Effective elastic moduli of a soft medium with hard polygonal inclusions and extremal behavior of effective Poisson's ratio

1995 ◽  
Vol 40 (1) ◽  
pp. 45-73 ◽  
Author(s):  
L. Berlyand ◽  
K. Promislow
Keyword(s):  
Poisson’S Ratio ◽  
Elastic Moduli ◽  
Poisson's Ratio ◽  
Effective Elastic Moduli ◽  
Extremal Behavior

scholarly journals Comprehensive Study on Elastic Moduli Prediction and Correlation of Glass and Glass Ceramic Derived from Waste Rice Husk

2017 ◽  
Vol 2017 ◽  
pp. 1-10
Author(s):  
Chee Sun Lee ◽  
Khamirul Amin Matori ◽  
Sidek Hj. Ab Aziz ◽  
Halimah Mohamed Kamari ◽  
Ismayadi Ismail ◽  
...  
Keyword(s):  
Theoretical Model ◽  
Rice Husk ◽  
Poisson’S Ratio ◽  
Elastic Moduli ◽  
Direct Calculation ◽  
Ultrasonic Pulse ◽  
Poisson's Ratio ◽  
Longitudinal Modulus ◽  
Pulse Echo ◽  
Quench Method

Zinc silicate (ZnO–SiO2) systems were fabricated using zinc oxide (ZnO) and white rice husk ash (WRHA) with compositions of (ZnO)x(WRHA)1−x (x = 0.55, 0.60, 0.65, and 0.70 wt.%) was symbolized by S1, S2, S3, and S4, respectively. The ZnO–SiO2 samples were fabricated by applying the melt-quench method and the physical and elastic properties of the samples were investigated. Physical properties used in this study are density and molar volume while the theoretical elastic moduli of the samples produced were obtained using direct calculation of theoretical model compared with the experimental elastic moduli obtained by acquiring ultrasonic velocities using ultrasonic pulse-echo technique. Values of experimental elastic moduli including longitudinal modulus (L), shear modulus (S), Young’s modulus (E), bulk modulus (K), and Poisson’s ratio (σ) were compared with theoretical model calculated using Rocherulle’s model. All the configurations of the elastic moduli obtained experimentally match very well with the configuration from Rocherulle’s model but Poisson’s ratio obtained experimentally differs from the values of Poisson’s ratio obtained through Rocherulle’s model.

On the analysis and prediction of elastic properties in alkali Na2O–B2O3–V2O5 glasses under the substitution of V2O5 by Na2O

2019 ◽  
Vol 60 (6) ◽  
pp. 213-221
Author(s):  
Amin Abd El-Moneim ◽  
Hassan Y. Alfifi
Keyword(s):  
Elastic Properties ◽  
Dissociation Energy ◽  
Packing Density ◽  
Poisson’S Ratio ◽  
Elastic Moduli ◽  
Unit Volume ◽  
Dominant Role ◽  
Glass Network ◽  
Poisson's Ratio ◽  
Structural Units

In this article, we have continued our recent work(30,42) on the prediction of elastic properties in alkali borovanadate glasses. Changes in the elastic moduli and Poisson’s ratio due to the substitution of V2O5 by Na2O in the ternary alkali Na2O–B2O3–V2O5 glasses have been analysed and predicted on the basis of the theories and approaches that existing in the field. Both the packing density and dissociation energy per unit volume of the glass were evaluated in terms of the basic structural units that constitute the glass network. In addition to this, the theoretical values of elastic moduli and Poisson’s ratio were calculated from the Makishima–Mackenzie’s model and compared with the corresponding experimental values. The results revealed that the concentrations of the basic structural units BO3, BO4, VO5 and VO4 play a dominant role in correcting the anomalous behaviour between experimental elastic moduli and calculated dissociation energy per unit volume. An excellent agreement between the theoretical and experimental elastic moduli was achieved for majority of the samples. The correlation between bulk modulus and the ratio between packing density and mean atomic volume has also been achieved on the basis of Abd El-Moneim and Alfifi’s approaches.

Evaluation of Effective Elastic Mechanical Properties of Graphene Sheets

2012 ◽  
Author(s):  
Khalid I. Alzebdeh
Keyword(s):  
Boundary Conditions ◽  
Young’S Modulus ◽  
Graphene Sheet ◽  
Poisson’S Ratio ◽  
Elastic Moduli ◽  
Young's Modulus ◽  
Unit Cell ◽  
Poisson's Ratio ◽  
Graphene Sheets ◽  
Numerical Predictions

The mechanical behaviour of a single-layer nanostructured graphene sheet is investigated using an atomistic-based continuum model. This is achieved by equating the stored energy in a representative unit cell for a graphene sheet at atomistic scale to the strain energy of an equivalent continuum medium under prescribed boundary conditions. Proper displacement-controlled (essential) boundary conditions which generate a uniform strain field in the unit cell model are applied to calculate one elastic modulus at a time. Three atomistic finite element models are adopted with an assumption that force interactions among carbon atoms can be modeled by either spring-like or beam elements. Thus, elastic moduli for graphene structure are determined based on the proposed modeling approach. Then, effective Young’s modulus and Poisson’s ratio are extracted from the set of calculated elastic moduli. Results of Young’s modulus obtained by employing the different atomistic models show a good agreement with the published theoretical and numerical predictions. However, Poisson’s ratio exhibits sensitivity to the considered atomistic model. This observation is supported by a significant variation in estimates as can be found in the literature. Furthermore, isotropic behaviour of in-plane graphene sheets was validated based on current modeling.

Effects of Overpressure on Mechanical Properties of Unconventional Shale Reservoirs through Novel Use of a Sonic Overpressure Indicator

2021 ◽  
pp. 1-9
Author(s):  
R. L. Eastwood ◽  
K. M. Smye
Keyword(s):  
Mechanical Properties ◽  
Young’S Modulus ◽  
Effective Stress ◽  
Poisson’S Ratio ◽  
Strain Energy ◽  
Elastic Moduli ◽  
Poisson's Ratio ◽  
Unconventional Reservoirs ◽  
Stress Coefficient ◽  
Shale Reservoirs

Summary Overpressure is a common feature among productive unconventional shale reservoirs, such as the Bone Spring (BSPG) and Wolfcamp (WFMP) Formations of the Delaware Basin (DB) of west Texas and southeastern New Mexico, and is thought to be a strong driver of well productivity. Compared with conventional reservoirs and shales in normal pressured conditions, the effects of overpressure on the mechanical properties of shales is not well understood. Here we present an analysis of overpressure in clay-bearing siliciclastic facies of the BSPG and WFMP Formations of the DB and implications for mechanical properties of the reservoir. Estimation of the effects of overpressure on mechanical properties of unconventional shale reservoirs is determined through use of the sonic overpressure indicator (SOPI). The method requires log model results that accurately characterize variations in lithology and porosity for the formations of interest. The SOPI (ΔT/ΔTN)2, where ΔT is the measured compressional sonic transit time, and ΔTN is the forward-modeled result for normally pressured conditions, can be used with elastic moduli and their interrelationships to compare estimates of mechanical properties including Poisson’s ratio ν, the Biot or effective stress coefficient α, and Young’s modulus E, in normal and overpressured conditions. Results presented here are broadly applicable to overpressured unconventional reservoirs that contain significant clay volume (>0.1 v/v) and exhibit low porosity (<0.08 v/v), comparable to that of siliciclastic-rich facies of the WFMP Formation. To account for increased VP/VS ratio, we regard overpressurization of shaly facies as an irreversible thermodynamic process that transforms a normally pressured siliciclastic system. At stress below the yield point, which is taken as the limit of normal pressure, the system responds elastically to stress; beyond this point, during overpressurization, the system responds as an elastic/plastic medium with strain hardening. We regard elastic moduli as descriptive of mechanical energy stored in this system. This perspective enables Poisson’s ratio for the overpressured system νOP to be computed from an estimate of the normally pressured system νN using (ΔT/ΔTN)2. Overpressure also results in a limited increase of the Biot or effective stress coefficient α. Moreover, recognition that overpressure results in a decrease of Young’s modulus, that is, EOP/EN < 1, provides a means of estimating the amount of strain energy stored by the formation due to overpressurization. We believe that when exposed to lower pressures by wellbore construction, this strain energy stored in overpressured unconventional reservoirs drives creep, which affects interpretations made using geomechanical models. We have developed and tested computational models based on biaxial or plane strain for vertical wells and uniaxial strain for horizontal wells that describe how creep likely affects estimation of minimum horizontal stress Shmin and pore pressure from instantaneous shut-in-pressure (ISIP) measurements. Thus, for overpressured unconventional reservoirs, ISIP determinations differ from tectonic Shmin by an amount related to ν and EOP/EN.

ELASTIC WAVE VELOCITIES IN ROCKS AT HIGH PRESSURES AND TEMPERATURES

Geophysics ◽  
1951 ◽  
Vol 16 (4) ◽  
pp. 577-593 ◽  
Author(s):  
D. S. Hughes ◽  
J. H. Cross
Keyword(s):  
Poisson’S Ratio ◽  
Elastic Moduli ◽  
Opposite Effect ◽  
High Pressures ◽  
Interstitial Water ◽  
Poisson's Ratio ◽  
Laboratory Measurements ◽  
Wave Velocities ◽  
Two Samples ◽  
High Pressures And Temperatures

The variation in dilatational and rotational velocities in rock samples with pressure and temperature has been studied. The measurements were taken at pressures from 1 bar (atmospheric) to 5,000 bars, and temperatures of 25°C. to 200°C. for all samples and up to 300°C. for two samples. We can thus reach a pressure equivalent to some 18 km or 60,000 feet of burial but our highest available temperature probably at most corresponds to no more than 8–9 km. The measured rotational velocities check very well with independent measurements. Laboratory measurements of the dilatational velocity are not available for comparison. From the measured dilatational and rotational velocities, the elastic moduli and Poisson’s ratio may be computed. Values of Poisson’s ratio are tabulated for all samples. In general, highly quartzitic rocks have low values 0.13–0.20 whereas the majority of rocks have values in the range 0.26–0.33. The effect of interstitial water has been investigated in one sandstone and one limestone. The sandstone shows an increase in velocity at low pressure and a decrease at high pressure whereas the limestone shows the opposite effect.

scholarly journals Ground instability of sinkhole areas indicated by elastic moduli and seismic attributes

2020 ◽  
Vol 222 (1) ◽  
pp. 289-304
Author(s):  
S H Wadas ◽  
S Tschache ◽  
U Polom ◽  
C M Krawczyk
Keyword(s):  
Shear Modulus ◽  
Shear Wave ◽  
Poisson’S Ratio ◽  
Elastic Moduli ◽  
Wave Reflection ◽  
P Wave ◽  
Poisson's Ratio ◽  
Dynamic Shear Modulus ◽  
Seismic Profiles ◽  
Low Shear

SUMMARY Elastic moduli derived from vertical seismic profiles (VSPs) and 2-D SH-wave reflection seismic profiles are used to characterize mechanical properties of rocks in sinkhole areas. VP and VS were used to calculate the Poisson’s ratio and the dynamic shear modulus. The study shows that 2-D shear wave reflection seismics is suited to depict the heterogeneities of the subsurface induced by subsurface erosion. Low shear wave velocities of ca. 120–350 m s–1 and low shear strength values between 25 and 250 MPa are identified for the subsurface erosion horizon that consists of soluble Permian evapourites and the disturbed overlying deposits. These low values are a result of cavities and fractures induced by dissolution, creating unstable zones. In compliance with the shear modulus the Poisson’s ratio derived from the VSPs shows values of 0.38–0.48 for both the presumed subsurface erosion horizon, and the deposits above. This is a further indicator of reduced underground stability. In the VSPs, anomalies of the shear modulus and the Poisson’s ratio correlate with low electrical resistivities of less than 10 Ωm from borehole logs, indicating high conductivity due to fluid content. Further investigation reveals a conversion of S-to-P wave for the subsurface erosion horizon, which is probably the result of dipping layers and an oriented fracture network. Seismic attribute analysis of the 2-D sections shows strong attenuation of high frequencies and low similarity of adjacent traces, which correlate with the degree of subsurface erosion induced wave disturbance of the underground.

scholarly journals Effects of Porosity on Elastic Moduli and Poisson's Ratio of Sintered Irons.

1998 ◽  
Vol 64 (627) ◽  
pp. 2795-2800 ◽  
Author(s):  
Norimitsu HIROSE ◽  
Junichi ASAMI ◽  
Toshiyuki TANAKI ◽  
Makoto YUASA ◽  
Isao SEKINE
Keyword(s):  
Poisson’S Ratio ◽  
Elastic Moduli ◽  
Poisson's Ratio
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