-step incremental model. The damage due to progressive debonding of mineral inclusions is taken into account. After the implementation of the proposed model, comparisons between numerical results and experimental data are presented.

Tailoring microstructure and texture of annealed Al-Mn alloy through the variation of homogenization and prior cold deformation strain

The grain structures and crystallographic textures desired for various applications of aluminium alloys are usually modified by recrystallization during annealing. In this study, the interactions between recrystallization and precipitation were investigated using the same Al-Mn alloy but with different homogenization procedures (which gives different microchemistries in terms of solute level and second phase particle state) and prior cold deformation strains, both of which are easy to realize in industrial practice. The results show that recrystallization and precipitation kinetics are both promoted at large deformations but their mutual interactions also exist. Recrystallization is retarded by precipitation through the suppressing of nucleation and pinning of grain boundary migration, while early finish of recrystallization delays precipitation by reducing their nucleation sites. The delicate interplay between recrystallization and precipitation during annealing leads to different combinations of grain structures and textures. An equiaxed fine grain structure can be obtained when recrystallization is not affected by fine particles while the combined effects of a strong fibrous deformation structure, suppressed nucleation of recrystallization and preferential growth lead to a coarse elongated grain structure. Different crystallographic textures desired for typical applications of Al-Mn alloys can be obtained after annealing simply through the different combinations of homogenization procedures and prior cold deformations.

Green sago starch nanoparticles as reinforcing material for green composites

This study reports a new method of fabrication and application of “green” starch nanoparticles (SNPs) from local sago (Metroxylon Sagu) starch granules employing a high-pressure homogenization procedure. This approach is environmentally friendly, highly feasible, low cost and chemical-free with large-scale production capacity. In this work, SNPs' morphological, particle size and thermal properties were studied. The effects of SNPs concentration (ranging from 0 to 8% w/w) as nano-fillers in composite films’ barrier, transparency and contact angle were also investigated. Our results have shown that the fabricated SNPs exhibited excellent uniformity and spherical shapes. Addition of SNPs have demonstrated to enhance polymeric structure of nanocomposite film due to decreased water vapour permeability and increased contact angle. Sago SNPs as fillers pose an excellent prospect in green composites fabrication for material and biomedical purposes with potential application as carriers for drug delivery.

Homogenization Procedure Effect on Microscopical Performance of Concrete Containing Supplementary Cementitious Materials

The advantages of supplementary cementitious materials (SCM) use in concrete, such as reduced cement consumption and overall material improvement (durability, chemical resistance, etc.), are widely known. Our research focuses on two major factors connected to high performance concrete (HPC) containing SCM, the content of selected SCM and the homogenization process used for concrete mixture. Both of these aspects of this research were addressed by the authors from macro-level of the material. In this contribution, the focus is directed on microscopical performance of concrete mixtures with highest macro-mechanical features with respect to both homogenization procedure and SCM containment.

Effect of agglomeration of the nanotubes on the vibration frequency of the multi-scale hybrid nanocomposite conical shells: a GDQ-based study

In the present manuscript, the generalized differential quadrature method (GDQM) will be employed in order to solve the free vibration problem of three-phase carbon fiber/nanotube/polymer hybrid nanocomposite conical shells, rested on a two-parameter elastic medium, regarding for the influence of the agglomeration of the carbon nanotubes (CNTs) on the dynamic responses of the shell for the first time. The equivalent material properties of the multi-scale hybrid nanocomposite will be derived according to a two-step homogenization procedure including the Eshelby-Mori-Tanaka method incorporated with the modified form of the rule of the mixture. Afterward, the strain-displacement relationships of the continuous system will be obtained using the classical shell theory for thin-walled conical shells. Extending the Hamilton’s principle for the conical shell, the motion equation of the problem will be enriched. At the end, the associated boundary condition will be used in associated with the GDQ discretization for the purpose of extracting the natural frequency of the continuous system. The verification tests reveal that the presented mathematical framework is powerful enough to estimate the dynamic response of the system. The results of this study show that existence of agglomeration phenomenon can dramatically affect the dynamic behaviors of the nanocomposite structure.

A multiscale data-driven approach for bone tissue biomechanics

The data-driven methodology with application to continuum mechanics relies upon two main pillars: (i) experimental characterization of stress–strain pairs associated to different loading states, and (ii) numerical elaboration of the elasticity equations as an optimization (searching) algorithm using compatibility and equilibrium as constraints. The purpose of this work is to implement a multiscale data-driven approach using experimental data of cortical bone tissue at different scales. First, horse cortical bone samples are biaxially loaded and the strain fields are recorded over a region of interest using a digital image correlation technique. As a result, both microscopic strain fields and macroscopic strain states are obtained by a homogenization procedure, associated to macroscopic stress loading states which are considered uniform along the sample. This experimental outcome is here referred as a multiscale dataset. Second, the proposed multiscale data-driven methodology is implemented and analyzed in an example of application. Results are presented both in the macroscopic and microscopic scales, with the latter considered just as a post-process step in the formulation. The macroscopic results show non-smooth strain and stress patterns as a consequence of the tissue heterogeneity which suggest that a preassumed linear homogeneous orthotropic model may be inaccurate for bone tissue. Microscopic results show fluctuating strain fields – as a consequence of the interaction and evolution of the microconstituents – an order of magnitude higher than the averaged macroscopic solution, which evidences the need of a multiscale approach for the mechanical analysis of cortical bone, since the driving force of many biological bone processes is local at the microstructural level. Finally, the proposed multiscale data-driven technique may also be an adequate strategy for the solution of intractable large size multiscale FE2 computational approaches since the solution at the microscale is obtained as a postprocessing. As a main conclusion, the proposed multiscale data-driven methodology is a useful alternative to overcome limitations in the continuum mechanical study of the bone tissue. This methodology may also be considered as a useful strategy for the analysis of additional biological or technological hierarchical multiscale materials.

THE ROLE OF SCHOOL ARTISTIC ACTIVITIES IN MINIMISING AGGRESSION FOR PRIMARY SChOOL STUDENTS

This research seeks to prepare a program of school’s artistic activities that develops different new skills and experiences that help to vent negative emotions positively and expressing them in the form of artistic creativity that provides the student’s opportunity to benefit from his energy, ability and talent, which earns him self-confidence and responsibility towards himself and towards others and forming a positive concept of self that erases undesirable behaviors and alleviates the intensity of aggression among students. The research relied on the descriptive analytical approach in terms of it’s theoretical framework, where it dealt with a series of studies related to the subject of research as well as addressed (concept of artistic activities and their fields and objectives, school activity, the foundations of planning and evaluating activities, the role of art in modifying behavior, the role of artistic activities in the construction of personality Child, concept, causes and forms of aggression). The research also followed the semi-experimental approach in its practical aspect, which included the selection and application of Measure of aggressive behavior and statistical treatment of it, the selection of children who received high grades by scale, and the identification of the sample of the final study, which consisted of (20) children from the primary stage between the ages of 9-12 years, and the procedure of homogenization among the members of the sample, and the preparation of The program of artistic activities (artistic expression - stereoscopic expression), tribal, dimensional and tracking measurement, statistical processing of data, conclusions and discussion, presentation of educational recommendations and proposal of future research in this field

Modeling of contact interface between two material layers in hybrid structures

In hybrid structures, material layers of different mechanical properties are integrated to increase bearing capacity. When the difference in mechanical properties or thickness of the material layers is very large, debonding usually occurs along the interface between the two layers. This study uses a homogenization procedure combined with asymptotic algorithm applied on weaker/thinner materials to determine the interface stiffnesses for such structures. All the material layers and the interface are assumed to be linear elastic. Comprising with the available methods and numerical simulation results showed that the proposed model is more suitable with the work of the structures in reality. Furthermore, in this method the interface stiffnesses can be easily determined through the number and length of cracks and the dry or saturated state of the medium are also considered.

A hierarchical multiscale model for the elastic-plastic damage behavior of 3D braided composites at high temperature

A hierarchical multiscale model is established to reveal the failure mechanism of three-dimensional (3D) braided composites at high temperature. Firstly, the tensile and bending tests of the composites were performed at three different temperatures, and the properties of microscale constituents, i.e., carbon fiber, epoxy resin and interface, were also calibrated by experiments at different temperatures. Then, the elastic-plastic damage constitutive laws were proposed to characterize the mechanical behavior of microscale and mesoscale components. These constitutive models were implemented by a user-defined subroutine UMAT in ABAQUS. Finally, based on the homogenization procedure and the multiscale analysis method, the effects of temperature on microscale, mesoscale and macroscale properties of 3D braided composites were analyzed sequentially. The results showed that the temperature has the significant effects on the performances of 3D braided composites. With the increase of temperature, the properties of 3D braided composites decreased, and the failure modes changed from fiber breakage to matrix plastic deformation. Besides, the macroscopic simulation of strain fields agreed well with the DIC measurements and the temperature-dependent failure modes agreed well with SEM observation. It is expected that the established multiscale framework can predict high-temperature behavior of 3D braided composites and reveal the different failure mechanisms at different temperatures.

Stochastic micromechanics-based investigations for the damage healing of unsaturated concrete using electrochemical deposition method

The (micro-) cracks or (micro-) voids will lead to the damage of concrete material. A stochastic micromechanical framework is proposed to investigate the damage healing of the unsaturated concrete with the electrochemical deposition method. Stochastic micromechanical representations are presented based on the material’s random microstructures. Differential scheme-based multilevel homogenization procedures are proposed to quantitatively predict the effective properties of the repaired concrete. The probability density functions are obtained for the material’s effective properties with an efficient stochastic simulation framework, which is composed of the univariate approximation for the multivariate function, Newton interpolations and Monte Carlo simulations. Numerical examples are employed to verify the proposed stochastic micromechanical framework, which indicates that the presented framework is computationally efficient and capable of describing the electrochemical deposition method healing process for the unsaturated concrete considering the material’s inherent randomness. Finally, the influences of the saturation degrees and the equivalent aspect ratios on the probabilistic behavior of the repaired concrete are discussed on the basis of the proposed models.

Micromechanical Modelling of Dynamic Behavior of Advanced Sheet Molding Compound (A-SMC) Composite

Passive safety, particularly in the transport industry, requires maximizing the dissipation of energy and minimizing the decelerations undergone by a vehicle following a violent impact (crash). This paper proposes a strategy for identifying an anisotropic local damage criterion in a moderate dynamic loading for Advanced Sheet Molding Compound (A-SMC) composite materials. Multi-scale damage modelling based on the Mori-Tanaka approach is put forward. Previously, the results of an experimental campaign carried out on a range of strain rates varying from quasi static to 200 s−1 were used to identify a probabilistic local damage criterion based on Weibull’s formulation and integrate the effect of damage at a fiber-matrix interface scale. Therefore, the progressive local damage occurring under a fast loading may be described. A two-step homogenization procedure allows describing the strain rate effect on the stress-strain curves. The model gives also rise to the prediction of the progressive anisotropic loss of stiffness. Comparing between the experimental and numerical results confirms the ability of the proposed approach to describe the visco-damage effect (delay of damage threshold and decrease in damage kinetics) emphasized in A-SMC composites.

A three-scale index for flow in karst conduits in carbonate rocks

A three-scale model for flow in karst conduit networks in fractured carbonates is rigorously constructed based on a reiterated homogenization procedure. The first upscaling, performed from the high-fidelity flow model, is based on sequential partially and fully topological model reduction procedures considering two discrete networks of solution-enlarged fractures and conduits. The subsequent macroscopization procedure projects the reduced model into the cells of a coarse computational grid, where homogenized equivalent properties are numerically constructed. Such a two-level upscaling gives rise to a macroscopic flow model characterized by mass-transfer functions between the geological structures. A notable consequence of the approach proposed herein is the appearance of a new karst index concept, whose underlying physics relies on the generalization of the traditional Peaceman’s theory of well index. Such a concept rules the mass exchange between conduits and matrix and can be extended to the general scenario of coupled flow in multi-branch karst conduit systems, displaying general non-circular cross sections and surrounding damage zones. The downscaling representation for the karst index can be further explored to improve accuracy of the exchange coefficient between the geological objects. Numerical experiments are carried-out showing the magnitude of the index for certain conduit and fracture arrangements, along with illustrating the impact upon flow patterns.

Application of aeration-assisted homogeneous liquid-liquid microextraction procedure using Box-Behnken design for determination of curcumin by HPLC.

A simple, efficient, and rapid sample preparation method based on aeration-assisted homogeneous liquid-liquid microextraction was developed for determination of curcumin in food samples by high-performance liquid chromatography. The centrifuge step has been eliminated in this procedure. The effects of some variables, such as pH, volume of extraction solvent, extraction time, and salt effect, were studied through a Box-Behnken design method. Under the optimum conditions, calibration curves of curcumin were linear in the range of 0.08-4000μg/mL with R2 =0.997. Limit of detection and relative standard deviation were 0.019 μg/mL and 3.01%, respectively. The preconcentration factor achieved was 166. The proposed method was successfully applied to determination of curcumin in various food samples.

Thermoelastic homogenization of periodic composites using an eigenstrain-based micromechanical model

This paper presents a study on effective thermoelastic properties of composite materials with periodic microstructures. The overall elastic moduli and coefficients of thermal expansion of such materials are evaluated by a micromechanical model based on the Eshelby equivalent inclusion approach. The model employs Fourier series in the representation of the periodic strain and displacement fields involved in the homogenization procedures and uses the Levin's formula for determining the effective coefficients of thermal expansion. Two main objectives can be highlighted in the work. The first of them is the implementation and application of an efficient strategy for computation of the average eigenstrain vector which represents a crucial task required by the thermoelastic homogenization model. The second objective consists in a detailed investigation on the behavior of the model, considering the convergence of results and efficiency of the strategy used to obtain the approximate solution of the elastic homogenization problem. Analyses on the complexity of the eigenstrain fields in function of the inclusion volume fractions and contrasts between the elastic moduli of the constituent phases are also included in the investigation. Comparisons with results provided by other micromechanical methods and experimental data demonstrate the very good performance of the presented model.

Rheology of a Dilute Suspension of Aggregates in Shear-Thinning Fluids.

The prediction of the viscosity of suspensions is of fundamental importance in several fields. Most of the available studies have been focused on particles with simple shapes, for example, spheres or spheroids. In this work, we study the viscosity of a dilute suspension of fractal-shape aggregates suspended in a shear-thinning fluid by direct numerical simulations. The suspending fluid is modeled by the power-law constitutive equation. For each morphology, a map of particle angular velocities is obtained by solving the governing equations for several particle orientations. The map is used to integrate the kinematic equation for the orientation vectors and reconstruct the aggregate orientational dynamics. The intrinsic viscosity is computed by a homogenization procedure along the particle orbits. In agreement with previous results on Newtonian suspensions, the intrinsic viscosity, averaged over different initial orientations and aggregate morphologies characterized by the same fractal parameters, decreases by increasing the fractal dimension, that is, from rod-like to spherical-like aggregates. Shear-thinning further reduces the intrinsic viscosity showing a linear dependence with the flow index in the investigated range. The intrinsic viscosity can be properly scaled with respect to the number of primary particles and the flow index to obtain a single curve as a function of the fractal dimension.