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.

Effect of strain on structure and electronic properties of monolayer C_(4)N_(4)

The first-principles calculations are performed to examine structural,mechanical,and electronic properties at large strain for a monolayer C_(4)N_(4),which has been predicted as an anchoring promising material to attenuate shuttle effect in Li–S batteries stemming from its large absorption energy and low diffusion energy barrier.Our results show that the ideal strengths of C_(4)N_(4)under tension and pure shear deformation conditions reach 13.9 GPa and 12.5 GPa when the strains are 0.07 and 0.28,respectively.The folded five-membered rings and diverse bonding modes between carbon and nitrogen atoms enhance the ability to resist plastic deformation of C_(4)N_(4).The orderly bond-rearranging behaviors under the weak tensile loading path along the[100]direction cause the impressive semiconductor–metal transition and inverse semiconductor–metal transition.The present results enrich the knowledge of the structure and electronic properties of C_(4)N_(4)under deformations and shed light on exploring other two-dimensional materials under diverse loading conditions.

Enhanced soft magnetic properties of SiO_(2)-coated FeSiCr magnetic powder cores by particle size effect

It has been known that metal FeSiCr powders with large average particle sizes have been typically employed to prepare magnetic powder cores(SMCs),with few studies reported on the influence of magnetic properties for original powders with various average particle sizes less than 10m.In this work,SiO_(2)-coated FeSiCr SMCs with different small particle sizes were synthesized using the sol-gel process.The contribution of SiO_(2)coating amount and voids to the soft magnetic properties was elaborated.The mechanism was revealed such that smaller particle sizes with less voids could be beneficial for reducing core loss in the SMCs.By optimizing the core structure,permeability and magnetic loss of 26 and 262 kW/cm^(3)at 100 kHz and 50 mT were achieved at a particle size of 4.8m and ethyl orthosilicate addition of 0.1 mL/g.The best DC stacking performance,reaching 87%,was observed at an ethyl orthosilicate addition rate of 0.25 mL/g under 100 Oe.Compared to other soft magnetic composites(SMCs),the FeSiCr/SiO_(2)SMCs exhibit significantly reduced magnetic loss.It further reduces the magnetic loss of the powder core,providing a new strategy for applications of SMCs at high frequencies.

Effect of matrix thermal properties on laser-induced plasma

The matrix thermal properties have an important impact on laser-induced plasma,as the thermal effect dominates the interaction between ns-pulsed laser and matter,especially in metals.We used a series of pure metals and aluminum alloys to measure plasma temperature and electron density through laser-induced breakdown spectroscopy,in order to investigate the effect of matrix thermal properties on laser-induced plasma.In pure metals,a significant negative linear correlation was observed between the matrix thermal storage coefficient and plasma temperature,while a weak correlation was observed with electron density.The results indicate that metals with low thermal conductivity or specific heat capacity require less laser energy for thermal diffusion or melting and evaporation,resulting in higher ablation rates and higher plasma temperatures.However,considering ionization energy,thermal effects may be a secondary factor affecting electron density.The experiment of aluminum alloy further confirms the influence of thermal conductivity on plasma temperature and its mechanism explanation.

Solvent transport dynamics and its effect on evolution of mechanical properties of nitrocellulose(NC)-based propellants under hot-air drying process

Appropriate drying process with optimized controlling of drying parameters plays a vital role in the improvement of the quality and performance of propellant products.However,few research on solvent transport dynamics within NC-based propellants was reported,and its effect on the evolution of mechanical properties was not interpreted yet.This study is conducted to gain a comprehensive understanding of hot-air drying for NC-based propellants and clarify the effect of temperature on solvent transport behavior and further the change of mechanical properties during drying.The drying kinetic curves show the drying time required is decreased but the steady solvent content is increased and the drying rate is obviously increased with the increase of hot-air temperatures,indicating hot-air temperatures have a significant effect on drying kinetics.A modified drying model was established,and results show it is more appropriate to describe solvent transport behavior within NC-based propellants.Moreover,two linear equations were established to exhibit the relationship between solvent content and its effect on the change of tensile properties,and the decrease of residual solvent content causes an obvious increase of tensile strength and tensile modulus of propellant products,indicating its mechanical properties can be partly improved by adjustment of residual solvent content.The outcomes can be used to clarify solvent transport mechanisms and optimize drying process parameters of double-based gun propellants.

Estimation of the effective properties of two-dimensional cellular materials:a review

In a vast number of engineering fields like medicine,aerospace or robotics,materials are required to meet unusual performances that simple homogeneous materials are often not able to fulfil.Consequently,many efforts are currently devoted to develop future generations of materials with enhanced properties and unusual functionalities.In many instances,biological systems served as a source of inspiration,as in the case of cellular materials.Commonly observed in nature,cellular materials offer useful combinations of structural properties and low weight,yielding the possibility of coexistence of what used to be antagonistic physical properties within a single material.Due to their peculiar characteristics,they are very promising for engineering applications in a variety of industries including aerospace,automotive,marine and constructions.However,their use is conditional upon the development of appropriate constitutive models for revealing the complex relations between the microstructure's parameters and the macroscopic behavior.From this point of view,a great variety of analytical and numerical techniques have been proposed and exhaustively discussed in recent years.Noteworthy contributions,suggesting different assumptions and techniques are critically presented in this review paper.

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.

Frequency-dependent dynamic effective properties of porous materials

The frequency-dependent dynamic effective properties (phase velocity, attenuation and elastic modulus) of porous materials are studied numerically. The coherent plane longitudinal and shear wave equations, which are obtained by averaging on the multiple scattering fields, are used to evaluate the frequency-dependent dynamic effective properties of a porous material. It is found that the prediction of the dynamic effective properties includes the size effects of voids which are not included in most prediction of the traditional static effective properties. The prediction of the dynamic effective elastic modulus at a relatively low frequency range is compared with that of the traditional static effective elastic modulus, and the dynamic effective elastic modulus is found to be very close to the Hashin-Shtrikman upper bound.

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.

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.

First-principles investigation of electronic structure,effective carrier masses, and optical properties of ferromagnetic semiconductor CdCr_2S_4

The electronic structures, the effective masses, and optical properties of spinel CdCr_2S_4 are studied by using the fullpotential linearized augmented planewave method and a modified Becke–Johnson exchange functional within the densityfunctional theory. Most importantly, the effects of the spin–orbit coupling（SOC） on the electronic structures and carrier effective masses are investigated. The calculated band structure shows a direct band gap. The electronic effective mass and the hole effective mass are analytically determined by reproducing the calculated band structures near the BZ center.SOC substantially changes the valence band top and the hole effective masses. In addition, we calculated the corresponding optical properties of the spinel structure CdCr_2S_4. These should be useful to deeply understand spinel CdCr_2S_4 as a ferromagnetic semiconductor for possible semiconductor spintronic applications.

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.

RANDOM MICROSTRUCTURE FINITE ELEMENT METHOD FOR EFFECTIVE NONLINEAR PROPERTIES OF COMPOSITE MATERIALS

Some theoretical methods have been reported to deal with nonlinear problems of composite materials but the accuracy is not so good. In the meantime, a lot of linear problems are difficult to be managed by the theoretical methods. The present study aims to use the developed method, the random microstructure finite element method, to deal with these nonlinear problems. In this paper, the random microstructure finite element method is used to deal with all three kinds of nonlinear property problems of composite materials. The analyzed results suggest the influences of the nonlinear phenomena on the effective properties of composite materials are significant and the random microstructure finite element method is an effective tool to investigate the nonlinear problems.

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.

MULTIPLE SCATTERING THEORY OF EFFECTIVE MECHANICAL PROPERTIES OF INHOMOGENEOUS MEDIA

The rate of hydrothermal reaction of SiO_2 and/or A1_2O_3 in the system of CaO-Al_2O_3-SiO_2-H_2O at 200℃ and the factors which influence the reactions are investigated by determining the reaction ratio.The rate of reactions depends on the reactive activities of raw materials, initial composition of mixture and relative activity of SiO_2 and A12O3. The hydrothermal reaction can be accelerated by sodium hydroxide,in the case of silica,which has low activity, this is quite obvious.

Effective Elastic Properties of Honeycomb Core with Fiber-Reinforced Composite Cells

Sandwich construction incorporating a honeycomb cellular core offers the attainment of structures that are very stiff and strong in bending while the weight is kept at a minimum. Generally, an aluminum or Nomex honeycomb core is used in applications requiring sandwich construction with fiber-reinforced composite facesheets. However, the use of a fiber-reinforced composite core offers the potential for even lower weight, increased stiffness and strength, low thermal distortion compatible with that of the facesheets, the absence of galvanic corrosion and the ability to readily modify the core properties to suit specialized needs. Furthermore, the material of the core itself will exhibit anisotropic material properties in this case. In order to design, analyze and optimize these structures, knowledge of the effective mechanical properties of the core is essential. In this paper, the effective three-dimensional mechanical properties of a composite hexagonal cell core are determined using a numerical method based on a finite element analysis of a representative unit cell. In particular, the geometry of the simplest repeating unit of the core as well as the appropriate loading and boundary conditions that must be applied is presented.

Effective Field Theory Techniques Applied to the Properties of the Axion

We utilize the effective field theory approach to study the properties of the axion. In particular, with s as well as u and d quarks regarded to be relatively light we derive a formula for the mass of the axion; a rough estimate of the rate for its dominant decay mode at low energy is also carried out.

Effect of wear conditions on tribological properties of electrolessly-deposited Ni-P-Gr-SiC hybrid composite coating

The friction and wear properties of the electrolessly-deposited Ni-P-Gr-SiC composites were investigated. The effects of graphite content, load and rotation speed on the friction coefficient and wear resistance of the composite coatings were mainly investigated. The worn surface and cross section of the coatings were characterized by scanning electron microscopy and energy-dispersive X-ray analysis. The results show that the composite coatings reveal good antifriction and wear resistance due to the synergic effect of graphite and SiC particles. The formation of graphite-rich mechanically mixed layer （GRMML） on the surface of Ni-P-Gr-SiC coating contributes to the good tribological behavior of the wear counterparts and SiC particles play a load bearing role in protecting GRMML from shearing easily.

THE EFFECTIVE PROPERTIES OF COMPOSITES WITH FIBER-END CRACKS

The paper describes use of self-consistent finite element method (SCFEM) for predicting effective properties of fiber composite with partially debonded interface. The effective longitudinal Young's modulus and shear modulus for unidirectional fiber reinforced composites with fiber-end cracks are calculated. Numerical results show that the effective properties are considerably influenced by the fiber-end cracks. The effects of microstructural parameters, such as fiber volume fraction, modulus ratio of the constituents and fiber aspect, on the effective properties of the composites were discussed.