scholarly journals Effective moduli of rocks predicted by the Kuster–Toksöz and Mori–Tanaka models

2021 ◽  
Vol 18 (4) ◽  
pp. 539-557
Author(s):  
Zidong Wang ◽  
Qian Zhang ◽  
Jianlin Liu ◽  
Li-Yun Fu
Keyword(s):  
Volume Fraction ◽  
Theoretical Models ◽  
Effective Modulus ◽  
Petroleum Exploration ◽  
Effective Moduli ◽  
Exploration And Exploitation ◽  
Finite Precision ◽  
First Order ◽  
Scattering Approximation ◽  
Anisotropic Rocks

Abstract Natural rocks are polymineral composites with complex microstructures. Such strong heterogeneities significantly affect the estimation of effective moduli by some theoretical models. First, we have compared the effective moduli of isotropic rocks predicted by the Kuster–Toksöz (KT) model and the Mori–Tanaka (MT) model. The widely used KT model only has finite precision in many cases because of its assumption that is restricted to the first-order scattering approximation. However, the MT model based on the Eshelby tensor in mesomechanics has the advantage of predicting effective moduli of rocks, especially when the volume fraction of embedded inclusions is sufficiently large. In addition, the MT model can be used to predict the effective modulus of anisotropic rocks, but the KT model cannot. For a certain kind of shale or tight sandstones, which are viewed as isotropic composites, both the models work well. For the medium containing spherical pores, both the models produce the same results, whereas for ellipsoidal pores the MT model is more accurate than the KT model, validated by the finite element simulations. In what follows, the applicable ranges of simplified formulas for pores with needle, coin and disk shapes, widely used in engineering, are quantitatively given based on the comparison with the results according to the reduced ellipsoidal formulas of the MT and KT models. These findings provide a comprehensive understanding of the two models in calculating the effective modulus of rocks, which are beneficial to such areas as petroleum exploration and exploitation, civil engineering, and geophysics.

Laser-Induced Pretransitional Ordering And Nonlinear Optical Properties Of Rigid-Rod Polymer Suspensions

1993 ◽  
Vol 328 ◽  
Author(s):  
Boris E. Vugmeister ◽  
Michelle S. Malcuit ◽  
John C. Kralik ◽  
Colleen Stevens
Keyword(s):  
Phase Transition ◽  
Colloidal Particles ◽  
Volume Fraction ◽  
Orientational Order ◽  
Critical Value ◽  
Orientational Relaxation ◽  
First Order ◽  
First Order Phase Transition ◽  
Rigid Rod ◽  
First Order Phase

ABSTRACTWe investigate the pretransitional behavior in laser-induced alignment of rigid rod-like polytetraflouroethylene (PTFE) suspensions. Using a laser-induced birefringence experiment, we measure both the orientational order parameter and the orientational relaxation time. We find that both increase as the volume fraction of colloidal particles approaches the critical value for the isotropic-nematic phase transition. Experimental results are compared with theory which takes into account the possibility of a first-order phase transition induced by a laser electric field.

A Synchrotron Radiation Study of Nonlinear Diffusion in Cu-Au

1990 ◽  
Vol 205 ◽  
Author(s):  
E. S. K. Menon ◽  
P. Huang ◽  
M. Kraitchman ◽  
J. J. Hoyt ◽  
P. Chow ◽  
...  
Keyword(s):  
Synchrotron Radiation ◽  
Nonlinear Diffusion ◽  
Pure Copper ◽  
Theoretical Models ◽  
Average Concentration ◽  
Third Order ◽  
Composition Modulation ◽  
First Order ◽  
Diffraction Peaks ◽  
Modulation Wavelength

AbstractAlternate layers of pure copper and gold were vapor deposited on a sodium chloride substrate, the average concentration of the films being Cu-16at% Au and the layering periodicity (modulation wavelength) being 3.31 nm. The composition modulation gives rise to satellite diffraction peaks around the (200) Bragg reflections. Synchrotron radiation at SSRL was able to detect up to third order satellite intensity the evolution of which was measured as a function of annealing time at 515 K. Although the first order satellite intensity decayed as expected exponentially with time, intensities of both second and third order satellites decreased very rapidly at first, then increased before decaying exponentially. These results are in conformity with theoretical models of satellite evolution during annealing in a onedimensional modulated system governed by a nonlinear diffusion equation.

A Percolation Equation for Modeling Experimental Results for Continuum Percolation Systems

2001 ◽  
Vol 699 ◽  
Author(s):  
D.S. McLachlan ◽  
C. Chiteme ◽  
W.D. Heiss ◽  
Junjie Wu
Keyword(s):  
Experimental Data ◽  
Ac Conductivity ◽  
Volume Fraction ◽  
Power Laws ◽  
Second Order ◽  
Experimental Results ◽  
Analytical Equation ◽  
Scaling Properties ◽  
First Order ◽  
Dc And Ac Conductivity

AbstractThe standard percolation equations or power laws, for dc and ac conductivity (dielectric constant) are based on scaling ansatz, and predict the behaviour of the first and second order terms, above and below the percolation or critical volume fraction (øc), and in the crossoverregion. Recent experimental results on ac conductivity are presented, which show that these equations, with the exception of real σm above øc and the first order terms in the crossover region, are only valid in the limit σi/σc = 0, where for an ideal dielectric σi=ωε0εr.A single analytical equation, which has the same parameters as the standard percolation equations, and which, for ac conductivity, reduces to the standard percolation power laws in the limit σi(ωε0εr)/σc = 0 for all but one case, is presented. The exception is the expression for real σm below øc, where the standard power law is always incorrect. The equation is then shown to quantitatively fit both first and second order dc and ac experimental data over the entire frequency and composition range. This phenomenological equation is also continuous, has the scaling properties required at a second order metal-insulator and fits scaled first order dc and ac experimental data. Unfortunately, the s and t exponents that are necessary to fit the data to the above analytical equation are usually not the simple dimensionally determined universal ones and depend on a number of factors.

Directional Tortuosity as a Predictor of Modulus Damage for Vertebral Cancellous Bone

2015 ◽  
Vol 137 (1) ◽  
Author(s):  
David P. Fyhrie ◽  
Roger Zauel
Keyword(s):  
Mechanical Properties ◽  
Cancellous Bone ◽  
Volume Fraction ◽  
Compressive Strain ◽  
Effective Modulus ◽  
Hard Tissue ◽  
Bone Volume Fraction ◽  
Tissue Microstructure ◽  
Induced Changes ◽  
Effective Mechanical Properties

There are many methods used to estimate the undamaged effective (apparent) moduli of cancellous bone as a function of bone volume fraction (BV/TV), mean intercept length (MIL), and other image based average microstructural measures. The MIL and BV/TV are both only functions of the cancellous microstructure and, therefore, cannot directly account for damage induced changes in the intrinsic trabecular hard tissue mechanical properties. Using a nonlinear finite element (FE) approximation for the degradation of effective modulus as a function of applied effective compressive strain, we demonstrate that a measurement of the directional tortuosity of undamaged trabecular hard tissue strongly predicts directional effective modulus (r2 > 0.90) and directional effective modulus degradation (r2 > 0.65). This novel measure of cancellous bone directional tortuosity has the potential for development into an anisotropic approach for calculating effective mechanical properties as a function of trabecular level material damage applicable to understanding how tissue microstructure and intrinsic hard tissue moduli interact to determine cancellous bone quality.

HDPE Matrix Composites Filled With Ca4La6(SiO4)4(PO4)2O2 for Microwave Substrate Applications

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
Dhanesh Thomas ◽  
Mailadil T. Sebastian
Keyword(s):  
Dielectric Loss ◽  
Relative Permittivity ◽  
Volume Fraction ◽  
Linear Thermal Expansion ◽  
Theoretical Models ◽  
Ceramic Composites ◽  
Filler Loading ◽  
Scanning Electron Micrographs ◽  
Melt Mixing ◽  
5 Ghz

Polymer–ceramic composites have been prepared by dispersing Ca4La6(SiO4)4(PO4)2O2 (CLSP) ceramic filler in high density polyethylene (HDPE) matrix through melt mixing. Scanning electron micrographs reveal the extent of filler dispersion. The dielectric properties at 1 MHz and 5 GHz have been investigated as a function of filler content. The relative permittivity increases with filler loading, maintaining a low dielectric loss. The composite with highest filler loading of 0.4 volume fraction shows a relative permittivity of 5.1 and dielectric loss of 2.3 × 10−3 at 5 GHz. Experimentally observed values of relative permittivity at 5 GHz have been compared with the values calculated using various theoretical models. Both the coefficient of linear thermal expansion and tensile strength have been observed to decrease with filler loading, reaching a minimum value of 117 ppm/ °C and 20.7 MPa, respectively, at 0.4 volume fraction of filler. The composite with maximum filler loading of 0.4 volume fraction shows the highest thermal conductivity (TC) and is 1.2 W m−1 K−1.

Thermal Conductivity of Nature Rubber Filled with Carbon Black

2009 ◽  
Vol 87-88 ◽  
pp. 86-91 ◽  
Author(s):  
Yan He ◽  
Hai Tao Li ◽  
Lian Xiang Ma
Keyword(s):  
Thermal Conductivity ◽  
Carbon Black ◽  
Volume Fraction ◽  
Theoretical Models ◽  
Filled Rubber ◽  
Filler Fraction ◽  
Thermal Conductivities

The thermal conductivities of two rubbers filled with different carbon black (N330 and N375) are measured by experiments, and compared with five theoretical models calculated results. It is shown that thermal conductivity of carbon-filled rubber is obviously enhanced with increase of the volume filler fraction of carbon black and the thermal conductivity of carbon-filled rubber is related to the microstructure and morphology of carbon black. The estimated thermal conductivities by using the model proposed in our previous paper are of the same variation as the experimental ones of N330 carbon/rubber and N375 carbon/rubber during the range of volume fraction from 2% to 20%.

scholarly journals Sensitivity analysis of free torsional vibration frequencies of thin-walled laminated beams under axial load

2019 ◽  
Vol 32 (5) ◽  
pp. 1347-1356 ◽  
Author(s):  
Czesław Szymczak ◽  
Marcin Kujawa
Keyword(s):  
Sensitivity Analysis ◽  
Cross Section ◽  
Torsional Vibration ◽  
Volume Fraction ◽  
Fibre Volume Fraction ◽  
Vibration Frequencies ◽  
Cross Sectional ◽  
First Order ◽  
Thin Walled ◽  
Frequency Changes

AbstractThe paper addresses sensitivity analysis of free torsional vibration frequencies of thin-walled beams of bisymmetric open cross section made of unidirectional fibre-reinforced laminate. The warping effect and the axial end load are taken into account. The consideration is based upon the classical theory of thin-walled beams of non-deformable cross section. The first-order sensitivity variation of the frequencies is derived with respect to the design variable variations. The beam cross-sectional dimensions and the material properties are assumed the design variables undergoing variations. The paper includes a numerical example related to simply supported I-beams and the distributions of sensitivity functions of frequencies along the beam axis. Accuracy is discussed of the first-order sensitivity analysis in the assessment of frequency changes due to the fibre volume fraction variable variations, and the effect of axial loads is discussed too.

scholarly journals Vincent Charles Illing, 1890-1969

1970 ◽  
Vol 16 ◽  
pp. 365-384
Keyword(s):  
Oil And Gas ◽  
Scientific Work ◽  
Petroleum Exploration ◽  
Petroleum Geology ◽  
Exploration And Exploitation ◽  
Petroleum Geologist ◽  
Industrial Work ◽  
The World

Vincent Charles Illing was an internationally distinguished petroleum geologist who exemplified in his career the advantages of integrated academic and industrial work. His name will always be linked with the Royal School of Mines, London, where he created and developed over forty years the only department of petroleum geology in this country and one of the foremost in the world. His studies of the occurrence of oil and gas were no mere academic exercise. He was unique in British geology in combining the duties and responsibilities of a professor with those of guiding petroleum exploration and exploitation in various parts of the world. He never relinquished his consultant’s role. His biography is of particular interest now that pragmatism in scientific work has regained much of its former respectability.

Dynamic Response of Cantilever FGM Cylindrical Shell

2011 ◽  
Vol 130-134 ◽  
pp. 3986-3993 ◽  
Author(s):  
Yu Xin Hao ◽  
Wei Zhang ◽  
L. Yang ◽  
J.H. Wang
Keyword(s):  
Cylindrical Shell ◽  
Volume Fraction ◽  
Nonlinear Oscillations ◽  
Equations Of Motion ◽  
Functionally Graded ◽  
Governing Equations ◽  
Temperature Dependent ◽  
Graded Materials ◽  
First Order ◽  
Two Degree Of Freedom

An analysis on the nonlinear dynamics of a cantilever functionally graded materials (FGM) cylindrical shell subjected to the transversal excitation is presented in thermal environment.Material properties are assumed to be temperature-dependent. Based on the Reddy’s first-order shell theory,the nonlinear governing equations of motion for the FGM cylindrical shell are derived using the Hamilton’s principle. The Galerkin’s method is utilized to discretize the governing partial equations to a two-degree-of-freedom nonlinear system including the quadratic and cubic nonlinear terms under combined external excitations. It is our desirable to choose a suitable mode function to satisfy the first two modes of transverse nonlinear oscillations and the boundary conditions for the cantilever FGM cylindrical shell. Numerical method is used to find that in the case of non-internal resonance the transverse amplitude are decreased by increasing the volume fraction index N.

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