Search Documents

By Rafael Colás

Computer visualization can be employed in industry as an aid to the understanding of the complex interactions between variables encountered in production. The examples of ingot casting of rimming steel and that of hot rolling of low carbon steel strip are presented. Both processes are mathematically modeled, and their results are presented in a graphical way. Such models have been proven to be an asset in quality improvements and increase of productivity as the personnel involved get a better understanding of their job.

Jan 1, 1993

By Li. Jiarong, Zuojian Liang, Qingyan Xu, Baicheng Liu, Shizhong Liu, Hailong Yuan

Single crystal solidification of turbine blades is a key technology for the production of reliable and high efficiency gas turbines. The solidification process of single crystal investment castings causes a number of problems that have to be solved such as the increase of casting defects and complexity of production process. Computer modeling and simulation is helpful to predict the defects and improve the process design. In the paper, a mathematical model for three dimensional simulation of solidification and single crystal growth of investment castings was developed based on CA, mechanism of crystal growth and basic transfer equations such as heat, mass transfer equations. Many factors including constitutional undercooling, curvature undercooling and anisotropy, which had vital influences on microstructure evolution, were considered in the model. Temperature, crystal growth interface and structure defects of investment castings of single crystal superalloy were investigated at withdrawal rates of 4.5mm/min and 7mm/min. Simulated results showed that microstructure evolution and structure defects were predicted reasonably and calculated results were coincident with experimental ones. The study indicated that three dimensional solidification simulation technique is a powerful tool for understanding the fundamental of solidification and the formation of structure defects in single crystal investment castings and finally for optimizing process design.

Jan 1, 2004

By Ross R. Bhappu

A theoretical and experimental investigation into pyrometallurgical refining of chloride leach/electrowin copper is described. The two techniques investigated were (i) vaporization and (ii) gaseous halogenation. Experiments were carried out with a packed bed of electrowon copper crystals and a boat of melted copper crystals. Nitrogen gas and Freon 12/nitrogen mixtures were used as the carrier and reac.tive gases. Vaporization was found to be effective in removing Bi, Pb and S while halogenation was effective. in removing As, Bi, Pb, S and Sb. Silver resisted all attempts at removal. Iron was removed but less effectively than the other impurities.

Jan 1, 1985

By Shi Guan-Yong, Niu Li-Ping, Dou Zhi-He

"In the preset work, the viscosity model (named modified KTH model) proposed by Sichen Du and S. Seetharaman et al and extended by Shu Qi-feng was applied to the ESR slag systems. A correlation to predict the viscosities of CaF 2-(CaO)-Al203 slags using interaction coefficients of different cations in the presence of oz-and viscosity interaction coefficients between oz-and F in the presence of different cations has been developed. The interaction coefficient between oz- and F- in the presence of Al3+ was determined from the experimental data as shown in known literatures. The good agreement between the calculated viscosities and the experimental data in the CaF2-(CaO)-Al203 systems has indicated that this approach can be successfully employed to predict the viscosities of ESR slags.IntroductionReliable viscosities data of high-temperature slag melts are important for the modeling and design of high temperature metallurgical processes. Although a number of experimental measurements have been carried out, the available viscosities data is still scarce compared to the needs of today's technology, especially in the case of complex melts. In process simulations, the needs of viscosity descriptions for complex systems which could enable the extrapolation of the data as functions of temperature and composition is strongly felt today."

Jan 1, 2013

By Xiang Zhu

Xidagou is the largest waste water discharge channel of the Anshan Iron and Steel Complex (AISC) with average flow rate of 8000 cubic meters per hour, which is about 75% of the total effluent of the AISC. The waste water from Xidagou seriously polluted the Taizi River Basin. In order to meet the Chinese Class V Standard for Surface Water Discharge and the Standard for Recycled Industrial Water Reuse, with the aid of the World Bank, the AISC began the treatability studies in 1991. Based on the bench-scale test, the AISC carried out pilot-scale treatability studies on three different treatment processes and five different chemical coagulants for more than half a year in 1992. The study results show that the processes of primary sedimentation- chemical mixing and flocculation-secondary sedimentation-filtration can meet the requirement and that PFS and PAM are effective and economic chemical coagulants.

Jan 1, 1994

By R. Schuhmann

The thermodynamic data and calculations which underlie the design of the Q-S process for coppermaking are summarized. The efficient production of crude copper and slag of low copper content in a single con¬tinuous converter requires the establishment and control of gradients in oxygen activity and other physico-chemical variables throughout the reactor. These gradients are established by stagewise introduction of oxygen and solid feed materials to provide: (a) flash oxidation of sulfides above the bath, utilizing the great bulk of the oxygen, (b) conversion of high grade matte or white metal to crude copper by bottom blowing with restricted bath turbulence, (c) close approach to equilibrium staging of converting and deconverting reactions along the length of the slag layer, from a maximum oxygen activity near the metal discharge end to a minimum at the slag discharge end, and (d) completion of slag cleansing by deconverting. In terms of the Phase Rule, the Q-S process involves a system with a minimum of 5 components (Cu, Fe, S, O, and SiO2) and several liquid, solid, and gaseous phases. Accordingly, basic data from previously reported studies on simpler systems are utilized to prepare an equilibrium diagram for the 5-component system and to generate a quantitative thermodynamic model for the Q-S process. This model shows in particular the ranges of oxygen activities (measured by equivalent CO2/CO ratios) involved in the Q-S process and the relations of oxygen activity to temperature and other important physico-chemical variables of coppermaking.

Jan 1, 1976

By Christina V. White

An experimental study was undertaken to investigate the feasibility of utilizing vapor transport for the treatment of heavy metal contaminated smelter soils. The focus of this project was to develop process chemistries that would make incineration a viable process for the treatment these soils. The experimentation concentrated on the elimination of arsenic, cadmium, and lead, and was performed in a laboramry scale rotary kiln setup. Three soil samples from non¬ferrous smelter sites, which contained various concentrations of contaminants, were utilized in the experimentation. Three chemistries were investigated for the volatilization of the heavy metals: Chloridizing volatilization, ferric chloride vapor complex formation, and the use of oxygen potential control. The samples were analyzed for residual heavy metals so that the extractions could be determined. However, the ultimate test was the leachability of the residual arsenic, cadmium, and lead, as determined by the TCLP test. The results firmly establish that incineration is a feasible process for the treatment of metal contaminated soils. It was found that no one process chemistry is suitable for all different soil samples. A two-step process consisting of a reducing step followed by a hydro-chlorination step was required to make Soil Sample-B pass the TCLP tests for all three heavy metals. Soil Sample-A passed the TCLP tests for arsenic, cadmium, and lead using a hydro-chlorination process at a minimum temperature of 700°C. In addition to passing the TCLP mm for Soil Sample-A and Soil Sample-B, 70 to 80 percent removal of the impurities was accomplished. This demonstrates that the leachability of the impurities was decreased primarily due to the removal of a large fraction of the contaminants, Soil Sample-C possessed very high levels of cadmium and lead and only moderate extractions of the impurities were generated from this soil. The arsenic TCLP test was passed at 500'C using a process gas containing ferric chloride and at temperatures of 700°C and above using chlorination of hydro-chlorination.

Jan 1, 1996

By K. Krishnapisharody, G. A. Irons

"The modeling of gas-liquid plumes in steelmaking ladles has been the subject of many investigations. In most studies, the “modified” Froude number, based on the momentum of the injected gas, has been employed to characterize two-phase plumes. This approach has several shortcomings and is critically reviewed in the present work. Based on an extensive review of previous work and theoretical considerations, it is demonstrated that the injected momentum and consequently, the modified Froude number has no significance to gas blowing operations in Ladle Metallurgy. Instead, an approach based on the “plume” Froude number, previously shown by the authors as the proper form for Froude similarity, is extended as a simpler alternative.IntroductionGas injection is central to most Ladle Metallurgy operations. During ladle processing, the steel melt is usually stirred by an inert gas like Argon through porous plug(s) fitted in the bottom of the ladle or a lance inserted deep into the melt. The purging serves several purposes viz., homogenizing the melt, flotation of inclusions, enhancing the rates both of refining reactions and dissolution of alloying elements and promoting inter-phase interactions in the ladle.The topic of gas injection into liquid baths has been the subject of several investigations in the past. A great deal of this work, both experimental and computational, was devoted to describing the structure and properties of two-phase plumes as reviewed recently [1]. Generally, the ascending two-phase mixture is sub-divided into three distinct regions [2]: the jet core, transition and the bubble plume, respectively. The jet region, where the momentum of the injected gas is transferred to the bulk liquid, is also called the ‘momentum region’. In a similar manner, the plume is called the ‘buoyancy region’ where the motion of liquid is caused by the buoyancy force exerted by the bubbles. The proper characterization of these regions is important for the analysis and modeling of stirring operations in Ladle Metallurgy. Although many mathematical correlations exist for this purpose, some issues of theoretical and practical interest to the modeling of gas-liquid plumes need further attention."

Jan 1, 2012

By Serdar Aksu, Fiona M. Doyle

"CMP will be an essential process in the production of integrated circuits containing copper interconnects. This study aims to improve our mechanistic understanding of the role that organic chelating agents might play in the reactive slurries used in copper CMP. Copper dissolution behavior in EDTA arid glycine was first examined by producing potential-pH diagrams for the copper-water-EDTA and copper-water-glycine 'systems. The results of potentiodynamic polarization experiments were then considered in light of these diagrams. . In-situ polarization experiments were conducted to gain insight into the electrochemistry of copper during dynamic polishing in slurries prepared from EDT A and glycine.IntroductionCopper has recently started to replace aluminum as the interconnect metal in integrated circuits. Copper interconnection offers faster and more reliable integrated circuits due to its higher electrical conductivity and superior electromigration resistance (1). The damascene method is used to form multilevel interconnects in the manufacture of integrated circuit devices with copper metallization (2, 3). Copper is deposited by CVD or electroplating into vias and trenches etched in the interlayer dielectric (IDL), over a diffusion barrier usually made from titanium, tantalum or their nitrides. Chemical mechanical planarization (CMP) then prepares the wafer for the next deposition step, by removing excess copper and planarizing the surface. During CMP, the wafer is rotated and pressed against a rotating platen covered with a polishing pad. Chemically active slurries containing submicron size abrasive particles (Si02, Al20 3, ceria, diamond, etc.) are applied. Both the mechanical action of the abrasive particles and the chemical action of slurry constituents remove material from the wafer surface. Planarization results because material is removed faster from protruding regions on the surface than from recessed regions. Since CMP can globally planarize .the entire wafer, it has become one of the key technologies for producing integrated circuits with copper metallization."

Jan 1, 2000

By Mike Johnson, Niels Verbaan, David Dreisinger

The Search Minerals Foxtrot project in Labrador is a surface deposit enriched in the highly sought after heavy rare earth elements. Early metallurgical work investigated beneficiation of the rare earth content of the Foxtrot resource using flotation, gravity separation and magnetic separation. The concentrate was then processed by acid baking and water leaching to produce a REE leachate for purification and recovery. The Search Minerals Direct Extraction Process was developed through bypassing the beneficiation process and directly acid treating a coarse crushed ore material prior to water leaching. The result is a simple, low risk technical process for direct recovery. Concurrently, the treatment of the water leach solution was modified to produce a high grade (98.9% total rare earth oxide) product for refining.

Jan 1, 2016

By Min Chen, Nan Wang, Zhen Tian, Yingying Shen

"The enrichment behavior of phosphorus in CaO-SiO2-FeOx-P2O5 slag was studied by making an investigation on the distribution of phosphorous content in slag and 2CaO·SiO2 phase. The research results showed that the existing 2CaO·SiO2 solid particles in slag were the sites for the phosphorous enrichment. The enrichment process of phosphorus in CaO-SiO2-FeOx-P2O5 slag can be recognized as: mass transfer of phosphorus from bulk slag toward the surface of 2CaO·SiO2 particle, superficial dissolution reaction of phosphorus to 2CaO·SiO2 and diffusion of phosphorus through the product layer of 2CaO·SiO2-3CaO·P2O5 solid solution to the inner of 2CaO·SiO2 particle. Compared to the 2CaO·SiO2 particles with larger size (500µm to 1000µm), the completion time of enrichment was shorter for the particles with smaller size (less than 50µm).IntroductionDuring ironmaking and steelmaking, significant amounts of slag are produced. Contrast to the high utilization of ironmaking slag, the treatment of steelmaking slag is more difficult and challengeable, and therefore, an alternative approach is to recycle the steelmaking slag inside the ironmaking and steelmaking process itself. The main limitation to the reuse of steelmaking slag inside the process is that the refining process may be aggravated caused by the phosphorous accumulation if it is used in the blast furnace burden [1]. At the same time, the phosphorous content of steelmaking slag (approximately 1%~5% P2O5) is too low for it to be used as raw material for fertilizer [2, 3]. Moreover, owing to the diminishing supply of global iron ores with low phosphorous content, the control of phosphorus in iron and steelmaking processes has become an increasing problem, and as a result, more amounts of high phosphorus containing steelmaking slag are produced. Therefore, a valuable approach is quite appreciated in which the steelmaking slag is recycled within the ironmaking and steelmaking process and at the same time, the high phosphorus-containing phases in the steelmaking slag, suitable for use as fertilizer can be separated and recycled effectively [4]."

Jan 1, 2011

By I. Gaballah

The kinetics of oxychlorination of pure CI-2O3 with C12+02 gas mixtures is studied by ThermoGravimetric Analysis (TGA) in non and isothermal conditions up to 1000 °C. The reaction of Cr2O3 with C12+O2 chlorination gas mixtures starts at about 550 °C and the reaction product is CrO2Cl2. The oxychlorination rate of Cr2O3 is almost proportional to the chlorine partial pressure and to the fourth root of the oxygen partial pressure in the chlorinating gas mixtures. At 800 °C, the maximum chlorination rate is obtained using a gas mixture having a C12/O2 ratio equal to 4. The apparent activation energy of the oxychlorination reaction of Cr2O3 is 87 and 46 kJ/mol at temperatures lower and higher than 650 °C, respectively. By varying the chlorine and the oxygen partial pressures of the oxychlorinating gas mixtures at temperatures higher than 550 °C, it is possible to extract selectively the chromium chlorinated compounds from the chromium bearing materials. a. Laboratoire Environnemem et Minéralurgie, BP 40, 54501 Vandceuvre, France, b. École Nationale Supérieure de Géologie, Rue du Doyen Marcel Rouhault, 54501 Vandoeuvre Cedex, France, c. Centre National de la Recherche Scientifique, 3 rue Michel - Ange, 75794 Paris Cedex, France, d. Insritut National Polytechnigne do Lorraine, Rue de la Font de Haye. 54501 Vandceuvre Cedex, France.

Jan 1, 1997

By Shaohua Ju

Siderite ore is abundant around the world, due to its inert properties of low grade, mudding when milling and low magnetic, and it is very hard to be beneficiated. Nowadays, decomposition by roasting becomes the main process for utilization of the siderite ore. The methods of energy input for roasting are normally electrical heating, coal or gas combustion. Because traditional roasting methods owns some disadvantiges, such as low energy utilization, high cost and/or large exhaust pollution, only about 10% of the siderite ores in China were used as iron concentrate. In this work, the possibility of roasting siderite ore with microwave energy is studied by both laboratory and pilot experiments. The result of laboratory experiments showed that the optimized condition is roasting for 20 min with a power density of 3 W/g, and the Fe content of the final sample obtained is about 59.12%. The pilot experiments result showed that the decomposition is thoroughly, and the main phases of the roasted material are magnetite and wustite, and the energy consumption of the roasting process is 695.8 KWh/t.

Jan 1, 2014

By Andreas H. Vassiliou

Organic materials are major constituents of the ore in several uranium deposits. Some of these deposits have been described as "urano-organic" because, the organic materials are believed to have provided the dominant control for the accumulation and deposition of uranium and are directly and intimately intermingled with the uranium. The nature of these urano-organic deposits has been problematic in terms of (a) the origin of the associated organic materials and (b) the specific form of' occurrence of uranium. The organic materials in urano-organic deposits have been genetically related to both coal and petroleum or their progenitors or deriva-tives. Analytical data presented here (infrared, chemical. D.T.A.) suggest that coaliferous materials or related plant derivatives represent the main source of the organic fractions in practically all major urano-organic ores analyzed from the Colorado Plateau and other areas. Recognition of the specific form of occurrence of uranium in urano-organic deposits has been problematic mainly because the uranium is usually in an extremely fine-grained and disseminated state in the organic matrix. Electron microprobe and X-ray diffraction analyses presented here show that fine-grained uranium minerals, specifically uraninite or coffinite. are disseminated in the organic matrix as the predominant form of uranium in most major deposits; however. the presence of true organo-uranium compounds is also suggested for some deposits.

Jan 1, 1981

By V. R. Voller

"The World Wide Web (the web) provides a very useful resource for the enhancement of teaching and research dissemination. This paper advocates that researchers take control of this resource and become actively involved in creating web content. Two examples of the use of the web in a materials setting is provided. The first illustrates how a concept quiz for teaching can be developed. The second shows how a materials processing model can be run in real time over the web. The paper closes with a summary of some resources that can be used to create web materials.IntroductionA recent copy of a newspaper advertisement read""Share what you know, learn what you don't""This neat phrase sums up a powerful teaching and research philosophy. In an educational setting a prime motivation for research is to uncover the unknown and venture in directions previously uncharted. The balance to this search for knowledge should be a desire to share that knowledge with others; whether it be with students in the classroom or research colleagues in a wider setting.The .World Wide Web and its associated multi-media software offer a perfect platform for researchers to share their knowledge with an extremely wide sector of the research community. To enable the use of this resource researchers must take the power that the web offers them into their own hands and create products that take maximum advantage of the medium. It is key that researches at the forefront become directly involved, otherwise a potential powerful medium will not realize it's true potential, and colorful products with no core content will proliferate. The object of this paper is to outline two ways in which the web can be used to enhance teaching and research objectives."

Jan 1, 2000

By Akira Yazawa

To realize highly efficient process in extractive metallurgy, continuous operation nearly in equilibrium is preferable, but most metallurgical processes consist of plural steps with different chemical potentials. Traditional two-step process of sintering followed by reduction is continuous in each step, but is heterogeneous reaction system far from equilibrium, and the chemical potentials are varied considerably along the distance the charge travels in a reactor. This route will become old-fasioned in next century due to the various inherent problems caused especially by sintering process. To establish reasonable new smelting processes, the important tasks of the metallurgists are how to introduce feed and reacting gas in the reactor, and also how to overcome the difference in chemical potential in the reactor system. Based on the ways to solve theses tasks, recent proposals of new smelting process for copper and lead are classified and discussed with the help of sulfur-oxygen potential diagram. On such potential diagram, each equilibrium step in continuous smelting is expressed at a fixed point, and two reactors with different chemical potentials must be connected by continuous molten flow through launder or partition wall. In the latter case, the reactor is apparently single, but some technical problems must be overcome. While, in a batch smelting like converter, potential variation is successively realized along a path on chemical potential diagram with the time elapsed. To establish immediate equilibrium, continuous steady flow of reactants into well mixed reactor is indispensable. In modern smelting process, the ore is mostly supplied in the form of powder which have huge surface area and fluid character, and consequently injection process must be very attractive. Several examples are discussed for both of copper and lead smelting, and promising future technologies are suggested.

Jan 1, 1988

By Z. Smieszek, J. Botor, Z. Miczkowski, S. Sobierajski

"From 1978, the direct process for the smelting of chalcocite concentrates in a flash furnace by the Outokumpu method has been applied at the Glogów II copper smelter. The chemical composition of these concentrates make it necessary to control the process very strictly. In this paper, the method for controlling and measuring the main technological parameters of the copper production by flash smelting is being presented. It includes the determination of the chemical composition of the concentrate, its grain structure, the temperature of liquid products of the process, oxygen content in process gases, as well as lead concentration in copper and copper concentration in slag.The main process parameters are determined from the mass and energy balances. The relations between parameters, such as an effect of grain structure of a concentrate on oxygen and oil consumption, and dependence of chemical composition of a concentrate on capacity and products quality are discussed. 1. IntroductionThe Polish copper concentrates, as most concentrates occurring worldwide, contain from 18% to 30% Cu, and less sulphur (7-11%) and iron (2-5%). The main copper-bearing mineral contained in the concentrates is chalcocite, while bornite and chalcopyrite are present in smaller quantities. Moreover, the organic carbon (5-7.5%), arsenic (0.05-0.3%) and lead (1.2-3.0%) are also contained in the concentrates. The gangue consists mainly of silica, aluminosilicates, calcium carbonate and magnesium carbonate. Their proportions make the addition of slag-forming agents unnecessary.The composition of Polish concentrates, especially their low iron content, allows their application in the direct flash smelting process for blister copper production. Low sulphur content is the factor which determines the necessity of oxygen application in this process."

Jan 1, 1989

By Jilai Xue, Jun Zhu, Yongqiang Liu

"Up-grading silicon feedstock by removing B and metal impurities can improve process efficiency and lower production cost in metallurgical processing for solar cells production. Hydrometallurgical study has been carried out in laboratory through alternative treatments of the metallurgical grade (MG) silicon (-200 mesh) by using hydrogen peroxide, hydrofluoric acid (4 mol/L) and NH4Cl-NH4 F (30:5) solution. The experiments were usually performed under mechanical agitation at 70 ? for 5 h. ICP-AES analysis showed that B content in MG silicon after the hydrometallurgical treatment has reduced by 92.4 %, and Fe, Al, and Ca contents by 98.8 %, 98.0 % and 81 %, respectively. Kinetics of these processes was also studied for better understanding of the effects of silicon powder size, acid concentration, leaching and oxidizing time on the processing chemistry.IntroductionAs one of the most clean and promising new energy, solar energy is used more and more in many countries all over the world, especially in United States, Japan and European Union. Most of industrialized states have made their national photovoltaic plans, which have stimulated further increase in use of solar energy. Photovoltaic Industry is at a high growth rate about 30 % [1-2]. For silicon solar cells to remain the mainstay for the photovoltaic industry it is necessary to develop a low-cost solar grade silicon feedstock [3]. At the same time, the availability of the currently M-G silicon from the semiconductor industries becomes limited [4]. With the advantages of low cost and low energy consumption, metallurgical routes to product solar–grade silicon get more attention [5]. These routes mainly include pickling, slagging, vacuum processing and directional solidification, etc [6]. Among them the most important processing step is the directional solidification, but it still can not satisfy the industrial demand for removing B. Removing B from Si remains as one of the most difficult and important processes in making M-G silicon [7]."

Jan 1, 2012

By S. L. Pohlman

Physical characteristics of possible importance in the acid leaching of Chrysocolla have been evaluated. Surface area studies and pore size distribution indicate: 1) a large surface area (350 m /gm); 2) an average pore size of 13 or 16 Å , depending upon use of the adsorption, or desorption, branch of the Type IV isotherm in the evaluation; ) the presence of a significant fraction of pores of size less than 15 Å determined by the accumulation surface area method. The initial structure is micro- crystalline on the basis of x-ray powder patterns; the silica leach residue is amorphous and has only 24 m2 /gm surface area, and loses integrity when dry. However, readsorption of copper onto the wet leach residue gives a product with integrity and 100 m2 /gm surface area. Visual observation of the leach residues supports evidence of a non-protective diffusion mechanism of leaching which is well correlated by the shrinking core model previously presented.

Jan 1, 1976

By Yan Beygelzimer, Alexander Spuskanyuk, Victor Varyukhin

"The main idea of the report is that the yield surface can be presented as thick, ""foamed surface"" with dimensionality exceeding two. By other words, perhaps, the yield surface is fractal, i.e. it belongs to the class of geometric objects with fractional dimensionality. Apparently, fractal structure of the yield surface is determined by the fractal structure of natural materials. ""Cloud of internal stresses"" term is introduced to describe the stress distribution in representative volume element. Its plastic flow is determined by the interaction of this cloud with the thick yield surface. Thick yield surface and internal stress cloud concepts allow to determine an additional correlation between micro mechanical models of polycrystals and phenomenological theory of plasticity.1. IntroductionClassical plastic flow models are not satisfying the modem requirements. There are two main directions in their development. The first, mathematical, is connected with the development of the general theory of rheological relationships; the second, physical, is connected with the development of the representative volume element (RVE) models which are based on specific ideas about deformation mechanisms. Within the framework of the first direction, the macroscopic experimental data is formalized; the second approach deals with the generalization of physical research results for the different scale levels that are involved in plastic deformation.These approaches have advantages and disadvantages. In phenomenological theories, the advantages are the mathematical simplicity and laconic formulation of constitutive relations, which allows using them in practical calculations. However, the mathematical models of this class can not be considered as general, they are useful only for the description of limited range of deforming processes. On the other hand, physical theories that are based on the description of real plastic deformation mechanisms are very explanatory and predictive, but they lack mathematical simplicity. The above circumstances lead us to the necessity of compromise that can be found in determining the constitutive relations for RVE, which structure and parameters would bear the information about rnicrolevel and mesolevel phenomena. In this synthesis direction, the fundamental role belongs to [1,2], etc."

Jan 1, 2001