Average Elastic Properties Research Articles

Control Parameters of Magnitude—Seismic Moment Correlation for the Crustal Earthquakes

In connection with conversion from energy class KR (KR = log10E R, where ER — seismic energy, J) to the universal magnitude estimation of the Tien Shan crustal earthquakes the development of the self-coordinated correlation of the magnitudes (mb , ML, Ms ) and KR with the seismic moment M0 as the base scale became necessary. To this purpose, the first attempt to develop functional correlations in the magnitude—seismic moment system subject to the previous studies has been done. It is assumed that in the expression M (mb , ML , Ms) = Ki + zi log10M0 , the coefficients ki and zi are controlled by the parameters of ratio (where ; f0 —corner frequency, Brune, 1970, 1971; M0, N×m). According to the new theoretical predictions common functional correlation of the advanced magnitudes Mm (mbm = mb , MLm = ML , MSm = MS ) from log10M0, log10t0 and the elastic properties (Ci) can be presented as , where , and , for the averaged elastic properties of the Earth’s crust for thembmthe coefficients Ci= –11.30 and di = 1.0, for MLm: Ci = –14.12, di = 7/6; for MSm : Ci = –16.95 and di = 4/3. For theTien Shan earthquakes (1960-2012 years) it was obtained that , and on the basis of the above expressions we received that MSm = 1.59mbm – 3.06. According to the instrumental data the correlation Ms = 1.57mb – 3.05 was determined. Some other examples of comparison of the calculated and observed magnitude - seismic moment ratios for earthquakes of California, the Kuril Islands, Japan, Sumatra and South America are presented.

Elastic properties of a macroscopic graphene sample from phonon dispersion measurements

The average elastic properties and the interatomic force constants of a quasi-freestanding graphene sample have been evaluated by analyzing the phonon dispersion measured by means of angle-resolved energy loss spectroscopy. We found a Poisson’s ratio of 0.19 and a Young’s modulus of 342N/m. Such findings are in excellent agreement with calculations performed for a free-standing graphene membrane. Present results indicate that the high crystalline quality of graphene grown on metal substrates leads to macroscopic samples of high tensile strength and bending flexibility to be used for technological applications such as electromechanical devices and carbon-fiber reinforcements.

Stochastic laminate analogy for simulating the variability in modulus of discontinuous composite materials

Abstract Recent composite technology research and development efforts have focused on discontinuous carbon fiber/epoxy molding systems derived from chopped aerospace-grade unidirectional tape prepreg. Although the average elastic modulus of this material has been shown to be as high as that of the continuous tape quasi-isotropic benchmark, experimental measurement by means of strain gage or extensometer has shown variation as high as 20%. Digital Image Correlation can be used successfully to obtain a full-field strain measurement, and it shows that a highly non-uniform strain distribution exists on the surface of the specimen, with distinct peaks and valleys. This pattern of alternating regions of high and low strain gradients, and which exhibit a characteristic shape and size, can be described in terms of Random Representative Volume Element (RRVE). The RRVE proposed here exhibits random elastic properties, which are assigned based on stochastic distributions. This approach leads to the analysis method proposed here, which is designed to compensate for the fact that traditional methods cannot capture the experimentally observed variation in modulus within a specimen and among different specimens. The method utilizes a randomization process to generate statistical distributions of fractions and orientations of chips within the RRVE, and then applies Classical Laminated Plate Theory to an equivalent quasi-isotropic tape laminate to calculate its average elastic properties. Validation of this method is shown as it applies to a finite element model that discretizes the structure in multiple RRVEs, whose properties are generated independently of the neighboring ones, and then are solved simultaneously. The approach generates accurate predictions of the strain distribution on the surface of the specimen.

Approximation to Cutoffs of Higher Modes of Rayleigh Waves for a Layered Earth Model

A cutoff defines the long-period termination of a Rayleigh-wave higher mode and, therefore is a key characteristic of higher mode energy relationship to several material properties of the subsurface. Cutoffs have been used to estimate the shear-wave velocity of an underlying half space of a layered earth model. In this study, we describe a method that replaces the multilayer earth model with a single surface layer overlying the half-space model, accomplished by harmonic averaging of velocities and arithmetic averaging of densities. Using numerical comparisons with theoretical models validates the single-layer approximation. Accuracy of this single-layer approximation is best defined by values of the calculated error in the frequency and phase velocity estimate at a cutoff. Our proposed method is intuitively explained using ray theory. Numerical results indicate that a cutoffs frequency is controlled by the averaged elastic properties within the passing depth of Rayleigh waves and the shear-wave velocity of the underlying half space.

Multiscale modelling and structural characterization of Fe enriched Al alloy

AbstractScale dependent modelling of inelastic behaviour of rapidly solidified Al Fe enriched powders subjected to cold compaction and subsequent hot extrusion is provided. The alloy is considered as a ductile “in situ” composite. The average elastic end plastic properties of bulk material depend on density evolution, temperature and matrix hardening. The model assumptions are based on microstructural observations. The microstructure characterization was carried out using Scanning Electro Microscopy (SEM) and Energy Dispersive X–ray (EDX) analysis. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Application of a micromechanics model to the overall properties of heterogeneous graphite

This paper deals with the overall properties of polycrystalline graphite, a material mainly composed of voids and dense inhomogeneities embedded in a less dense matrix. First, we examine the overall average elastic properties and conductivities of such a material. Second, we evaluate the void shape effects on the overall Young’s modulus. Finally, we compare the results obtained from the analytical model with experimental data from radiolytic oxidation of graphite.

Micromechanical model for elasticity of the cell cytoskeleton

Semiflexible polymer networks, such as cell cytoskeleton, differ significantly from their flexible counterparts in their deformation energy storage mechanism. As a result, the network elasticity is governed by both enthalpic and entropic variations. In addition, the enthalpic effect shows two distinct regimes of energy storage mechanism, the affine and nonaffine regimes. In the past, computation-based modeling on random networks, such as the Mikado model, was used to demonstrate the physical mechanism of mechanical deformation of semiflexible networks. These models are computationally intensive and hence are difficult to apply to studying whole cells. In this paper, we develop a micromechanical model to predict the average macroscopic elastic properties of a random, semiflexible, biopolymer network. The model employs a unit cell consisting of four semiflexible chains and four equivalent axial-bending springs. The proposed unit-cell-based micromechanical model represents a statistically average realization of the actual network and gives the average mechanical properties, such as the shear modulus. Comparisons between the model predictions and Mikado model results confirm that this micromechanical model captures the essential deformation physics revealed from previous studies on the actual network and is capable of predicting the transition between nonaffine and affine deformations. This model can be used to develop efficient continuum constitutive models of the cytoskeleton in the future.

Calculation of averaged elastic properties of materials having noncircular character of pole figures

An important application of quantitative description of textures of materials is calculation of the averaged physical properties of polycrystals. In this study, such properties are elastic parameters of materials. In recent years, the effect of crystallographic texture on the average values of elastic properties of polycrystals has been analyzed in many studies. Researchers often restrict themselves to the consideration of average values of Young’s or shear moduli, which are related to the components of the elastic compliance tensor. The simplest scheme of averaging of all components of the elastic compliance tensor is considered. Complicated (not angular) normal distributions of general character are used as the weight function. A practical example of application of these techniques to calculation of elastic compliance moduli of magnesium and titanium polycrystals is proposed.

Predição das propriedades elásticas de compósitos termoestruturais com reforço multidirecional

Os compósitos são uma classe de materiais que apresentam propriedades superlativas em relação aos materiais isotrópicos (metais, cerâmicos, polímeros), se considerarmos sua alta resistência aliada ao baixo peso. O reforço, a matriz e a interface entre ambos, definem o desempenho do componente em serviço e a temperatura de trabalho destes materiais. Particularmente, compósitos de uso a temperaturas superiores à 1000ºC são denominados de compósitos termoestruturais. Estes materiais suportam demandas termo-mecânicas significativas, sendo utilizados em gargantas de tubeira de foguetes, proteções térmicas re-irradiativas e materiais de fricção. Via de regra, esses materiais são manufaturados mediante a utilização de preformas fibrosas, que nada mais são que um "esqueleto" de reforço que translada resistência e rigidez ao material. A utilização de preformas permite a concepção e obtenção de componentes com geometrias complexas e dimensões as mais diversas, permitindo assim uma flexibilidade no projeto do componente a ser obtido. Embora apresentem virtudes incontestáveis, o custo desses materiais ainda é proibitivo para aplicações rotineiras. Também o custo dos testes mecânicos que validem suas propriedades em relação aos materiais de uso convencional torna-se oneroso, além de demandar equipamentos especiais. O presente trabalho aborda a predição das propriedades elásticas de compósitos termoestruturais de Carbono Reforçado com Fibras de Carbono (CRFC), com configurações de reforço tri-direcional (3D) e tetra-direcional (4D). As propriedades foram calculadas à temperatura ambiente para efeito de comparação ao grafite sintético, ainda utilizado em gargantas de tubeira de motores foguete de pequeno porte. Os cálculos de predição de propriedades elásticas foram baseados no método de homogeneização considerando a hipótese de mechas de fibras retas pela rigidez média ponderada.

A new method for calculation of elastic properties of anisotropic material by constant pressure molecular dynamics

A new method based on constant pressure molecular dynamics (MD) with the software package Materials Studio (MS) was developed to calculate the anisotropic elastic properties of 1,3,5-tri-amino-2,4,6-tri-nitrobenzene (TATB) which is a typical and widely studied explosive molecular and its single crystal is a typical triclinic lattice. Key points of the method are introduced. Firstly, a P1 periodic super cell of TATB which ab plane was designated as (0 1 0) planar of the crystal was modeled. After several fixing and relaxing steps, the cell was pre-equilibrated for 500 ps and followed a 100 ps MD with trajectory at 298 K in NVT ensemble. The averaged isotropic elastic properties were calculated by MS analysis module of elastic properties (static). Secondly, NPT ensemble was chosen and different stresses in six different directions were added through many tries to keep the cell parameters fluctuating around those values in NVT ensemble while performing constant pressure MD. The MS averaged isotropic elastic properties as well as elastic constant matrix of the well equilibrated NPT system were then obtained. Thirdly, different magnitude of compressive or tensile stress was applied to the cell in one direction and the equilibrated box lengths were averaged statistically to calculate the strains in three directions. Anisotropic tensile moduli as well as Poisson’s ratios were then obtained via the strain–stress profile and the averaged values over those in three directions were given. Finally, the average values were compared with those in NVT or NPT ensemble to validate the titled method. Deviation within less than 20% revealed that the method can be certainly applied to the study on elastic properties of anisotropic materials.

Ab Initio and Molecular Dynamics Studies of Crystalline TNAD (trans-1,4,5,8-Tetranitro-1,4,5,8-tetraazadecalin)

The structural and electronic properties of the energetic crystal TNAD (trans-1,4,5,8-tetranitro-1,4,5,8- tetraazadecalin) have been studied using plane-wave ab initio calculations based on the density function theory method with the ultrasoft pseudopotentials. It is found that the predicted crystal structure is in good agreement with experimental data and there are strong inter- and intramolecular interactions in bulk TNAD. Band structure calculations indicate that TNAD is an insulator with the band gap of ca. 3.3 eV. The hydrostatic compression effect on TNAD has been studied in the pressure range of 0-600 GPa. The results show that a pressure less than 10 GPa does not significantly change the geometric parameters, charge distributions, and electronic bands. When the pressure is over 10 GPa, increasing the pressure determines significant changes of the geometrical and electronic structures and large broadening of the electronic bands together with a sharp decrease of the band gap. Isothermal-isobaric molecular dynamics simulations at atmospheric pressure were further performed on the TNAD crystal in the temperature range 5-500 K. Average equilibrium lattice parameters and elastic properties as functions of temperature were determined. The thermal expansion coefficients calculated for the crystal indicate anisotropic behavior with the largest expansion along the b axis.

Elastic properties determined from in situ X-ray diffraction

In situ powder diffraction experiments were performed at the Swiss Light Source MS4 beamline on specimens under tensile deformation. Evaluation of the intensity and position of several Bragg peaks as a function of the applied tensile load allows the average elastic properties of grains as well as of the macroscopic sample to be determined without the necessity of accurate macroscopic strain measurements. The feasibility of the method developed is demonstrated for polycrystalline Si.

Crystal structures of sulfamates MeLi(NH2SO3)2 (Me: K, Rb and Cs) and physical properties of KLi(NH2SO3)2 (refractive indices, thermal expansion, elastic properties)

Abstract New sulfamates KLi(NH2SO3)2, RbLi ⋅ (NH2SO3)2 and CsLi(NH2SO3)2 were prepared from non-stoichiometric (ratio Li: Me = 3:1) aqueous solutions of LiNH2SO3 and MeNH2SO3 (Me = K, Rb, Cs) at room temperature. Large single crystals of KLi(NH2SO3)2 were grown from these solutions by controlled lowering of the temperature between 293 K and 288 K. The crystal structures were investigated using single-crystal X-ray diffraction methods. KLi(NH2SO3)2: space group P21, Z = 2, a = 5.196(1) Å, b = 8.475(1) Å, c = 8.868(1) Å, β = 105.05(1)°, T meas. = 293 K, R1 = 0.026; RbLi(NH2SO3)2: space group P1̅, Z = 4, a = 7.844(1) Å, b = 9.804(1) Å, c = 10.825(1) Å, α = 108.77(1)°, β = 93.29(1)°, γ = 98.64(1)°, T meas. = 293 K, R1 = 0.033; CsLi(NH2SO3)2 : space group P1̅, Z = 2, a = 5.535(1) Å, b = 7.877(1) Å, c = 9.857(1) Å, α = 74.07(1)°, β = 76.33(1)°, γ = 87.07(1)°, T meas. = 200 K; R1 = 0.023. The common feature of the three crystal structures are alternating layers of Me+ and lithium cations together with anionic [NH2SO3]– tetrahedra. Li+ coordination polyhedra and [NH2SO3]– anions, linked via common corners, form one type of these sheets. Additionally, these layers are stabilized by hydrogen bonds. Me+ coordination polyhedra are linked to each other and to the above mentioned layers by common corners and edges. RbLi(NH2SO3)2 and CsLi(NH2SO3)2 possess similar structures. Generally, the observed interatomic distances and angles agree with crystal chemical expectations. Differential scanning calorimetry measurements showed that KLi(NH2SO3)2 undergoes a first-order structural phase transition at 401 K and melts at 423 K. Between 153 K and 423 K no indications of further phase transitions were observed. In addition, the refractive indices and the tensor of thermal expansion were measured. Further, the elastic and thermoelastic constants of KLi(NH2SO3)2 were determined from ultrasonic resonant frequencies of thick plane-parallel plates and their shift upon variation of temperature, respectively. The elastic behaviour of KLi(NH2SO3)2 is similar to the average elastic properties of LiNH2SO3 and KNH2SO3.

The abundance of ultramafic rocks in Atlantic Ocean crust

Combined P- and S-wave velocity profiles have been widely used to assess the composition of the oceanic crust, but no quantitative estimates of the abundances of mafic and ultramafic rocks which are compatible with the seismic structure of the crust have been made. In this study, a Voigt–Reuss–Hill (VRH) average model based on the average elastic properties of partially serpentinized peridotites and oceanic diabases and gabbros is used to make quantitative estimates of lithological composition from the seismic structure of the crust. The VRH model is applied to several expanding spread profiles from the north Atlantic, in which P- and S-wave velocities are independently constrained. A purely gabbroic composition is sufficient to explain the seismic structure in most cases, but the lower oceanic crust could also be composed of interlayered gabbros and ultramafic rocks, and the average ultramafic content of the crust could be as high 13 per cent. In that case, the magmatic crust would be about 1 km thinner than the seismic crust. A small volume of serpentine (< 5 per cent) could be distributed through the crust without being detected by seismic methods. Even a 1 per cent volume fraction of serpentine would be a significant source of water delivered to the mantle by subduction of the crust. The seismic properties of the upper mantle are consistent with the properties of dunite, as opposed to peridotite. The low-velocity zone in the crust at NAT ESP 5 could be composed of amphibole-rich gabbros, but the VRH model indicates that it is probably composed of a mixture of gabbro with partially serpentinized peridotite, having a total serpentine content of 10–20 per cent. In either case, the low-velocity zone probably represents a zone of hydrous alteration.

The mechanical properties of Saccharomyces cerevisiae.

Cell-wall mechanical properties play an integral part in the growth and form of Saccharomyces cerevisiae. In contrast to the tremendous knowledge on the genetics of S. cerevisiae, almost nothing is known about its mechanical properties. We have developed a micromanipulation technique to measure the force required to burst single cells and have recently established a mathematical model to extract the mechanical properties of the cell wall from such data. Here we determine the average surface modulus of the S. cerevisiae cell wall to be 11.1 +/- 0.6 N/m and 12.9 +/- 0.7 N/m in exponential and stationary phases, respectively, giving corresponding Young's moduli of 112 +/- 6 MPa and 107 +/- 6 MPa. This result demonstrates that yeast cell populations strengthen as they enter stationary phase by increasing wall thickness and hence the surface modulus, without altering the average elastic properties of the cell-wall material. We also determined the average breaking strain of the cell wall to be 82% +/- 3% in exponential phase and 80% +/- 3% in stationary phase. This finding provides a failure criterion that can be used to predict when applied stresses (e.g., because of fluid flow) will lead to wall rupture. This work analyzes yeast compression experiments in different growth phases by using engineering methodology.

Upper Crustal Velocity Structure in Slovenia from Rayleigh Wave Dispersion

The inversion of surface-wave dispersion curves can provide information on the average elastic properties of the upper crustal layers that are usually poorly sampled by body waves. The broad band digital records of earthquakes which recently occurred in Slovenia and neighbouring regions are used to extract the group velocity of the fundamental mode of Rayleigh waves, using frequency-time analysis (FTAN). The obtained dispersion curves permit a good resolution for the velocity and the thickness of the upper crust. The thickness of the uppermost sedimentary layer varies between 4 and 6 km and its shear-wave velocity is less than 3 km/s. The lower sedimentary layer is 7 to 9 km thick and its shear-wave velocity ranges from about 3.05 km/s in eastern Slovenia, to about 3.25 km/s in western Slovenia. The shear-wave velocity in the crystalline layer is around 3.5–3.7 km/s in the eastern part, while in the western part it reaches a rather high value of about 3.85 km/s.

Influence of Grain Number on Graphite Quantitative Texture Study

The present work is devoted to the study of the grain number influence on the quantitative texture analysis and on the values of averaged elastic properties. Number of grains does not influence mathematical definition of orientation distribution function (ODF) (Bunge, H.J. (1982). Texture Analysis in Material Science. Butterworths, London; Matthies, S., Vinel, G.W. and Helming, K. (1987). Standard Distributions in Texture Analysis. Akademie‐Verlag, Berlin.); nevertheless, intuitively clear that, averaging procedure implies a ‘‘large’’ number of grains to make sense. In the present work we applied the already suggested procedure (Lychagina, T.A. and Nikolayev, D.I. (2003). Phys. Stat. Sol. (a), 195(N2), 322–334.) for the case of hexagonal symmetry to evaluate the influence of the grain number in the sample on the calculated elastic properties. This procedure was carried out for graphite that is one of the widespread, applicable and highly anisotropic materials.

The averaged mechanical properties of prismatic lattice formed by ellipsoidal inclusions

The objective of this paper is to evaluate the averaged elastic properties of 3-D grained composites in which identical inclusions form a prismatic network interacting with the matrix material. The inclusions are of ellipsoidal shape with transverse circular sections located at the nodes of a doubly-periodic lattice with an orthogonal elementary cell. When the arrays of inclusions are set at equal spacings in normal directions through the thickness of the matrix, the material formed is an anisotropic composite with tetragonal symmetry at planes transverse to the fiber axis. The longitudinal and transverse elastic and shear moduli as well as the longitudinal Poisson's ratios of such composites are evaluated in this paper. The averaged properties are studied in terms of the aspect ratio and volume fraction of the inclusions as well as the relative rigidity of the constituent phases. Employing the Eshelby's theory for the stress field around a single ellipsoidal inhomogeneity, which is surrounded by the effective anisotropic material, and considering the Mori-Tanaka's concept for the mutual interaction of the neighboring inclusions, we may evaluate the averaged elastic properties of grained composites with aligned ellipsoidal inclusions at finite concentrations. The results provided in a closed-form solution concern the stiffness of 3-D grained composites with parallely dispersed ellipsoidal inclusions forming a prismatic network inside the principal material. It is shown that the stiffness is affected by both the geometry of the inclusions and their concentration. The use of different composite models in the analysis shows that intense variations of stiffness occur mainly in hard composites weakened by soft ellipsoidal inclusions. These findings come in full verification with experimental or theoretical results from the literature.

Stress state of a matrix and an inclusion consisting of a twisted multifilament superconductor with a normally-conducting core in the presence of an interaction of the longitudinal current with a transverse magnetic field

A study is made of the stress state arising in an infinite matrix into which is “potted” a long cylindrical inclusion consisting of a twisted multifilament composite superconductor with a core of normal metal as a result of the interaction of the longitudinal component of the transport current with a uniform external magnetic field. It is shown that the approximation of a homogeneous conductor with average elastic properties can be used to calculate the macroscopic stresses in a NbTi-Cu wire embedded in an epoxy matrix.

Numerical identification of properties of particle-reinforced composite materials

The paper deals with numerical identification of the average elastic properties of particle-reinforced composite materials. The finite element method for the determination of deformation energy of the characteristic volume element was used. In earlier analytical investigations, an approximation function of the averaged elastic properties of the composite was derived. An identification procedure allows the estimation of the unknown approximation parameters from numerical experiments. The obtained functions describe precisely the numerical data for any relationships between constituents of the material.