Random Bulk Properties of Heterogeneous Rectangular Blocks With Lognormal Young's Modulus: Effective Moduli

2015 ◽  
Vol 82 (1) ◽  
Author(s):  
Leon S. Dimas ◽  
Daniele Veneziano ◽  
Tristan Giesa ◽  
Markus J. Buehler
Keyword(s):  
Young’S Modulus ◽  
Elastic Properties ◽  
Young's Modulus ◽  
Three Dimensional ◽  
Heterogeneous Materials ◽  
Effective Elastic Properties ◽  
Specific Effects ◽  
Spatial Fluctuations ◽  
2D And 3D ◽  
Good Agreement

We investigate the effective elastic properties of disordered heterogeneous materials whose Young's modulus varies spatially as a lognormal random field. For one-, two-, and three-dimensional (1D, 2D, and 3D) rectangular blocks, we decompose the spatial fluctuations of the Young's log-modulus F=lnE into first- and higher-order terms and find the joint distribution of the effective elastic tensor by multiplicatively combining the term-specific effects. The analytical results are in good agreement with Monte Carlo simulations. Through parametric analysis of the analytical solutions, we gain insight into the effective elastic properties of this class of heterogeneous materials. The results have applications to structural/mechanical reliability assessment and design.

Elastic and Thermal Properties of Silicon Compounds from First-Principles Calculations

2016 ◽  
Vol 71 (7) ◽  
pp. 657-664 ◽  
Author(s):  
Haijun Hou ◽  
H.J. Zhu ◽  
W.H. Cheng ◽  
L.H. Xie
Keyword(s):  
Young’S Modulus ◽  
Elastic Properties ◽  
First Principles ◽  
Young's Modulus ◽  
Three Dimensional ◽  
Formation Enthalpy ◽  
Debye Model ◽  
Silicon Compounds ◽  
Calculated Equilibrium ◽  
Good Agreement

AbstractThe structural and elastic properties of V-Si (V3Si, VSi2, V5Si3, and V6Si5) compounds are studied by using first-principles method. The calculated equilibrium lattice parameters and formation enthalpy are in good agreement with the available experimental data and other theoretical results. The calculated results indicate that the V-Si compounds are mechanically stable. Elastic properties including bulk modulus, shear modulus, Young’s modulus, and Poisson’s ratio are also obtained. The elastic anisotropies of V-Si compounds are investigated via the three-dimensional (3D) figures of directional dependences of reciprocals of Young’s modulus. Finally, based on the quasi-harmonic Debye model, the internal energy, Helmholtz free energy, entropy, heat capacity, thermal expansion coefficient, Grüneisen parameter, and Debye temperature of V-Si compounds have been calculated.

Application of nanoindentation for uncertainty assessment of elastic properties in mudrocks from micro- to well-log scales

Geophysics ◽  
2017 ◽  
Vol 82 (6) ◽  
pp. D327-D339 ◽  
Author(s):  
Clotilde Chen Valdes ◽  
Zoya Heidari
Keyword(s):  
Young’S Modulus ◽  
Clay Minerals ◽  
Elastic Properties ◽  
Young's Modulus ◽  
Soft Rock ◽  
Elastic Stiffness ◽  
Mechanical Tests ◽  
Well Log ◽  
Eagle Ford ◽  
Effective Elastic Properties

Uncertainty in estimates of elastic properties of soft mudrock components, such as clay minerals and kerogen, can influence well-log-based evaluation of effective elastic properties in organic-rich mudrocks. Existing methods, such as effective medium models for well-log-based assessment of elastic properties, assume a constant stiffness and an idealized shape for rock components. However, these characteristics might vary depending on the distribution and size of that particular component, as well as its adjacent components. Furthermore, there is a significant uncertainty in elastic properties of kerogen in the case of organic-rich mudrocks. The uncertainty associated with the aforementioned parameters on effective elastic properties of rocks has not been investigated in existing publications. In this paper, we quantified the variability in elastic properties of individual mudrock components caused by their spatial distribution, size, and rock fabric at the microscale and their impacts on well-log-based evaluation of effective elastic properties. We performed nanoindentation mechanical tests on samples from the Haynesville and the lower Eagle Ford Formations, to measure Young’s modulus and hardness at targeted locations. Then, we quantified the variability of Young’s modulus in the microscale and its impact on effective elastic properties at the micro- and well-log scales. Results reveal significant uncertainties in measurements of elastic properties of soft rock components, associated with their location and size. Young’s moduli of individual clay components are higher when located adjacent to stiff rock components, such as large quartz and calcite grains. Results reveal that 25% and 12% uncertainties in measured elastic properties of clay minerals affect well-log-based estimates of effective elastic stiffness coefficients up to 29% and 11% in the Haynesville and the lower Eagle Ford Formations, respectively. These uncertainties can be more significant in cases with a higher concentration of clay minerals and kerogen.

scholarly journals A Quasi-Static Quantitative Ultrasound Elastography Algorithm Using Optical Flow

Sensors ◽  
2021 ◽  
Vol 21 (9) ◽  
pp. 3010
Author(s):  
Raphael Lamprecht ◽  
Florian Scheible ◽  
Marion Semmler ◽  
Alexander Sutor
Keyword(s):  
Optical Flow ◽  
Young’S Modulus ◽  
Elastic Properties ◽  
Young's Modulus ◽  
Image Data ◽  
Maximum Error ◽  
Ultrasound Elastography ◽  
Static Compression ◽  
Tissue Properties ◽  
A Performance

Ultrasound elastography is a constantly developing imaging technique which is capable of displaying the elastic properties of tissue. The measured characteristics could help to refine physiological tissue models, but also indicate pathological changes. Therefore, elastography data give valuable insights into tissue properties. This paper presents an algorithm that measures the spatially resolved Young’s modulus of inhomogeneous gelatin phantoms using a CINE sequence of a quasi-static compression and a load cell measuring the compressing force. An optical flow algorithm evaluates the resulting images, the stresses and strains are computed, and, conclusively, the Young’s modulus and the Poisson’s ratio are calculated. The whole algorithm and its results are evaluated by a performance descriptor, which determines the subsequent calculation and gives the user a trustability index of the modulus estimation. The algorithm shows a good match between the mechanically measured modulus and the elastography result—more precisely, the relative error of the Young’s modulus estimation with a maximum error 35%. Therefore, this study presents a new algorithm that is capable of measuring the elastic properties of gelatin specimens in a quantitative way using only the image data. Further, the computation is monitored and evaluated by a performance descriptor, which measures the trustability of the results.

scholarly journals A parametric prediction of the Young’s modulus of polymers enhanced with ΜWCNTs

2018 ◽  
Vol 233 ◽  
pp. 00025
Author(s):  
P.V. Polydoropoulou ◽  
K.I. Tserpes ◽  
Sp.G. Pantelakis ◽  
Ch.V. Katsiropoulos
Keyword(s):  
Young’S Modulus ◽  
Elastic Properties ◽  
Young's Modulus ◽  
Experimental Results ◽  
Scale Model ◽  
Fe Model ◽  
Multi Scale ◽  
Unit Cells ◽  
Random Dispersion

In this work a multi-scale model simulating the effect of the dispersion, the waviness as well as the agglomerations of MWCNTs on the Young’s modulus of a polymer enhanced with 0.4% MWCNTs (v/v) has been developed. Representative Unit Cells (RUCs) have been employed for the determination of the homogenized elastic properties of the MWCNT/polymer. The elastic properties computed by the RUCs were assigned to the Finite Element (FE) model of a tension specimen which was used to predict the Young’s modulus of the enhanced material. Furthermore, a comparison with experimental results obtained by tensile testing according to ASTM 638 has been made. The results show a remarkable decrease of the Young’s modulus for the polymer enhanced with aligned MWCNTs due to the increase of the CNT agglomerations. On the other hand, slight differences on the Young’s modulus have been observed for the material enhanced with randomly-oriented MWCNTs by the increase of the MWCNTs agglomerations, which might be attributed to the low concentration of the MWCNTs into the polymer. Moreover, the increase of the MWCNTs waviness led to a significant decrease of the Young’s modulus of the polymer enhanced with aligned MWCNTs. The experimental results in terms of the Young’s modulus are predicted well by assuming a random dispersion of MWCNTs into the polymer.

scholarly journals High-Temperature Elastic Properties of Yttrium-Doped Barium Zirconate

Metals ◽  
2021 ◽  
Vol 11 (6) ◽  
pp. 968
Author(s):  
Fumitada Iguchi ◽  
Keisuke Hinata
Keyword(s):  
High Temperature ◽  
Young’S Modulus ◽  
Elastic Properties ◽  
Measurement Method ◽  
Young's Modulus ◽  
Barium Zirconate ◽  
Shear Moduli ◽  
Ceramic Fuel ◽  
Yttrium Concentration ◽  
Ceramic Fuel Cells

The elastic properties of 0, 10, 15, and 20 mol% yttrium-doped barium zirconate (BZY0, BZY10, BZY15, and BZY20) at the operating temperatures of protonic ceramic fuel cells were evaluated. The proposed measurement method for low sinterability materials could accurately determine the sonic velocities of small-pellet-type samples, and the elastic properties were determined based on these velocities. The Young’s modulus of BZY10, BZY15, and BZY20 was 224, 218, and 209 GPa at 20 °C, respectively, and the values decreased as the yttrium concentration increased. At high temperatures (>20 °C), as the temperature increased, the Young’s and shear moduli decreased, whereas the bulk modulus and Poisson’s ratio increased. The Young’s and shear moduli varied nonlinearly with the temperature: The values decreased rapidly from 100 to 300 °C and gradually at temperatures beyond 400 °C. The Young’s modulus of BZY10, BZY15, and BZY20 was 137, 159, and 122 GPa at 500 °C, respectively, 30–40% smaller than the values at 20 °C. The influence of the temperature was larger than that of the change in the yttrium concentration.

FEM Stress Analysis and Strength of Scarf Adhesive Joints of Similar Adherend Subjected to Impact Tensile Loadings

2007 ◽  
Author(s):  
Toshiyuki Sawa ◽  
Yuya Hirayama ◽  
He Dan
Keyword(s):  
Young’S Modulus ◽  
Principal Stress ◽  
Stress Wave ◽  
Young's Modulus ◽  
Three Dimensional ◽  
Maximum Principal Stress ◽  
Adhesive Joints ◽  
Stress Wave Propagation ◽  
Adhesive Thickness ◽  
Three Dimensional Finite Element

The stress wave propagation and stress distribution in scarf adhesive joints have been analyzed using three-dimensional finite element method (FEM). The FEM code employed was LS-DYNA. An impact tensile loading was applied to the joint by dropping a weight. The effect of the scarf angle, Young’s modulus of the adhesive and adhesive thickness on the stress wave propagations and stress distributions at the interfaces have been examined. As the results, it was found that the point where the maximum principal stress becomes maximum changes between 52 degree and 60 degree under impact tensile loadings. The maximum value of the maximum principal stress increases as scarf angle decreases, Young’s modulus of the adhesive increases and adhesive thickness increases. In addition, Experiments to measure the strains and joint strengths were compared with the calculated results. The calculated results were in fairly good agreements with the experimental results.

A Simple Statistical Theory for Grain Growth in Materials.

1990 ◽  
Vol 209 ◽  
Author(s):  
P. Mulheran ◽  
J.H. Harding
Keyword(s):  
Growth Rate ◽  
Monte Carlo ◽  
Statistical Theory ◽  
Stochastic Model ◽  
Grain Growth ◽  
Three Dimensional ◽  
Monte Carlo Procedure ◽  
Short Time ◽  
2D And 3D ◽  
Good Agreement

A Monte Carlo procedure has been used to study the ordering of both two and three dimensional (2d and 3d) Potts Hamiltonians, further to the work of Anderson et al. For the 3d lattice, the short time growth rate is found to be much slower than previously reported, though the simulated microstructure is in agreement with the earlier studies. We propose a new stochastic model that gives good agreement with the simulations.

Coating agent-induced mechanical behavior of 3D self-assembled nanocrystals

2017 ◽  
Vol 19 (35) ◽  
pp. 23887-23897 ◽  
Author(s):  
Arzu Çolak ◽  
Jingjing Wei ◽  
Imad Arfaoui ◽  
Marie-Paule Pileni
Keyword(s):  
Mechanical Behavior ◽  
Young’S Modulus ◽  
Young's Modulus ◽  
Three Dimensional ◽  
Coating Agent ◽  
Self Assembled

The Young's modulus of three-dimensional self-assembled Ag nanocrystals, as so-called supracrystals, is correlated with the type of coating agent as well as the nanocrystal morphology.

scholarly journals Three-dimensional seismic analysis of concrete gravity dams considering foundation flexibility

2021 ◽  
Vol 25 (1) ◽  
pp. 88-98
Author(s):  
Mokhtar Messaad ◽  
Messoud Bourezane ◽  
Mohamed Latrache ◽  
Amina Tahar Berrabah ◽  
Djamel Ouzendja
Keyword(s):  
Young’S Modulus ◽  
Seismic Analysis ◽  
Young's Modulus ◽  
Three Dimensional ◽  
Shear Stresses ◽  
Total System ◽  
Dam Reservoir ◽  
Principal Stresses ◽  
Foundation Soil ◽  
North West

Abstract Concrete dams are considered as complex construction systems that play a major role in the context of both economic and strategic utilities. Taking into account reservoir and foundation presence in modeling the dam-reservoir-foundation interaction phenomenon leads to a more realistic evaluation of the total system behavior. The article discusses the dynamic behavior of dam-reservoir-foundation system under seismic loading using Ansys finite element code. Oued Fodda concrete dam, situated at Chlef, in North-West of Algeria, was chosen as a case study. Parametric study was also performed for different ratios between foundation Young's modulus and dam Young's modulus E f /E d (which varies from 0.5 to 4). Added mass approach was used to model the fluid reservoir. The obtained results indicate that when dam Young's modulus and foundation Young's modulus are equal, the foundation soil leads to less displacements in the dam body and decreases the principal stresses as well as shear stresses.

Secondary Fluorescence of 3D Heterogeneous Materials Using a Hybrid Model

2020 ◽  
Vol 26 (3) ◽  
pp. 484-496
Author(s):  
Yu Yuan ◽  
Hendrix Demers ◽  
Xianglong Wang ◽  
Raynald Gauvin
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Analytical Model ◽  
Hybrid Model ◽  
Three Dimensional ◽  
Heterogeneous Materials ◽  
X Ray ◽  
The Monte Carlo Method ◽  
Secondary Fluorescence ◽  
Good Agreement

AbstractIn electron probe microanalysis or scanning electron microscopy, the Monte Carlo method is widely used for modeling electron transport within specimens and calculating X-ray spectra. For an accurate simulation, the calculation of secondary fluorescence (SF) is necessary, especially for samples with complex geometries. In this study, we developed a program, using a hybrid model that combines the Monte Carlo simulation with an analytical model, to perform SF correction for three-dimensional (3D) heterogeneous materials. The Monte Carlo simulation is performed using MC X-ray, a Monte Carlo program, to obtain the 3D primary X-ray distribution, which becomes the input of the analytical model. The voxel-based calculation of MC X-ray enables the model to be applicable to arbitrary samples. We demonstrate the derivation of the analytical model in detail and present the 3D X-ray distributions for both primary and secondary fluorescence to illustrate the capability of our program. Examples for non-diffusion couples and spherical inclusions inside matrices are shown. The results of our program are compared with experimental data from references and with results from other Monte Carlo codes. They are found to be in good agreement.

Sign in / Sign up

Export Citation Format

Share Document