Equivalent Homogeneous Model Research Articles

Theoretical prediction on corrugated sandwich panels under bending loads

In this paper, an aluminum corrugated sandwich panel with triangular core under bending loads was investigated. Firstly, the equivalent material parameters of the triangular corrugated core layer, which could be considered as an orthotropic panel, were obtained by using Castigliano’s theorem and equivalent homogeneous model. Secondly, contributions of the corrugated core layer and two face panels were both considered to compute the equivalent material parameters of the whole structure through the classical lamination theory, and these equivalent material parameters were compared with finite element analysis solutions. Then, based on the Mindlin orthotropic plate theory, this study obtain the closed-form solutions of the displacement for a corrugated sandwich panel under bending loads in specified boundary conditions, and parameters study and comparison by the finite element method were executed simultaneously.

Determination of thermo-elastic parameters for dynamical modeling of 2.5D C/SiC braided composites

An approach on determining elastic parameters and Coefficient of thermal expansion (CTE) of a 2.5-dimensional (2.5D) braided composites is proposed in this paper, by adopting mesoscopic mechanics integrated Finite element (FE) modeling. According to the geometric features of meso-structure, Representative volume cell (RVC) models of composite for predicting thermo-elastic parameters are established. On the basis of the models, homogenized parameter prediction is carried out in three steps: Firstly, equivalent elastic properties is predicted subject to periodic displacement boundary conditions; secondly, the equivalent thermal modulus is determined by using the periodic non-adiabatic temperature boundary conditions; thirdly, using the obtained elastic parameters and thermal modulus to calculate the equivalent coefficient of thermal expansion. A multiscale finite element analysis is conducted: The thermo-elastic parameters of yarn is calculated using the RVC model; subsequently, the equivalent parameters of the yarn are substituted into the RVC of 2.5D braided C/SiC composites, to predict the thermo-elastic parameters. Results indicate that the CTE determined by homogenized parameter prediction of 2.5D C/SiC composites shows good agreements with the experimental results. At last, the refined FE model and the equivalent homogeneous model are employed to verify the effectiveness of the predicted parameters in terms of effective modeling. After the comparative analysis on thermal modal data between refined model and equivalent model, the acquired results demonstrate the effectiveness of the proposed method in determining thermo-elastic parameters.

Description of multilayer walls by means of equivalent homogeneous models

The accurate characterization of building envelopes represents the first step to realize a model of built structures, upon which is possible to work for the design of appropriate retrofit measures. External building walls, indeed, are one of the most significant paths of heat transfer between outer and inner environment and, as such, their control is crucial to go in the direction of energy saving. Simple models that capture the essential thermal characteristics of building walls, which are usually layered structures, would be desirable. A homogeneous wall that can be equivalent, under appropriate circumstances, to a given multilayer structure would provide an example of such a simple model. Homogeneous walls that are completely equivalent to generic multilayer walls are in general not achievable. However, we show in this work that this is possible in particular cases, i.e. if one focuses only on temperature or on heat flux behavior. It is shown that, in such situations, both an exact and an approximate solution for equivalent thermophysical properties can be devised. The evaluation of the level of approximation introduced is presented. In addition, the significance and the implications of the introduced equivalent models is discussed both regarding their exact and their approximate formulations.

The mechanical properties of human dentin for 3-D finite element modeling: Numerical and analytical evaluation.

The FEM is often used in investigations of dentin loading conditions; however, its anisotropy is mostly neglected. The purpose of the study was to evaluate the anisotropy and the elastic properties of an equivalent homogenous material model of human dentin as well as to compare isotropic and anisotropic dentin FE-models. Analytical and numerical dentin homogenization according to Luciano and Barbero was performed and E-modulus (E), Poisson's ratios (v) G-modulus (G) were calculated. The E-modulus of the dentin matrix was 28.0 GPa, Poisson's ratio (v) was 0.3; finite element models of orthotropic and isotropic dentin were created, loaded and compared using Ansys® 14.5 and CodeAster® 11.2 software. Anisotropy of the dentin ranged from 6.9 to 35.2%. E-modulus and G-modulus were as follows: E1 = 22.0-26.0 GPa, E2/E3 = 15.7-23.0 GPa; G12/G13 = 6.96-9.35 GPa and G23 = 6.08-8.09 GPa (highest values in the superficial layer). In FEM analysis of the displacement values were higher in the isotropic than in the orthotropic model, reaching up to 16% by shear load, 37% by compression and 23% in the case of shear with bending. Strain values were higher in the isotropic model, up to 35% for the shear load, 31% for compression and 35% in the case of shear with bending. The decrease in the volumetric fraction and diameter of tubules increased the G and E values. Anisotropy of the dentin applied during FEM analysis decreased the displacements and strain values. The numerical and analytical homogenization of dentin showed similar results.

Quasi-steady state conditions in heterogeneous aquifers during pumping tests

Classical Thiem's well hydraulic theory, other aquifer test analyses, and flow modeling efforts often assume the existence of “quasi-steady” state conditions. That is, while drawdowns due to pumping continue to grow, the hydraulic gradient in the vicinity of the pumping well does not change significantly. These conditions have built upon two-dimensional and equivalent homogeneous conceptual models, but few field data have been available to affirm the existence of these conditions. Moreover, effects of heterogeneity and three-dimensional flow on this quasi-steady state concept have not been thoroughly investigated and discussed before. In this study, we first present a quantitative definition of quasi-steady state (or steady-shape conditions) and steady state conditions based on the analytical solution of two- or three-dimensional flow induced by pumping in unbounded, homogeneous aquifers. Afterward, we use a stochastic analysis to investigate the influence of heterogeneity on the quasi-steady state concept in heterogeneous aquifers. The results of the analysis indicate that the time to reach an approximate quasi-steady state in a heterogeneous aquifer could be quite different from that estimated based on a homogeneous model. We find that heterogeneity of aquifer properties, especially hydraulic conductivity, impedes the development of the quasi-steady state condition before the flow reaching steady state. Finally, 280 drawdown-time data from the hydraulic tomographic survey conducted at a field site corroborate our finding that the quasi-steady state condition likely would not take place in heterogeneous aquifers unless pumping tests last a long period.Research significance(1) Approximate quasi-steady and steady state conditions are defined for two- or three-dimensional flow induced by pumping in unbounded, equivalent homogeneous aquifers. (2) Analysis demonstrates effects of boundary condition, well screen interval, and heterogeneity of parameters on the existence of the quasi-steady, and validity of approximate quasi-steady concept. (3) Temporal evaluation of information content about heterogeneity in head observations are analyzed in heterogeneous aquifer. (4) 280 observed drawdown-time data corroborate the stochastic analysis that quasi-steady is difficult to reach in highly heterogeneous aquifers.

Equivalent homogeneous model of D31-mode longitudinal piezoelectric transducers

This article focuses on modelling of D31-mode longitudinal piezoelectric transducers. A simple equivalent one-dimensional homogeneous model of D31-mode longitudinal piezoelectric transducers is proposed in this article. Homogeneous properties of the model are derived by a simple analytical mixing method based on the operation principle of D31-mode longitudinal piezoelectric transducers. Compared with other models in the literature, the proposed homogeneous model can consider passive layers in D31-mode longitudinal piezoelectric transducers for more accurate predictions in either static or dynamic behaviour. The proposed model is validated by a three-dimensional finite element model. Besides, based on the homogeneous model and borrowing the network theory, an exact equivalent circuit is formulated. A more straightforward form of the equivalent circuit can further facilitate analysis and modelling of D31-mode longitudinal piezoelectric transducers. Also, the proposed homogeneous model is wrapped into a transfer matrix form. The formulated transfer matrix of D31-mode longitudinal piezoelectric transducers can be used with the transfer matrix method to facilitate the calculations, when D31-mode longitudinal piezoelectric transducers are connected with numerous mediums in the operation direction. The effectiveness of the equivalent circuit and the transfer matrix is also verified.

Numerical modeling and testing of mechanical behavior of AM Titanium alloy bracket for aerospace applications

A key issue in designing a new product made through the Additive Manufacturing (AM) is the prediction of mechanical properties of material. Several experimental results show that AM-based products are often affected by widespread porosity, low density regions within their volume and anisotropy. Those effects are due to the manufacturing process, despite of efforts spent to improve the process parameters. This paper presents the numerical modelling of a geometrically complex structural bracket for aerospace application, which was re-designed through a topological optimization and produced in Ti-6Al-4V by means of the AM. The design activity herein described required to resort to a suitable model of constitutive properties of material by facing the problem of a large number of porosity/low density areas, as detected by a tomographic analysis of the mechanical component. According to some references an equivalent isotropic and homogeneous model of material was applied. Nevertheless the limitations of that approach were investigated through a validation of the numerical model and a testing activity. It was demonstrated that the Finite Element model based upon the assumptions of homogeneous and isotropic material might be effective in predicting the material and component strength, at least in static design, but even in case of design against fatigue, provided that a suitable experimental characterization of material was performed. The procedure of optimization was then assessed and compared to some preliminary tests performed on the real component, thus providing a preliminary good practice to the industrial partner involved in this research activity.

Geologic influence on groundwater salinity drives large seawater circulation through the continental shelf

AbstractObservations of offshore freshened groundwater and saline groundwater discharge along continental shelves have important implications for water resources, ecosystem function, and the composition of the ocean, but they cannot be explained by basic theory. We show that these independent observations are linked and result from processes that drive variable‐density groundwater flow through the spatial heterogeneity that is ubiquitous in geologic formations. We use lithologic data to develop geostatistical models that mimic the architecture of coastal aquifers. Simulation of groundwater flow and salt transport through these random realizations shows that heterogeneity produces spatially complex subsurface salinity distributions that extend tens of kilometers offshore, even at steady state. The associated density gradients drive high saline groundwater circulation rates that cannot be predicted by equivalent homogeneous models. Results suggest that these phenomena may be common along continental shelves, potentially altering estimates of ocean chemical budgets and impacting coastal water management for future generations.

Development of a molecular dynamic based cohesive zone model for prediction of an equivalent material behavior for Al/Al2O3 composite

The interfacial behavior of composites is often simulated using a cohesive zone model (CZM). In this approach, a traction-separation (T-S) relation between the matrix and reinforcement particles, which is often obtained from experimental results, is employed. However, since the determination of this relation from experimental results is difficult, the molecular dynamics (MD) simulation may be used as a virtual environment to obtain this relation. In this study, MD simulations under the normal and shear loadings are used to obtain the interface behavior of Al/Al2O3 composite material and to derive the T-S relation. For better agreement with Al/Al2O3 interfacial behavior, the exponential form of the T-S relation suggested by Needleman [1] is modified to account for thermal effects. The MD results are employed to develop a parameterized cohesive zone model which is implemented in a finite element model of the matrix-particle interactions. Stress-strain curves obtained from simulations under different loading conditions and volume fractions show a close correlation with experimental results. Finally, by studying the effects of strain rate and volume fraction of particles in Al(6061-T6)/Al2O3 composite, an equivalent homogeneous model is introduced which can predict the overall behavior of the composite.

Optimal design of thermal loaded composites filled with curvilinear fibers

The problem of optimal design of shape and orientation of fibers in composite material, leading to the local inhomogeneity of its parameters, is considered in this paper. The paper concerns the problem of curvilinear fibers arrangement in the composite material, so that the structural element made from this material can fulfill the requirements imposed on its thermal properties. An equivalent homogeneous orthotropic model of the composite is utilized for this purpose and next, basing on this model, the attempt is taken to determine the most profitable orientation and arrangement of fibers in the layers of the composite in order to obtain the desired behavior of structure. To solve this problem, the optimization method based on evolutionary algorithm is applied, and it is supplemented with finite element method for heat transfer analysis.

Comparative investigation on microstructure-based modelling for the orthogonal cutting of AISI1045

With the feed rate decreasing to the dimension of grain size and tool edge radius, cutting process is often carried out in the grain interior and grain boundary. In this paper, the orthogonal cutting process of hot-rolled AISI1045 steel is studied and its metallographic microstructure is analyzed for the establishment of microstructure-based models which incorporate the effect of ferrite and pearlite grains. In order to discover the contribution of microstructure and edge radius to the cutting process, three contrast simulation models including equivalent homogeneous material model with rounded-edge cutting insert (model I), rectangular grain model with sharp edge cutting insert (model II), and rectangular grain model with rounded-edge cutting insert (model III) are built up for the orthogonal cutting processes of hot-rolled AISI1045. Then Voronoi grain model (model IV) and real grain model (model V) are also developed to compare with model III to study the effect of grain shape on the cutting process. The simulation models are compared with the experiments in terms of chip morphology, cutting force, and specific cutting force. And the examination on the stress distribution shows that the real grain model with tool edge radius discovers more details about the mechanics in primary shear zone.

Multiscale analysis of heat treatments in steels: Theory and practice

Multiphase steels offer impressive mechanical properties. However, their characterisation still represents a challenge. In a quenching process, phenomena such as undesirable strains or residual stresses are inevitable and can be the cause for non-admissible final parts. Microstructural phase transformations generally magnify the problem. The non-existence of efficient non-destructive experimental procedures capable of measuring them leads to the need of numerical tools capable of quantifying these undesirable effects.In this work, a numerical multiscale transient model, that uses the Asymptotic Expansion Homogenisation (AEH) methodology combined with Finite Element Method (FEM), is proposed for the analysis of heat treatments in steels. The implementation of the AEH method is carried out using the commercial program Abaqus, considering an uncoupled and transient problem with implicit time integration. Within the homogenisation method, the existence of two distinct scales is assumed, defining a micro- and a macroscale. In the smaller scale, the evolution of a steel periodic microstructure is analysed in detail and an equivalent homogeneous material model is established for macroscopic use. Moreover, it is presented in this work that AEH is a rigorous and effective homogenisation method that allows the modelling of the thermomechanical and transient thermal behaviour in periodic materials, particularly in heat treatments.

Simulation of Meso-Scale Machining of AISI1045 Based on Multiphase Model

In the meso-scale machining, feed rate, grain size and tool edge radius are in the same order of magnitude, and cutting process is often carried out in the grain interior and grain boundary. In this paper the meso-cutting process of hot-rolled AISI1045 steel is studied and its metallographic microstructure is analyzed for the establishment of multiphase models which incorporate the effect of ferrite and pearlite grains. In order to discover the applicability of multiphase models to the simulation of meso-cutting, three contrast simulation models including multiphase model with rounded-edge cutting insert (model I), multiphase model with sharp edge cutting insert (model II) and equivalent homogeneous material model with rounded-edge cutting insert (model III) are built up for the meso-orthogonal cutting processes of hot-rolled AISI1045. By comparison with the experiments in terms of chip morphology, cutting force and specific cutting force, the most suitable model is identified. Then the stress distiribution is analyzed. And it is found that multiphase model with tool edge radius can give a more accurate prediction of the global variables and reveal more about these important local variables distribution.

Radar signatures of snowflake riming: A modeling study.

The capability to detect the state of snowflake riming reliably from remote measurements would greatly expand the understanding of its global role in cloud‐precipitation processes. To investigate the ability of multifrequency radars to detect riming, a three‐dimensional model of snowflake growth was used to generate simulated aggregate and crystal snowflakes with various degrees of riming. Three different growth scenarios, representing different temporal relationships between aggregation and riming, were formulated. The discrete dipole approximation was then used to compute the radar backscattering properties of the snowflakes at frequencies of 9.7, 13.6, 35.6, and 94 GHz. In two of the three growth scenarios, the rimed snowflakes exhibit large differences between the backscattering cross sections of the detailed three‐dimensional models and the equivalent homogeneous spheroidal models, similarly to earlier results for unrimed snowflakes. When three frequencies are used simultaneously, riming appears to be detectable in a robust manner across all three scenarios. In spite of the differences in backscattering cross sections, the triple‐frequency signatures of heavily rimed particles resemble those of the homogeneous spheroids, thus explaining earlier observational results that were compatible with such spheroids.

Analysis of Steel Phase Transformations Using a Multiscale Transient Model

Multiphase steels offer impressive mechanical properties. However, their characterization still represents a challenge. In a quenching processes, phenomena such as undesirable strains or residual stress are inevitable and can be the cause for non-admissible final parts. Microstructural phase transformations generally magnify the problem. This fact leads to the need of numerical tools capable of quantifying these residual stresses, due to the non-existence of efficient non-destructive experimental procedure capable of measuring them. In this work, a numerical multiscale transient model, that uses the Asymptotic Expansion Homogenisation (AEH) method combined with finite element method (FEM), is proposed. The implementation of the AEH method is carried out using the commercial program Abaqus, considering an uncoupled and quasi-static transient problem with implicit time integration. Within the homogenisation method, the existence of two distinct scales is assumed, defining a micro and a macroscale. Within the smaller scale, the evolution of a steel periodic microstructure is analysed in detail and an equivalent homogeneous material model is established for macroscopic use. However, the microstructural evolution leads to the need of new equivalent homogeneous models in order to predict the macro response. Consequently, several mechanical, thermomechanical and transient thermal homogenization procedures are carried in order to establish different equivalent homogeneous models.

Modeling the degradation of old subway galleries using a continuum approach

The underground transit system of the Paris metro was built in the early 20th century. Many tunnels and galleries of this underground system were constructed with old masonry whose properties have changed with time and increasing use, and its strength may have deteriorated under the impact of several weathering factors. Therefore, research has been initiated to diagnose structural deterioration of the tunnels and galleries used by the Paris metro system. This paper outlines the current state of the metro galleries in which cracks have developed in the tunnel lining caused by degradation of the abutment materials. The initial state of the stresses applied to the structure immediately after the construction is also analyzed through a double comparison (analytical–numerical and numerical 2D–3D). Then the damage of the galleries is modeled by taking into account the effect of the tunnel linings’ reduced strength. By means of an equivalent homogeneous model and a strain-softening approach, deformations associated with crack appearance can be located. The numerical results show that the state of different components of the underground structure during the lifetime of the galleries can be assessed.

Compression–shear strength criterion of coal–rock combination model considering interface effect

Surrounding rocks around coal tunnel in western mining area of China are typical composite structures composed of weakly cemented soft rock and hard coal, and the tunnel stability is closely related to the overall mechanical behavior of the combination body. The equivalent homogeneous model of coal–rock combination body and its stress state expressions were firstly established based on the strain energy equivalency principle. Then, the general compression–shear failure criterion of the equivalent model which takes into account the cohesive strength of the interface between coal and soft rock was derived by assuming that the yielded mediums all met Mohr–Coulomb criterion. Furthermore, accuracy of the proposed analytical model was verified by carrying out laboratory test for coal-mudstone specimen, and it found that the theoretical results were in good agreement with the test values. Strength of the combination body lies between the strong body and weak body. Finally, the effects of interface cohesion strength, rock thickness and stress level on the failure behavior of combination model were analyzed based on the analytical model. Results show that the proposed model not only contains the classical sliding failure theory for two-dimensional weak plane presented by Jaeger, but also reflect strength behavior of a more complex composite model composed of different rock mediums and structural plane. Thus, the analytical model provides theoretical basis for further studying the mechanical behavior of coal–rock combination model.

A simple homogenization scheme for 3D finite element analysis of composite bolted joints

Usually a three-dimensional (3D) finite element model is used for analyzing laminated composite bolted joints, because the stress and strain vary in all directions due to factors such as bolt bending and tilting, bolt pre-load and secondary bending. In general, the advantage of symmetry can greatly reduce the modeling and computational time in a 3D analysis. However, due to different lamination angles in laminated composite structures, symmetric model may not always be possible in most of the cases. To overcome this problem, an equivalent homogeneous 3D elasticity model is developed and presented in this paper for simplified analysis of laminated composite bolted joints. This type of model is beneficial for determining the basic mechanical behaviors of a laminated composite joint with significantly lesser computational effort. The present formulation is based on Mindlin–Reissner plate theory which takes into account the effect of transverse shear deformation in composite laminates. The present method is capable of finding equivalent homogeneous model for the laminated composite joints having any type of lamination scheme. This homogenization scheme is also useful for developing simplified analytical models (e.g., spring based models) for laminated composite bolted joints.

Design of Homogeneous and Composite Materials From Shielding Effectiveness Specifications

A procedure to synthesize a suitable biphasic composite material from the given Shielding effectiveness (SE) specifications is proposed herein. In particular, this paper presents an analytic approach for calculating parameters of a Debye-like equivalent homogeneous material, which meets the SE requirements in given frequency range. Establishing the relationship of the SE with the intrinsic material and morphological properties of a composite will make it possible to effectively find an equivalent homogeneous lossy Debye-like material model, starting from the given SE frequency characteristic. The Maxwell Garnett mixing rule is used to synthesize a composite made by aligned cylindrical inclusions. A few examples of how this procedure works are presented; validation by time domain numerical simulations is provided.

The effect of wall roughness on two-phase flow in a rough-walled Hele-Shaw cell

Many studies focus on the flow of multiple phases in smooth fractures yet most real fractures are rough thus flow regime maps and results for multiphase flow in smooth fractures are not completely applicable to flow in rough fractures. The effect of wall roughness is difficult to understand in multiphase flow in fractures since it leads to heterogeneities of the fracture aperture and potentially alters the roles of capillary and viscous forces in the flow. Here, the effects of wall roughness, fracture orientation, and fluids flow direction within a fracture, modeled as narrow gap in a Hele-Shaw cell, on co-current flow of oil and water were examined. The results are presented in the form of oil and water relative permeability curves. The results demonstrate that roughness impacts phase distribution, flow regimes, and phase relative permeability (a measure of phase interference); roughness increases oil–water phase interference and hysteresis of the flow resistance when scanning up and down in water saturation. Fractal analysis of images of the phase arrangement in the fracture reveals that the fractal dimension (reflects geometry and complexity), lacunarity (gappiness and complexity), and tortuosity relate the complexity of flow and the change in relative permeability behavior. The experimentally derived relative permeability data were fitted to the saturation exponent model and to an equivalent homogenous single-phase model.