Theoretical modeling framework for an unsaturated freezing soil

Based on the authors' theoretical modeling framework of the saturated freezing soil, this paper further discusses the air phase in the unsaturated freezing soil in two ideal situations: air in the soil is linked to the atmosphere (the open porous medium) and air in the soil is isolated from the atmosphere (the sealed porous medium). The corresponding theoretical modeling framework for a multi-phase porous medium with interaction of water, heat and deformation is established in this paper. The proposed theoretical model is then extended to the general case (unsaturated half-open and half-sealed porous medium). Also, a finite element numerical solution to the heat-moisture-deformation coupling behavior of the unsaturated freezing soil is obtained. The computer software for solving this problem is also developed. The in-situ measurements for Hua Shixia highway roadbed located in Qinghai–Tibetan Plateau are introduced to compare with the numerical results obtained by the proposed model. The measurement results indicate that the numerical results for the temperature field variations with time are found to be in good correlation with the roadbed depth, just as the relative freezing deformations are correlated with road surface. Numerical modeling results, when compared to field measurements of temperature and deformation, are within 10 to 20%. The comparative analysis shows that proposed theoretical modeling framework and its numerical solution for the temperature–moisture-deformation coupling behavior is suitable and acceptable.     

Dynamical Electromechanical Model for Magnetic Bearings

Magnetic bearings are electromechanical systems. From a mechanical point of view, their modeling is plainly related to general rotor dynamics modeling. But the forces acting between the rotor and the stator are of an electromagnetic nature. This paper presents the analysis of the potentially unstable dynamical behavior of magnetic bearings. It adopts an electromechanical point of view and represents the forces acting on the system by dampers, springs, and an electrical phase shift. The coefficients of the model are found by parameter identification with a finite-element model of the system.     

The effective properties of smart composites with linear coupling behaviors

The analytical expressions for effective thermal, mechanical, electrical, and magnetic moduli of biphasic smart composites with the linear coupling behavior are developed by employing Mori–Tanaka theory and Dunn model, combined with the equivalent inclusion method for an ellipsoidal inclusion embedded in a transversely isotropic medium. These expressions reflected directly the contributions of each phase and that of the coupling taken place between any combinations of thermal, mechanical, electric, and magnetic behavior and provide a physical insight into how a composites consisting of inclusions perform. For a fibrous reinforced smart composite, the explicit expressions for the sum and product properties are derived and are helpful in understanding the coupling behaviors. The effective properties and the coupling effects as a function of microstructure are discussed theoretically and numerically for piezocomposite and piezomagnetic composite. The results are compared with that of the rule of mixture.     

On wave propagation in laminated composites—II. Propagation normal to the laminates

A continuum model is developed for elastic waves propagating in a direction normal to the laminates of a laminated medium. The developments are analogous to those used in a companion paper for waves traveling along the laminates and indicate that the behavior is “nonlocal” in time as a result of the history-dependence of the current state. A zeroth-order model is deduced which consists of a system of integro-differential equations. The behavior of this system is then analysed and it is found that during an early phase, the motion is confined to a boundary layer and consists of highly damped waves. During a later phase the behavior is found to approach that of a macroscopically homogeneous medium. The behavior during both phases is described by two distinct differential systems. The early phase behavior is then determined for a laminated half-space subjected to a step normal stress.     

Investigation on the asymptotic expansion technique applied toelectromagnetic problems

The application of the asymptotic multiple scale expansion to the analysis of laminated cores is discussed. The computations are developed in a one-dimensional structure modeling a periodic layered medium to investigate its electromagnetic behavior. The technique essentially consists of using two variables for describing the overall and small-scale behavior, respectively and of expressing the approximate solution through a truncated series of powers. The approximate solution, analytically computed, is compared with the exact one. An excellent agreement is found in the evaluation of magnetic and electric quantities (magnetic flux density, current density) and in the estimation of Joule losses due to eddy currents. Finally the study evidences some interesting features of the asymptotic expansion technique which, in the considered problem, imply a generalization of the results and a significant reduction of computational efforts     

A hybrid crystal plasticity and phase transformation model for high carbon steel

Presence of retained austenite in two-phase steels can have a significant effect on the response of the material. The current state-of-the-art in multi-phase modeling of polycrystalline plasticity has limits on scaling, explicit phase modeling, and tracking multiple plasticity types. To address these issues, a hybrid material model is developed for high-carbon steels. The model can account for crystal plasticity of martensite and stress-assisted transformation from austenite to martensite in dual-phase high-carbon steel. The parameters of the model are calibrated to experimental stress-strain and volumetric transformation strain data. The combination of scalability and multiple phase representation gives a useful tool for the investigation of two-phase high-carbon steel behavior.     

Theory of magnetically polarizable superconductors

Superconductors containing a magnetically polarizable medium under an applied magnetic field are discussed theoretically. It is shown that instead of the Pauli limiting field found by Chandrasekhar and Clogston for nonmagnetic superconductors, the maximum critical field is limited by the effect of the susceptibility X_f due to the polarizable medium and is greatly reduced as X_f increases, indicating the appearance of the first-order phase transition from the superconducting to the normal state. The magnetic behavior of the ferromagnet superconductor ErRh₄B₄ under applied fields is analyzed in terms of this idea.     

Theory of magnetically polarizable superconductors. II

A microscopic theory of superconductors containing a magnetically polarizable medium is given. By taking into account the Zeeman effect, we derive the crossover behavior from a second- to a first-order phase transition, the magnetization curve in the high-field region, and the magnetization jump at the first-order phase transition temperature. The theory gives a qualitative account of the magnetic behavior, including the remarkable convex curvature of the magnetization curves, observed in the ferromagnetic superconductor ErRh₄B₄ with applied external field parallel to the magnetic easy axis.     

Modeling of chloride diffusion in hetero-structured concretes by finite element method

With a two-dimensional structure model, the finite element method was used to simulate the chloride diffusion behavior in a heterogeneous concrete composed of two phases with distinct diffusivities, compared with its derived homogeneous medium that was given a single effective diffusion coefficient by the mean field theory. In contrast to the smooth chloride concentration profiles for the homogeneous medium, a three-dimensional concentration distribution network has been found in the hetero-structured concrete, characterized by a complicated band-like profile along the diffusion depth. Moreover, it features an undulating and narrowing width as the diffusion time and diffusion depth increase. The modeling results also manifest that the chloride diffusion in hetero-structured concretes appears to lag behind that for the homogeneous ones, showing an increasingly notable discrepancy between the two chloride concentration profiles as the diffusion proceeds. Nonetheless, such a concentration difference may be remarkably reduced when the chloride binding and time-reducing effect of diffusivity are supposed to happen within the cement paste phase of the hetero-structured concrete and its derived homogeneous medium.     

One-Dimensional Quantum Compass Model in an Out-plane Magnetic Field

The one-dimensional quantum compass model (1D-QCM) in an out-plane magnetic field is investigated by numerical and analytical methods. The presence of the 1D-QCM in an area of the ground-state magnetic phase diagram where the odd couplings are antiferromagnetic and larger than the even couplings is studied. Using pseudo spin ladder operators indicates that the 1D-QCM in an out-plane magnetic field can be mapped to the one-dimensional Ising model in a transverse magnetic field (ITF). Analytical investigation of the effective ITF Hamiltonian predicts the occurrence of two quantum phase transitions with increasing magnetic field. Also, the critical fields are obtained from this method, which are completely in agreement with the results of the numerical experiment based on the Lanczos method. This numerical method accurately determined the behavior of the energy gap, magnetization and string order parameter, and therefore it is a very useful method for indicating the ground-state phases of the system.     

On Elasto-plastic waves in laminated composites

The propagation of elasto-plastic waves in a laminated medium is considered. Based on the assumption of perfectly elastic fiber layers and an elasto-plastic behavior of the matrix layers, a continuum model is deduced for wave motion either parallel to or normal to the direction of layers. The derivation is based on asymptotic expansions in terms of a small parameter given by the ratio of wave velocities of the two constituents. As a result, a system of integro-differential equations is obtained in which microstructure effects appear as a consequence of the “non-locality” in time of the laminated medium. By examining the asymptotic behavior of this system, two differential systems are deduced describing the early and late phases of the motion. It is found that during the early phase, the motion is confined to an O(l) boundary-layer where l is a macro-scale, and consists of highly damped waves whereas the behavior during the later phase is predominantly that of a macroscopically homogeneous medium.Considering that pulse attenuation occurs mainly during the early phase, it is concluded that the early phase motion constitutes the critical phase of motion in a laminated medium.     

Prediction of multiphase equilibria in associating fluids by a contact-site quasichemical equation of state

A contact-site quasichemical equation of state has been used Tor the modeling of different kinds of fluid phase equilibria (between a gas phase and one or more liquids) over a wide range of conditions. Among the systems of interest are the ternary mixtures water + alkanols + hydrocarbons (alkanes or alkynes), water + alkanols (or acetone)+ CO₂, water + polyoxyethyleneglycol ethers + heavy alkanes. The model has been applied to describing the thermodynamic properties of the binary subsystems and to predict the phase behavior of the ternary systems. For longer-chain alkanols and hydrocarbons a group-contribution approach is implemented, which allows the modeling when no experimental data are available. The model gives reasonable predictions of phase behavior and the correct trends in the calculated phase diagrams in most cases. The concentrations of associates in liquid and gas phases are estimated by the model and compared with some experimental and computer simulation data. The predictive abilities of the model, its limitations, and possible ways of its improvement are discussed.Paper presented at the Twelfth Symposium on Thermophysical Properties, June 19–24, 1994, Boulder, Colorado, U.S.A.     

A thermodynamic framework for the modeling of crystallizable shape memory polymers

Shape memory polymers are a relatively new class of materials that have the ability to retain a temporary shape, which can be reset to the original shape with the use of a suitable trigger, typically an increase in temperature. The temporary shapes can be very complex and the deformations involved large. These materials are finding use in a large variety of important applications; hence the need to model their behavior. In this paper, we develop constitutive equations to model the thermo-mechanical behavior of crystallizable shape memory polymers. Crystallizable shape memory polymers are called crystallizable because the temporary shape is fixed by a crystalline phase, while return to the original shape is due to the transition of this crystalline phase. The modeling is carried out using a framework that was developed recently for studying crystallization in polymers and is based on the theory of multiple natural configurations. In this paper we formulate constitutive equations for the original amorphous phase and the semi-crystalline phase that is formed after the onset of crystallization. In addition we model the transition of the crystalline phase to capture the return of the polymer to its original shape. These models for shape memory effects in polymers have been developed within a full thermodynamic framework, extending our previous work in which the models were developed within a mechanical setting [G. Barot, I.J. Rao, Constitutive modeling of the mechanics associated with crystallizable shape memory polymers, ZAMP 57 (4) (2006) 652-681]. The model is applied to the problem of inflation and extension of a hollow cylinder. The results are consistent with what has been observed in experiments.     

On wave propagation in laminated composites—I. propagation parallel to the laminates

The problem of elastic wave propagation in a laminated medium is considered. Using asymptotic expansions in terms of a small parameter given by the ratio of wave velocities of the two constituents a continuum model is deduced in which microstructure effects appear as a consequence of “non-locality” in time of the laminated medium. This is manifested by a history-dependence of the current state of the medium, which results in a system of integro-differential equations. The laminated medium is found to be highly dissipative. The asymptotic behavior of this system is then examined and two differential systems are obtained for the early and late phases of the motion. It is found that the entire dynamic behavior of a laminated medium consists of two distinct phases of motion which are described as follows. During an early phase, the motion is confined to an O(l) boundary-layer where l is a typical macro-scale, and is characterized by damped waves. During this phase of the motion an applied pulse undergoes substantial attenuation. At a later phase and beyond this layer, the behavior is predominantly that of a macroscopically homogeneous medium, where the attenuated pulse emerging from the boundary-layer propagates essentially without distortion. As a result, it is concluded that the early phase boundary-layer motion constitutes the crucial phase of motion in a laminated medium, whereas the later phase is of no practical consequence inasmuch as pulse attenuation is essentially completed during the early phase. Thus, current efforts aimed at a continuum characterization of the later phase motion appear entirely unwarranted.     

An empirical model for modified bituminous binder master curves

Modeling the mechanical behavior of asphalt binders and mixtures has been the subject of intensified research in recent decades. Master curves of the norm of the complex modulus |G*| in the linear viscoelastic domain are frequently used for modeling, while phase angle master curves are less frequently considered for this purpose. Therefore in this research, an empirical model is introduced for phase angle master curves of modified and neat bituminous binders. The model is based on a general form of a double-logistic (DL) mathematical function. The |G*| master curve was then modeled using a mutual relationship between the phase angle and |G*|. Master curves of three neat and seven modified binders were generated and used to validate the DL model. The results showed that the model is capable of properly predicting the plateau region of phase angle master curves. In particular, the asymptotic behavior of the master curves at high frequencies can be modeled correctly. The model also describes irregularities in the high temperature range of the phase angle master curve. In general, model outputs such as the phase angle value at the plateau, glassy modulus, rheological index and crossover frequency correctly predict the behavior of the neat and modified binders.     

Analysis of Losses in a Magnetostrictive Device Under Dynamic Supply Conditions

This paper, starting from previous experiences in modeling the magneto-mechanical behavior of magnetoelastic materials, faces the problem of loss evaluation of a magnetostrictive device. Measurements and simulations in a prototype actuator are here presented and compared, showing a general good agreement. The model is consequently used for a reliable loss separation. The effects of magnetization bias, preload and supply frequency on electric and magnetic losses are deepened and discussed.      

磁流变液机理及行为描述的理论研究现状

概述了解释磁流变液链化机理的3种理论即磁畴理论、相变理论和偶极矩理论,以及链化机理的定量分析和数值模拟.同时介绍了3种描述磁流变液行为的理论方法和途径即宏观本构描述、微观分析描述和数值模拟描述.上述磁流变液的基础理论研究对优化磁流变材料的配置和设计高性能磁流变装置具有重要意义.     

A Resonant Micromachined Magnetic Field Sensor

The design, modeling, and simulation of a novel micromachined magnetic field sensor are discussed. The sensor uses an electrostatic resonator whose fundamental resonant frequency is modified by a Lorentz force generated from the interaction of the sensor structure and the present magnetic field. The sensor was fabricated in a standard bulk micromachining process without the need for any additional processing steps. Since the sensor does not employ any magnetic materials, it does not exhibit hysteresis. A comprehensive model of the sensor behavior is derived which encompasses the interactions of the involved physical domains. Validity of the modeling results was verified by finite-element simulations, and later, through experiments. The sensitivities of the fabricated sensors are in the range of 48-87 Hz/T, depending on sensor structure and dimensions. The design of the sensor allows for its fabrication in many standard microelectromechanical system processes and is compatible with CMOS processes. The theoretical minimum detectable signal with current devices is on the order of 217 nT. Methods to improve the sensitivity of the current sensors are suggested. A linear response to a wide range of magnetic fields makes this design suitable for applications where large fields need to be measured with high resolution.     

Phase Behavior Modeling of Asphaltene Precipitation for Heavy Crudes: A Promising Tool Along with Experimental Data

Thermodynamic modeling is known as a promising tool for phase behavior modeling of asphaltene precipitation under different conditions such as pressure depletion and CO₂ injection. In this work, a thermodynamic approach is used for modeling the phase behavior of asphaltene precipitation. The precipitated asphaltene phase is represented by an improved solid model, while the oil and gas phases are modeled with an equation of state. The PR-EOS was used to perform flash calculations. Then, the onset point and the amount of precipitated asphaltene were predicted. A computer code based on an improved solid model has been developed and used for predicting asphaltene precipitation data for one of Iranian heavy crudes, under pressure depletion and CO₂ injection conditions. A significant improvement has been observed in predicting the asphaltene precipitation data under gas injection conditions. Especially for the maximum value of asphaltene precipitation and for the trend of the curve after the peak point, good agreement was observed. For gas injection conditions, comparison of the thermodynamic micellization model and the improved solid model showed that the thermodynamic micellization model cannot predict the maximum of precipitation as well as the improved solid model. The non-isothermal improved solid model has been used for predicting asphaltene precipitation data under pressure depletion conditions. The pressure depletion tests were done at different levels of temperature and pressure, and the parameters of a non-isothermal model were tuned using three onset pressures at three different temperatures for the considered crude. The results showed that the model is highly sensitive to the amount of solid molar volume along with the interaction coefficient parameter between the asphaltene component and light hydrocarbon components. Using a non-isothermal improved solid model, the asphaltene phase envelope was developed. It has been revealed that at high temperatures, an increase in the temperature results in a lower amount of asphaltene precipitation and also it causes the convergence of lower and upper boundaries of the asphaltene phase envelope. This work illustrates successful application of a non-isothermal improved solid model for developing the asphaltene phase envelope of heavy crude which can be helpful for monitoring and controlling of asphaltene precipitation through the wellbore and surface facilities during heavy oil production.