A Generalized Self-Consistent Mechanics Method for Solids Containing Elliptical Inclusions

1995 ◽  
Vol 62 (3) ◽  
pp. 566-572 ◽  
Author(s):  
Y. Huang ◽  
K. X. Hu
Keyword(s):  
Aspect Ratio ◽  
Current Approach ◽  
Effective Moduli ◽  
Shear Moduli ◽  
Aspect Ratios ◽  
Isotropic Distribution ◽  
Energy Equivalence ◽  
Self Consistent ◽  
Consistent Method

The determination of the effective moduli for a material containing elliptical inclusions is the objective of this paper. This is done by incorporating an inclusion/matrix/composite model into a general energy equivalence framework. Through the evaluation of the average strain in each individual inclusion, the current approach can handle the inclusion’s orientation dependency in a straightforward manner. The case of an in-plane isotropic distribution of elliptical inclusions is addressed in detail. For the case of reinforcements, or hard inclusions, the effect of the inclusion aspect ratio on in-plane effective moduli is small if the aspect ratio is larger than 0.5. For aspect ratios less than 0.3, the effective moduli increase dramatically, which implies that flat reinforcements are much more effective than traditional cylindrical reinforcements. It is also established that the generalized self-consistent method predicts a stronger dependence of effective moduli on the inclusion aspect ratio than does the Mori-Tanaka method, especially for shear moduli.

scholarly journals Strength Analysis of Alternative Airframe Layouts of Regional Aircraft on the Basis of Automated Parametrical Models

Aerospace ◽  
2021 ◽  
Vol 8 (3) ◽  
pp. 80
Author(s):  
Dmitry V. Vedernikov ◽  
Alexander N. Shanygin ◽  
Yury S. Mirgorodsky ◽  
Mikhail D. Levchenkov
Keyword(s):  
Aspect Ratio ◽  
High Aspect Ratio ◽  
High Performance ◽  
Strength Analysis ◽  
Labor Input ◽  
Aerodynamic Loading ◽  
Aspect Ratios ◽  
Wide Range ◽  
Parametrical Design

This publication presents the results of complex parametrical strength investigations of typical wings for regional aircrafts obtained by means of the new version of the four-level algorithm (FLA) with the modified module responsible for the analysis of aerodynamic loading. This version of FLA, as well as a base one, is focused on significant decreasing time and labor input of a complex strength analysis of airframes by using simultaneously different principles of decomposition. The base version includes four-level decomposition of airframe and decomposition of strength tasks. The new one realizes additional decomposition of alternative variants of load cases during the process of determination of critical load cases. Such an algorithm is very suitable for strength analysis and designing airframes of regional aircrafts having a wide range of aerodynamic concepts. Results of validation of the new version of FLA for a high-aspect-ratio wing obtained in this work confirmed high performance of the algorithm in decreasing time and labor input of strength analysis of airframes at the preliminary stages of designing. During parametrical design investigation, some interesting results for strut-braced wings having high aspect ratios were obtained.

Aspect Ratio Analysis Using Image Processing for Rice Grain Quality

2010 ◽  
Vol 6 (5) ◽  
Author(s):  
Amit K Aggarwal ◽  
Ratan Mohan
Keyword(s):  
Image Processing ◽  
Aspect Ratio ◽  
Local Market ◽  
Rice Grain ◽  
Ratio Analysis ◽  
Ratio Distribution ◽  
Aspect Ratios ◽  
Percent Accuracy ◽  
Aspect Ratio Distribution

Determination of aspect ratio distribution is important for elongated, needle-shaped particles whose utility and/or value may depend on this feature. In this work rice grain is taken as an example of such a particle and its aspect ratio distribution in various samples is found using image processing. The samples examined were from three different grades (commonly termed as full, half and broken) sold in local market and priced according to their size. From the analysis, reference aspect ratios were assigned to classify the grains and hence determine the extent of off-size in each market grade. Further, the effectiveness of the technique to quantify mixed or adulterated grades was studied. It was found that it is possible to know the undesired content within 10 percent accuracy.

Overall Mechanical Properties of Particulate Porous Composites Following Two-Step Homogenization Scheme

2012 ◽  
Vol 232 ◽  
pp. 45-50 ◽  
Author(s):  
Salma Barboura ◽  
Salah Ramtani
Keyword(s):  
Experimental Data ◽  
Mechanical Properties ◽  
Iterative Process ◽  
Current Approach ◽  
Elastic Media ◽  
Effective Moduli ◽  
Multiphase Composites ◽  
Self Consistent ◽  
Homogenization Scheme ◽  
Porous Composites

The present work tries to make an attempt to improve previous work which offers a simple but effective way to construct satisfied predicating model. Indeed, recent work due to Peng et al. [13] and dealing with a two-step homogenization scheme is revisited here by introducing an iterative process which allows us to take into account differently the porosity of the elastic media. Several homogenization schemes (dilute, Mori-Tanaka, self-consistent ...) are presented and compared with experimental data. One can say that the current approach provides reasonably accurate predictions for the effective moduli of multiphase composites without using the n parameter as proposed by Peng et al. [13]

Prediction of Biot’s coefficient from rock-physical modeling of North Sea chalk

Geophysics ◽  
2008 ◽  
Vol 73 (2) ◽  
pp. E89-E96 ◽  
Author(s):  
Casper Olsen ◽  
Kathrine Hedegaard ◽  
Ida L. Fabricius ◽  
Manika Prasad
Keyword(s):  
Aspect Ratio ◽  
North Sea ◽  
Free Parameter ◽  
The Self ◽  
P Wave ◽  
Biot’S Coefficient ◽  
Aspect Ratios ◽  
Consistent Model ◽  
Self Consistent ◽  
Water Saturated

We predict Biot’s coefficient for North Sea chalk based on density and P-wave velocity for water-saturated chalk. We compare three effective medium models: Berryman’s self-consistent model, the isoframe model, and the bounding-average method (BAM). The self-consistent model is used with two combinations of aspect ratios. In one combination, the aspect ratio is equal for pores and grains. In the other combination, the aspect ratio for grains is kept constant close to 1 and the aspect ratio for pores varies. All the models include one free parameter that determines the stiffness of the rock for a fixed porosity. This free parameter is compared with Biot’s coefficient to discuss whether the free parameter is related to pore-space compressibility for North Sea chalk. We also discuss how consistent the models are between P-wave modulus and shear modulus for dry and water-saturated chalk. The acoustic velocity and the density data for dry and water-saturated chalk are all laboratory data. The isoframe model and the BAM model predict Biot’s coefficient with a smaller error than the self-consistent model does. The free parameter in the isoframe model and the BAM model is related to Biot’s coefficient. The free parameter in the self-consistent model is related only to Biot’s coefficient for water-saturated chalk when the aspect ratios for pores and grains are equal. The isoframe and the BAM model are generally more consistent for chalk than the self-consistent model is.

Are self-consistent models capable of jointly modeling elastic velocity and electrical conductivity of reservoir sandstones?

Geophysics ◽  
2016 ◽  
Vol 81 (4) ◽  
pp. D377-D382 ◽  
Author(s):  
Tongcheng Han ◽  
Michael Ben Clennell ◽  
Arthur C. H. Cheng ◽  
Marina Pervukhina
Keyword(s):  
Electrical Conductivity ◽  
Electrical Properties ◽  
Aspect Ratio ◽  
Physical Property ◽  
S Waves ◽  
Ratio Spectrum ◽  
Aspect Ratios ◽  
Self Consistent ◽  
Spectrum Distribution ◽  
Reservoir Sandstones

Self-consistent (SC) models are commonly used for simulating elastic and electrical properties of reservoir rocks. We have developed a technique to test the capability of SC models to jointly model elastic velocity and electrical conductivity of porous media using a database of measurements of these properties on reservoir sandstones. The pores were represented by randomly oriented spheroidal shapes with a spectrum distribution of aspect ratios, and elasticity theory was used to compute the variation of aspect ratios and volume fractions of the pores subject to varying differential pressures. Using this method, the pore aspect ratio spectra of a reservoir sandstone were obtained separately from the measured elastic (P- and S-waves) velocity and electrical conductivity under loading. We have determined that when the SC formalism is used, there is a systematic discrepancy in the estimated pore structure predicted by the two measurements. Despite the supposed applicability of the SC method to this class of problem, the pore aspect ratio spectrum inverted from one physical property (e.g., velocity or conductivity) failed in practice to predict the other physical property (e.g., conductivity or velocity), at least for porous sandstones. Our results suggested the requirement of a new model to link the elastic and electrical properties to a unified pore aspect ratio spectrum of rocks.

scholarly journals Linking preferred orientations to elastic anisotropy in Muderong Shale, Australia

Geophysics ◽  
2015 ◽  
Vol 80 (1) ◽  
pp. C9-C19 ◽  
Author(s):  
Waruntorn Kanitpanyacharoen ◽  
Roman Vasin ◽  
Hans-Rudolf Wenk ◽  
David. N. Dewhurst
Keyword(s):  
Aspect Ratio ◽  
Volume Fraction ◽  
Elastic Anisotropy ◽  
Ambient Pressure ◽  
Preferred Orientation ◽  
Validity And Reliability ◽  
Crystallographic Preferred Orientation ◽  
Aspect Ratios ◽  
Average Aspect Ratio ◽  
Self Consistent

The significance of shales for unconventional hydrocarbon reservoirs, nuclear waste repositories, and geologic carbon storage has opened new research frontiers in geophysics. Among many of its unique physical properties, elastic anisotropy had long been investigated by experimental and computational approaches. Here, we calculated elastic properties of Cretaceous Muderong Shale from Australia with a self-consistent averaging method based on microstructural information. The volume fraction and crystallographic preferred orientation distributions of constituent minerals were based on synchrotron x-ray diffraction experiments. Aspect ratios of minerals and pores, determined from scanning electron microscopy, were introduced in the self-consistent averaging. Our analysis suggested that phyllosilicates (i.e., illite-mica, illite-smectite, kaolinite, and chlorite) were dominant with [Formula: see text]. The shape of clay platelets displayed an average aspect ratio of 0.05. These platelets were aligned parallel to the bedding plane with a high degree of preferred orientation. The estimated porosity at ambient pressure was [Formula: see text] and was divided into equiaxial pores and flat pores with an average aspect ratio of 0.01. Our model gave results that compared satisfactorily with values derived from ultrasonic velocity measurements, confirming the validity and reliability of our approximations and averaging approach.

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