Geotechnical stability analysis considering strain softening using micro-polar continuum finite element method

Geotechnical stability analyses based on classical continuum may lead to remarkable underestimations on geotechnical safety.To attain better estimations on geotechnical stability,the micro-polar continuum is employed so that its internal characteristic length(lc)can be utilized to model the shear band width.Based on two soil slope examples,the role of internal characteristic length in modeling the shear band width of geomaterial is investigated by the second-order cone programming optimized micro-polar continuum finite element method.It is recognized that the underestimation on factor of safety(FOS)calculated from the classical continuum tends to be more pronounced with the increase of lc.When the micro-polar continuum is applied,the shear band dominated by lc is almost kept unaffected as long as the adopted meshes are fine enough,but it does not generally present a slip surface like in the cases from the classical continuum,indicating that the micro-polar continuum is capable of capturing the non-local geotechnical failure characteristic.Due to the coupling effects of lc and strain softening,softening behavior of geomaterial tends to be postponed.Additionally,the bearing capacity of a geotechnical system may be significantly underestimated,if the effects of lc are not modeled or considered in numerical analyses.

Instantaneous phase-stepping interferometry based on a pixelated micro-polarizer array

In this paper, we propose an instantaneous phase-stepping method for determining phase distribution of interference fringes utilizing a camera that is equipped with a micro-polarizer array on the sensor plane. An optical setup of polarization interferometry using a Mach-Zehnder interferometer with two polarizers is constructed. Light emerging from the interferometer is recorded using a camera that has a micro-polarizer array. This micro-polarizer array has four different optical axes. That is, an image obtained by the camera contains four types of information corresponding to four different optical axes of the polarizer. The four images separated from the image recorded by the camera are reconstructed using gray level interpolation. Subsequently, the distributions of the Stokes parameters that represent the state of polarization are calculated from the four images. The phase distribution of the interference fringe pattern produced by the Mach-Zehnder interferometer is then obtained from these Stokes parameters, The effectiveness of the proposed method is demonstrated by measuring a static carrier pattern and time-variant fringe patterns. It is emphasized that this method is applicable to time-variant phenomena because multiple exposures are unnecessary for sufficient data acquisition in the completion of the phase analysis.

Viscous fluid damping in a laterally oscillating finger of a comb-drive micro-resonator based on micro-polar fluid theory

Viscous damping is a dominant source of energy dissipation in laterally oscillating micro-structures. In microresonators in which the characteristic dimensions are comparable to the dimensions of the fluid molecules, the assumption of the continuum fluid theory is no longer justified and the use of micro-polar fluid theory is indispensable. In this paper a mathematical model was presented in order to predict the viscous fluid damping in a laterally oscillating finger of a micro-resonator considering micro-polar fluid theory. The coupled governing partial differential equations of motion for the vibration of the finger and the micro-polar fluid field have been derived. Considering spin and no-spin boundary conditions, the related shape functions for the fluid field were presented. The obtained governing differential equations with time varying boundary conditions have been transformed to an enhanced form with homogenous boundary conditions and have been discretized using a Galerkin-based reduced order model. The effects of physical properties of the micro-polar fluid and geometrical parameters of the oscillating structure on the damping ratio of the system have been investigated.

Flotation and adsorption of quaternary ammonium cationic collectors on diaspore and kaolinite

The flotation and adsorption behaviors of dodecyltrimethylammonium chloride（DTAC） and cetyltrimethylammonium chloride（CTAC） on diaspore and kaolinite were studied.Solution depletion methods were used to determine adsorption isotherms.Fluorescence probe test along with Zeta potential measurement was also conducted for further investigation into the adsorption of quaternary amines at the mineral-water interface.The results show that the flotation recovery of kaolinite decreases with an increase in pH when DTAC and CTAC are used as collectors,while diaspore is on the contrary.As the carbon chain length of the collectors increases,the flotation recoveries of minerals increase.However,the increment rate of kaolinite is significantly lower than that of diaspore.In the low surfactant concentration range,the cationic surfactants adsorb readily on diaspore surfaces just due to electrostatic interactions.As for kaolinite surfaces,ion exchange process also exists.With a further increase in surfactant concentration,the adsorption was ascribed to the hydrophobic association of chain-chain interactions.Micro-polarity of mineral surfaces study shows that CTAC has a better hydrophobic characteristic than DTAC.Larger aggregates are formed with CTAC on diaspore than on kaolinite in the same solution concentration.The results also indicate that the chain length of cationic surfactants has a greater influence on the adsorption of diaspore than on kaolinite,which is consistent with the flotation result.

High-temperature Reference Electrodes Used in Molten Fluorides

The thermodynamic and dynamic behaviour of Ni^(2+)|Ni couple in FLINAK melt is investigated by us- ing EMF measurement and micropolarization method.The couple shows the Nernstian reversibility and a large exchange current density(6 mA·cm^(-2)).A single crystal LaF_3 which is a fluoride ion conductor used as a membrane of the Ni^(2+)|Ni couple reference electrode is reliable in FLINAK melts at 973 K.The poten- tial of LaF_3 membrane reference electrode is constant within±2 mV.The boron nitride used as a salt bridge was not good in FLINAK melts.The platinum electrode is studied by using micropolarization.The equilibrium potential of Pt electrode is dependent on the absorption and the electrochemical reaction.The potential is stable for a constant composition at constant temperature.

Studying thin film damping in a micro-beam resonator based on non-classical theories

In this paper, a mathematical model is presented for studying thin film damping of the surrounding fluid in an in-plane oscillating micro-beam resonator. The proposed model for this study is made up of a clamped-clamped micro-beam bound between two fixed layers. The microgap between the micro-beam and fixed layers is filled with air. As classical theories are not properly capable of predicting the size dependence behaviors of the micro-beam,and also behavior of micro-scale fluid media, hence in the presented model, equation of motion governing longitudinal displacement of the micro-beam has been extracted based on non-local elasticity theory. Furthermore, the fluid field has been modeled based on micro-polar theory. These coupled equations have been simplified using Newton-Laplace and continuity equations. After transforming to non-dimensional form and linearizing, the equations have been discretized and solved simultaneously using a Galerkin-based reduced order model. Considering slip boundary conditions and applying a complex frequency approach, the equivalent damping ratio and quality factor of the micro-beam resonator have been obtained. The obtained values for the quality factor have been compared to those based on classical theories. We have shown that applying non-classical theories underestimate the values of the quality factor obtained based on classical theo-ries. The effects of geometrical parameters of the micro-beam and micro-scale fluid field on the quality factor of the resonator have also been investigated.

Motion of a permeable shell in a spherical container filled with non-Newtonian fluid

This paper presents an analytical study of creeping motion of a permeable sphere in a spherical container filled with a micro-polar fluid. The drag experienced by the permeable sphere when it passes through the center of the spherical container is studied. Stream function solutions for the flow fields are obtained in terms of modified Bessel functions and Gegenbauer functions. The pressure fields, the micro-rotation components, the drag experienced by a permeable sphere, the wall correction factor, and the flow rate through the permeable surface are obtained for the frictionless impermeable spherical container and the zero shear stress at the impermeable spherical container. Variations of the drag force and the wall correction factor with respect to different fluid parameters are studied. It is observed that the drag force, the wall correction factor, and the flow rate are greater for the frictionless impermeable spherical container than the zero shear stress at the impermeable spherical container. Several cases of interest are deduced from the present analysis.

Einstein’s General Relativity and Pure Gravity in a Cosserat and De Sitter-Witten Spacetime Setting as the Explanation of Dark Energy and Cosmic Accelerated Expansion

Ordinary energy and dark energy density are determined using a Cosserat-Cartan and killing-Yano reinterpretation of Einstein’s special and general relativity. Thus starting from a maximally symmetric space with 528 killing vector fields corresponding to Witten’s five Branes model in eleven dimensional M-theory we reason that 504 of the 528 are essentially the components of the relevant killing-Yano tensor. In turn this tensor is related to hidden symmetries and torsional coupled stresses of the Cosserat micro-polar space as well as the Einstein-Cartan connection. Proceeding in this way the dark energy density is found to be that of Einstein’s maximal energy mc2 where m is the mass and c is the speed of light multiplied with a Lorentz factor equal to the ratio of the 504 killing-Yano tensor and the 528 states maximally symmetric space. Thus we have E (dark) = mc2 (504/528) = mc2 (21/22) which is about 95.5% of the total maximal energy density in astounding agreement with COBE, WMAP and Planck cosmological measurements as well as the type 1a supernova analysis. Finally theory and results are validated via a related theory based on the degrees of freedom of pure gravity, the theory of nonlocal elasticity as well as ‘t Hooft-Veltman renormalization method.