Analytical solution for the effective elastic properties of rocks with the tilted penny-shaped cracks in the transversely isotropic background

Seismic prediction of cracks is of great significance in many disciplines,for which the rock physics model is indispensable.However,up to now,multitudinous analytical models focus primarily on the cracked rock with the isotropic background,while the explicit model for the cracked rock with the anisotropic background is rarely investigated in spite of such case being often encountered in the earth.Hence,we first studied dependences of the crack opening displacement tensors on the crack dip angle in the coordinate systems formed by symmetry planes of the crack and the background anisotropy,respectively,by forty groups of numerical experiments.Based on the conclusion from the experiments,the analytical solution was derived for the effective elastic properties of the rock with the inclined penny-shaped cracks in the transversely isotropic background.Further,we comprehensively analyzed,according to the developed model,effects of the crack dip angle,background anisotropy,filling fluid and crack density on the effective elastic properties of the cracked rock.The analysis results indicate that the dip angle and background anisotropy can significantly either enhance or weaken the anisotropy degrees of the P-and SH-wave velocities,whereas they have relatively small effects on the SV-wave velocity anisotropy.Moreover,the filling fluid can increase the stiffness coefficients related to the compressional modulus by reducing crack compliance parameters,while its effects on shear coefficients depend on the crack dip angle.The increasing crack density reduces velocities of the dry rock,and decreasing rates of the velocities are affected by the crack dip angle.By comparing with exact numerical results and experimental data,it was demonstrated that the proposed model can achieve high-precision estimations of stiffness coefficients.Moreover,the assumption of the weakly anisotropic background results in the consistency between the proposed model and Hudson's published theory for the orthorhombic rock.

Effective property of piezoelectric composites containing coated nano-elliptical fibers with interfacial debonding

Based on both the spring layer interface model and the Gurtin-Murdoch surface/interface model,the anti-plane shear problem is studied for piezoelectric composites containing coated nano-elliptical fibers with imperfect interfaces.By using the complex function method and the technique of conformal mapping,the exact solutions of the electroelastic fields in fiber,coating,and matrix of piezoelectric nanocomposites are derived under far-field anti-plane mechanical and in-plane electrical loads.Furthermore,the generalized self-consistent method is used to accurately predict the effective electroelastic moduli of the piezoelectric nanocomposites containing coated nano-elliptical fibers with imperfect interfaces.Numerical examples are illustrated to show the effects of the material constants of the imperfect interface layers,the aspect ratio of the fiber section,and the fiber volume fraction on the effective electroelastic moduli of the piezoelectric nanocomposites.The results indicate that the effective electroelastic moduli of the piezoelectric nanocomposites can be significantly reduced by the interfacial debonding,but it can be improved by the surface/interface stresses at the small scale,which provides important theoretical reference for the design and optimization of piezoelectric nanodevices and nanostructures.

Theoretical study on dynamic effective electroelastic properties of random piezoelectric composites with aligned inhomogeneities

The closed-form solutions of the dynamic problem of heterogeneous piezoelectric materials are formulated by introducing polarizations into a reference medium and using the generalized reciprocity theorem.These solutions can be reduced to the ones of an elastodynamic problem.Based on the effective medium method,these closedform solutions can be used to establish the self-consistent equations about the frequencydependent effective parameters,which can be numerically solved by iteration.Theoretical predictions are compared with the experimental results,and good agreement can be found.Furthermore,the analyses on the effects of microstructure and wavelength on the effective properties,resonance frequencies,and attenuation are also presented,which may provide some guidance for the microstructure design and analysis of piezoelectric composites.

Modeling Method of C/C-ZrC Composites and Prediction of Equivalent Thermal Conductivity Tensor Based on Asymptotic Homogenization

This article proposes a modeling method for C/C-ZrC composite materials.According to the superposition of Gaussian random field,the original gray model is obtained,and the threshold segmentation method is used to generate the C-ZrC inclusion model.Finally,the fiber structure is added to construct the microstructure of the three-phase plain weave composite.The reconstructed inclusions can meet the randomness of the shape and have a uniform distribution.Using an algorithm based on asymptotic homogenization and finite element method,the equivalent thermal conductivity prediction of the microstructure finite element model was carried out,and the influence of component volume fraction on material thermal properties was explored.The sensitivity of model parameters was studied,including the size,mesh sensitivity,Gaussian complexity,and correlation length of the RVE model,and the optimal calculation model was selected.The results indicate that the volume fraction of the inclusion phase has a significant impact on the equivalent thermal conductivity of the material.As the volume fraction of carbon fiber and ZrC increases,the equivalent thermal conductivity tensor gradually decreases.This model can be used to explore the impact of materialmicrostructure on the results,and numerical simulations have studied the relationship between structure and performance,providing the possibility of designing microstructure based on performance.

Wave propagation of a functionally graded plate via integral variables with a hyperbolic arcsine function

Several studies on functionally graded materials(FGMs)have been done by researchers,but few studies have dealt with the impact of the modification of the properties of materials with regard to the functional propagation of the waves in plates.This work aims to explore the effects of changing compositional characteristics and the volume fraction of the constituent of plate materials regarding the wave propagation response of thick plates of FGM.This model is based on a higher-order theory and a new displacement field with four unknowns that introduce indeterminate integral variables with a hyperbolic arcsine function.The FGM plate is assumed to consist of a mixture of metal and ceramic,and its properties change depending on the power functions of the thickness of the plate,such as linear,quadratic,cubic,and inverse quadratic.By utilizing Hamilton’s principle,general formulae of the wave propagation were obtained to establish wave modes and phase velocity curves of the wave propagation in a functionally graded plate,including the effects of changing compositional characteristics of materials.

Novel implementation of homogenization method to predict effective properties of periodic materials

Representative volume element （RVE） method and asymptotic homogenization （AH） method are two widely used methods in predicting effective properties of pe- riodic materials. This paper develops a novel implementa- tion of the AH method, which has rigorous mathematical foundation of the AH method, and also simplicity as the RVE method. This implementation can be easily realized using commercial software as a black box, and can use all kinds of elements available in commercial software to model unit cells with rather complicated microstructures, so the model may remain a fairly small scale. Several examples were car- fled out to demonstrate the simplicity and effectiveness of the new implementation.

Influences of interphase on dynamic effective properties of composites reinforced by dispersed spherical particles

The influences of interphase on dynamic effective properties of composites reinforced by randomly dispersed spherical particles were studied. A thin homogeneous elastic interphase with different shear and bulk moduli, located between the reinforced particle and the host matrix, was introduced to model the interfacial bonding state. The effects of such an interphase on the coherent plane waves were studied numerically. Numerical simulations were carried out for SiC-Al composites with four typical cases of interphase. It was found that the property of interphase has significant influences on the effective propagation constants of coherent waves and the dynamic effective elastic moduli of the composites. The influences on the coherent longitudinal wave and the coherent shear waves were different and dependent upon the frequency range. Moreover, several imperfect interface models, i.e., the spring model, mass model, and spring-mass model, were studied numerically and compared with the interphase model, It was found that the spring model is a more suitable model than the mass model for the light and weak interphase whereas the mass model is a more suitable model than the spring model for the heavy and strong interphase.

Influence of spherical inclusions on effective thermoelectric properties of thermoelectric composite materials

A homogenization theory is developed to predict the influence of spherical inclusions on the effective thermoelectric properties of thermoelectric composite materials based on the general principles of thermodynamics and Mori-Tanaka method.The closed-form solutions of effective Seebeck coefficient,electric conductivity,heat conductivity,and figure of merit for such thermoelectric materials are obtained by solving the nonlinear coupled transport equations of electricity and heat.It is found that the effective figure of merit of thermoelectric material containing spherical inclusions can be higher than that of each constituent in the absence of size effect and interface effect.Some interesting examples of actual thermoelectric composites with spherical inclusions,such as insulated cavities,inclusions subjected to conductive electric and heat exchange and thermoelectric inclusions,are considered,and the numerical results lead to the conclusion that considerable enhancement of the effective figure of merit is achievable by introducing inclusions.In this paper,we provide a theoretical foundation for analytically and computationally treating the thermoelectric composites with more complicated inclusion structures,and thus pointing out a new route to their design and optimization.

Therapeutic Actions of the Chinese Herbal Formulae with Cold and Heat Properties and Their Effects on Ultrastructures of Synoviocytes in Rats of the Collagen-Induced Arthritis

The therapeutic actions of Qing Luo Yin (QLY清络饮) with heat property and Wen Luo Yin (WLY温络饮) with cold property on pain, swelling of the ankle, arthritis index and ultrastructures of synoviocytes were compared in rats of type II collagen-induced arthritis (CIA), with tripterygium glycosidorum (TG) used as control. The results indicated that both QLY and WLY could reduce pain, swelling of the ankle and the arthritis index of CIA, and QLY had better effects in reducing the swelling of the ankle and controlling the secondary pathological lesions as compared with WLY. Investigation on the ultrastructures of synoviocytes indicated that both QLY and WLY could reduce the number of Golgi apparatus, rough surface endoplasmic reticulum, dense bodies, matrix filaments and vacuoles so as to suppress the excessive secretion of synoviocytes in rats of CIA.

RANDOM MICROSTRUCTURE FINITE ELEMENT METHOD AND ITS VERIFICATION FOR EFFECTIVE PROPERTIES OF COMPOSITE MATERIALS

The present study aims at developing a new method-RandomMicrostructure Finite Element Method (RMFEM) for the effectiveproperties of com- Posite materials. In this method, a randommicrostructure Model is used to simulate the microstructure of thereal composite materials. The physical fields in such a randomMicrosturucture model under specified boundary and initial Conditionsare analyzed by finite element method.

INVESTIGATION OF UNSTEADY EXCITATION EFFECTS ON AERODYNAMIC PROPERTIES OF AIRFOILS

In this paper, the techniques to manage and control the flow over airfoils by using the external unsteady excitations are investigated. The mechanisms of these excitation effects are also explored. The principal goal of this study is to gain a better understanding and to find the possible ways for enhancing the aerodynamic efficients. The experimental investigations are carried out in two low-speed wind tunnels. The test models are two dimensional airfoils with different section geometries. Four means of excitations have been used in these experiments. (1) The pitch oscillation of the airfoil high-angle-of-attack situation. (2) The moving surface effects of the airfoil with a leading edge rotating cylinder. (3) Oscillating leading edge flaperon. (4) Small oscillating spoiler located near the leading edge of the airfoil. The lift, drag and pitch moment coefficients are measured in these experiments. But, we will put the emphasis only on the 'dynamic amplifying effects' on aerodynamic lift in this paper. Results obtained indicate that the beneficial aerodynamic effects of section lift increase can be obtained at the high angle of attack near stall regime, as long as the frequency and amplitute of the excitation are appropriately selected.

Effective electromechanical properties of cellular piezoelectret:A review

Due to the large quasi-piezoelectric d33 coefficient in the film thickness direction, cellular piezoelectret has emerged as a new kind of compliant electromechanical transducer materials. The macroscopic piezoelectric effect of cellular piezoelectret is closely related to the void microstructures as well as the material constants of host polymer. Complex void microstmctures are usually encountered in the optimum design of cellular piezoelectret polymer film with ad- vanced piezoelectric properties. Analysis of the effective electromechanical properties is generally needed. This article presents an overview of the recent progress on theoretical models and numerical simulation for the effective electromechanical properties of cellular piezoelectret. Emphasis is placed on our own works of cellular piezoelectret published in past several years.

The magnetic properties and magnetocaloric effects in binary R-T(R = Pr,Gd,Tb,Dy,Ho,Er,Tm;T = Ga,Ni,Co,Cu)intermetallic compounds

In this paper, we review the magnetic properties and magnetocaloric effects（MCE） of binary R–T（R = Pr, Gd, Tb,Dy, Ho, Er, Tm; T = Ga, Ni, Co, Cu） intermetallic compounds（including RGa series, RNi series, R_（12）Co_7 series, R_3 Co series and RCu_2series）, which have been investigated in detail in the past several years. The R–T compounds are studied by means of magnetic measurements, heat capacity measurements, magnetoresistance measurements and neutron powder diffraction measurements. The R–T compounds show complex magnetic transitions and interesting magnetic properties.The types of magnetic transitions are investigated and confirmed in detail by multiple approaches. Especially, most of the R–T compounds undergo more than one magnetic transition, which has significant impact on the magnetocaloric effect of R–T compounds. The MCE of R–T compounds are calculated by different ways and the special shapes of MCE peaks for different compounds are investigated and discussed in detail. To improve the MCE performance of R–T compounds,atoms with large spin（S） and atoms with large total angular momentum（J） are introduced to substitute the related rare earth atoms. With the atom substitution, the maximum of magnetic entropy change（？SM）, refrigerant temperature width（Twidth）or refrigerant capacity（RC） is enlarged for some R–T compounds. In the low temperature range, binary R–T（R = Pr, Gd,Tb, Dy, Ho, Er, Tm; T = Ga, Ni, Co, Cu） intermetallic compounds（including RGa series, RNi series,R_（12）Co_7 series, R_3 Co series and RCu_2series） show excellent performance of MCE, indicating the potential application for gas liquefaction in the future.

Effect of Irradiation on Crystallinity and Mechanical Properties of Ultrahigh-Molecular-Weight Polyethylene

Ultrahigh-molecular-weight polyethylene(UtlMWPE) has been irradiated (0-40 Mrad) with a Co^(60) source at room temperature under vacuum. Their crystallinity has been investigated by DSC and SAXS A significant increase of heat of fusion can be seen at low irradiation doses, which is attributed to crystallization caused by chain scission during the process of irradiation. It is also observed that thickness of lamellae changes with irradiation dose. Young's modulus has been improved significantly after irradiation at low doses.

Size-dependent electromechanical properties in piezoelectric superlattices due to flexoelectric effect

Piezoelectric superlattice is a potential component for nanoelectromechanical systems. Due to the strong nonlocal effect such as flexoelectric effect at interfaces, classical piezoelectric theory is unable to accurately describe the electromechanical response of piezoelectric superlattice at nanoscale scale. Based on the previous nonlocal thermodynamics theory with flexoelectric effect Liu et al. （2016）, the size- dependent electromechanical properties of piezoelectric superlattices made of BaTiO3 （BTO） and PbTiO3 （PRO） layers are investigated systematically in the present work. Giant strain gradient is found near the interface between BTO and PTO layers, which leads to the significant enhancement of polarization in the superlattice due to the flexoelectric effect. For the piezoelectric BTO-PTO superlattices with different unit- cell sizes, the thickness of interface with nontrivial strain gradient is almost constant. The influence of strain gradient at the interface becomes significant when the size of superlattice decreases, As a result, a strong size dependence of electromechanical properties is predicted for the piezoelectric BTO-PTO superlattices, In particular, for the superlattices with a specific thickness ratio of BTO and PTO layers, the piezoelectric response can be several times larger than that of bulk structure. The present work demonstrates a practical wast to design the piezoelectric superlattices with high piezoelectric coefficient by using the nonlocal effect at nanoscale.

Effects of Doping on the Magnetic Properties and Frustration of Hexagonal YMn0.9A0.1O3（A=Al,Fe,and Cu）

The doping effects on the frustration and the magnetic properties in hexagonal compounds ot YMn0.9A0.1O3 （A=A1, Fe and Cu） are investigated. Experimental results indicate that both the non-magnetic and magnetic ion dopants lead to the increase of magnetic moments and the decrease of the absolute value of Curie-Weiss temperature （｜θcw｜）- Compared with pure YMnOa, the geometrical frustration of YMn0.9 A0. 1O3 is greatly suppressed and the magnetic coupling in that exhibits dopant-dependent. In addition, for the doped YMno.gAo.103, the antiferromagnetic transition temperature （TN） is also suppressed slightly, which shows an abnormal dilution effect and it may be ascribed to the reduction of frustration due to the chemical substitution.

Effect of Trace Sc and Zr on the Mechanical Properties and Microstructure of A1 Alloy 2618

An experimental 2618(Al-Cu-Mg-Fe-Ni) alloy added with trace Sc and Zr was prepared by ingot metallurgy (IM) method. The aging behavior of the alloy was studied by Vickers hardness measurement at 200℃ and 300℃. and the tensile properties of alloy specimens were measured at 20℃, 200℃, 250℃ and 300℃. The microstructure was observed by using optical microscope, SEM and TEM. It was found that the addition of Sc and Zr to 2618 alloy resulted in a primary Al_3(Sc,Zr) phase which could refine the grain because it acts as nuclei of heterogeneous crystallization in the melt during solidification. The secondary Al_3(Sc,Zr) particles were full coherent with matrix and had obvious precipitation hardening effect. They also made the S' phase precipitate more homogeneous. So the strength of alloy increases at both ambient and elevated temperatures without a decrease of ductility. The ductile fracture of alloy occurs by microvoid nucleation, growth and coalescence, so the microvoid coalescence is the dominant fracture mechanism.

Effect of Sintering Temperature and Zinc Content on Some Properties of Li-Zn Ferrites

Li-Zn mixed ferrites with composition formula ZnxLi0.5-x/2Fe2.5-x/2O4 (0.2≤x≤0.8) were prepared by the usual ceramic method in 1000~1150℃. The effects of Zn substitution and sintering temperature on the formation, densification, microstructure and a.c. electrical conductivity have been studied. Under the effect of changing the firing temperature and Zn content, high sintered Li-Zn ferrite bodies are achieved. More fine structure bodies having high electrical resistance are obtained at high Zn content

Effects of Thickness and Temperature on Thermoelectric Properties of Bi2Te3-Based Thin Films

Bi_2Te_3 thin films and GeTe/B_2Te_3 superlattices of different thicknesses are prepared on the silicon dioxide substrates by magnetron sputtering technique and thermally annealed at 573 K for 30 min. Thermoelectric（TE）measurements indicate that optimal thickness and thickness ratio improve the TE performance of Bi_2Te_3 thin films and GeTe/B_2Te_3 superlattices, respectively. High TE performances with figure-of-merit（ZT） values as high as 1.32 and 1.56 are achieved at 443 K for 30 nm and 50 nm Bi_2Te_3 thin films, respectively. These ZT values are higher than those of p-type Bi_2Te_3 alloys as reported. Relatively high ZT of the GeTe/B_2Te_3 superlattices at 300-380 K were 0.62-0.76. The achieved high ZT value may be attributed to the unique nano-and microstructures of the films,which increase phonon scattering and reduce thermal conductivity. The results indicate that Bi_2Te_3-based thin films can serve as high-performance materials for applications in TE devices.