Computational Elucidation of Elastic Percolation Threshold in Isotropic and Anisotropic Microstructures with Voronoi Tessellation

2019 ◽  
Vol 11 (03) ◽  
pp. 1950029 ◽  
Author(s):  
V. Fadaei Naeini ◽  
M. H. Zarei ◽  
M. Baniassadi ◽  
M. Shirani ◽  
M. Baghani
Keyword(s):  
Percolation Threshold ◽  
Elastic Properties ◽  
Voronoi Tessellation ◽  
Elastic Behavior ◽  
The Finite Element Method ◽  
Shear Deformations ◽  
Aspect Ratios ◽  
Shear Modes ◽  
Percolation Thresholds ◽  
Anisotropic Case

In this paper, the mechanical properties of randomly shaped microstructures containing two different elastic materials are investigated. Representative volume elements (RVE) containing random tessellations were created using a random generating procedure. The procedure divides the RVE surface by Voronoi tessellations and the elastic behavior of the surface is analyzed under tensile and shear deformations using the finite element method (FEM). Components of stress tensor for each element obtained from FE analysis were used to compute the overall elastic properties of the microstructure. Percolation threshold was defined based on the instantaneous gradient of the tensile and shear modulus diagrams. Numerical results reveal that the percolation thresholds in tensile and shear modes for isotropic RVE are almost the same while there is a remarkable difference between percolation thresholds for an anisotropic case. Furthermore, in the procedure performed in this study, a distinct inconsistency in elastic properties of anisotropic microstructure in longitudinal and transverse directions is observed. The mentioned method presents a paradigmatic overview for generating random isotropic and anisotropic tessellations with different aspect ratios on microstructures and evaluating their overall properties and percolation limit for them.

Towards Predicting Relative Belt Edge Endurance With the Finite Element Method

1990 ◽  
Vol 18 (4) ◽  
pp. 216-235 ◽  
Author(s):  
J. De Eskinazi ◽  
K. Ishihara ◽  
H. Volk ◽  
T. C. Warholic
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Three Dimensional ◽  
The Finite Element Method ◽  
Shear Deformations ◽  
Element Analysis ◽  
Vertical Loading ◽  
Predicted Values ◽  
Element Method

Abstract The paper describes the intention of the authors to determine whether it is possible to predict relative belt edge endurance for radial passenger car tires using the finite element method. Three groups of tires with different belt edge configurations were tested on a fleet test in an attempt to validate predictions from the finite element results. A two-dimensional, axisymmetric finite element analysis was first used to determine if the results from such an analysis, with emphasis on the shear deformations between the belts, could be used to predict a relative ranking for belt edge endurance. It is shown that such an analysis can lead to erroneous conclusions. A three-dimensional analysis in which tires are modeled under free rotation and static vertical loading was performed next. This approach resulted in an improvement in the quality of the correlations. The differences in the predicted values of various stress analysis parameters for the three belt edge configurations are studied and their implication on predicting belt edge endurance is discussed.

Modes of Wave Propagation and Dispersion Relations in Inclusion Reinforced Composite Plates

2010 ◽  
Author(s):  
Yu Cheng Liu ◽  
Jin Huang Huang
Keyword(s):  
Composite Plate ◽  
Elastic Moduli ◽  
Lamb Waves ◽  
Plate Thickness ◽  
Composite Plates ◽  
Dispersion Relations ◽  
Elastic Behavior ◽  
Effective Elastic Moduli ◽  
Aspect Ratios ◽  
Reinforced Composite

This paper mainly analyzes the wave dispersion relations and associated modal pattens in the inclusion-reinforced composite plates including the effect of inclusion shapes, inclusion contents, inclusion elastic constants, and plate thickness. The shape of inclusion is modeled as spheroid that enables the composite reinforcement geometrical configurations ranging from sphere to short and continuous fiber. Using the Mori-Tanaka mean-field theory, the effective elastic moduli which are able to elucidate the effect of inclusion’s shape, stiffness, and volume fraction on the composite’s anisotropic elastic behavior can be predicted explicitly. Then, the dispersion relations and the modal patterns of Lamb waves determined from the effective elastic moduli can be obtained by using the dynamic stiffness matrix method. Numerical simulations have been given for the various inclusion types and the resulting dispersions in various wave types on the composite plate. The types (symmetric or antisymmetric) of Lamb waves in an isotropic plate can be classified according to the wave motions about the midplane of the plate. For an orthotropic composite plate, it can also be classified as either symmetric or antisymmetric waves by analyzing the dispersion curves and inspecting the calculated modal patterns. It is also found that the inclusion contents, aspect ratios and plate thickness affect propagation velocities, higher-order mode cutoff frequencies, and modal patterns.

scholarly journals Evaporation-induced self-assembling of few-layer graphene into a fractal-like conductive macro-network with a reduction of percolation threshold

2015 ◽  
Vol 17 (12) ◽  
pp. 7634-7638 ◽  
Author(s):  
I. Janowska
Keyword(s):  
Percolation Threshold ◽  
Layer Graphene ◽  
Self Assembling ◽  
Percolation Thresholds ◽  
Few Layer Graphene

The evaporation-induced self-assembling of a few-layer graphene results in macroscopic branched fractal-like conductive patterns with reduced percolation thresholds.

scholarly journals Depositional and Diagenetic Controls on Macroscopic Acoustic and Geomechanical Behaviors in Wufeng-Longmaxi Formation Shale

2021 ◽  
Vol 9 ◽  
Author(s):  
Jixin Deng ◽  
Chongyi Wang ◽  
Qun Zhao ◽  
Wei Guo ◽  
Genyang Tang ◽  
...  
Keyword(s):  
Elastic Properties ◽  
Failure Modes ◽  
Elastic Behavior ◽  
Compositional Variation ◽  
Primary Control ◽  
Longmaxi Formation ◽  
Young’S Moduli ◽  
Splitting Failure ◽  
Quartz Cement ◽  
Geochemical Analyses

This integrated study provides significant insight into parameters controlling the dynamic and static elastic behaviors of shale. Acoustic and geomechanical behaviors measurement from laboratory have been coupled with detailed petrographic and geochemical analyses, and microtexture observations on shale samples from the Wufeng−Longmaxi Formation of the southeast Sichuan Basin. The major achievement is the establishment of the link between depositional environment and the subsequent microtexture development, which exerts a critical influence on the elastic properties of the shale samples. Microtexture and compositional variation between upper and lower sections of the Wufeng−Longmaxi Formation show that the former undergoes normal mechanical and chemical compaction to form clay supported matrices with apparent heterogonous mechanical interfaces between rigid clasts and the aligned clay fabric. Samples from lower sections exhibited a microcrystalline quartz-supported matrix with a homogeneous mechanical interface arising from syn-depositional reprecipitation of biogenic quartz cement. This type of microtexture transition exerts primary control on elastic behavior of the shale samples. A clear “V” shaped trend observed from acoustic velocities and static Young’s moduli document contrasting roles played by microtexture, porosity and organic matter in determining elastic properties. Samples with a quartz-supported matrix exhibit elastic deformation and splitting failure modes. The increment of the continuous biogenic quartz cemented medium with limited mechanic interface. By contrast, samples showing a predominantly clay-supported matrix exhibited more signs of plastic deformation reflecting heterogeneous mechanical interfaces at grain boundaries.

Shear properties of passive ventricular myocardium

2002 ◽  
Vol 283 (6) ◽  
pp. H2650-H2659 ◽  
Author(s):  
Socrates Dokos ◽  
Bruce H. Smaill ◽  
Alistair A. Young ◽  
Ian J. LeGrice
Keyword(s):  
Shear Deformation ◽  
Simple Shear ◽  
Ventricular Myocardium ◽  
Left Ventricular ◽  
Shear Deformations ◽  
Shear Properties ◽  
Nonlinear Viscoelastic ◽  
Myocardial Layers ◽  
Shear Modes ◽  
Simple Shear Deformation

We examined the shear properties of passive ventricular myocardium in six pig hearts. Samples (3 × 3 × 3 mm) were cut from adjacent regions of the lateral left ventricular midwall, with sides aligned with the principal material axes. Four cycles of sinusoidal simple shear (maximum shear displacements of 0.1–0.5) were applied separately to each specimen in two orthogonal directions. Resulting forces along the three axes were measured. Three specimens from each heart were tested in different orientations to cover all six modes of simple shear deformation. Passive myocardium has nonlinear viscoelastic shear properties with reproducible, directionally dependent softening as strain is increased. Shear properties were clearly anisotropic with respect to the three principal material directions: passive ventricular myocardium is least resistant to simple shear displacements imposed in the plane of the myocardial layers and most resistant to shear deformations that produce extension of the myocyte axis. Comparison of results for the six different shear modes suggests that simple shear deformation is resisted by elastic elements aligned with the microstructural axes of the tissue.

scholarly journals Low electrical percolation thresholds and nonlinear effects in graphene-reinforced nanocomposites: A numerical analysis

2018 ◽  
Vol 52 (20) ◽  
pp. 2767-2775 ◽  
Author(s):  
Xiaoxin Lu ◽  
Julien Yvonnet ◽  
Fabrice Detrez ◽  
Jinbo Bai
Keyword(s):  
Numerical Model ◽  
Aspect Ratio ◽  
Percolation Threshold ◽  
Barrier Height ◽  
Nonlinear Effects ◽  
Tunneling Effect ◽  
Graphene Sheets ◽  
Microstructural Parameters ◽  
Electric Behavior ◽  
Percolation Thresholds

A numerical model of graphene-reinforced nanocomposites taking into account the electric tunneling effect is employed to analyze the influence of microstructural parameters on the effective electric conductivity and the percolation thresholds of the composite. The generation procedure for the random microstructures of graphene-reinforced nanocomposites is described. Effects of the barrier height, of graphene aspect ratio and alignment of graphene sheets have been quantitatively evaluated. The results show that both higher graphene aspect ratio and lower barrier height can lead to smaller percolation threshold, and the alignment of graphene sheets results in anisotropic electrical behavior without affecting the percolation threshold. The numerical model also shows the importance of the tunneling effect to reproduce the nonlinear electric behavior and the low percolation thresholds reported in the literature. Finally, results are compared with available experimental data.

Determination of effective properties of granite rock: A numerical investigation

MRS Advances ◽  
2018 ◽  
Vol 3 (37) ◽  
pp. 2159-2168
Author(s):  
Rehema Ndeda ◽  
S. E. M Sebusang ◽  
R. Marumo ◽  
Erich O. Ogur
Keyword(s):  
Elastic Properties ◽  
Close Agreement ◽  
Effective Properties ◽  
Volume Element ◽  
The Finite Element Method ◽  
Effective Elastic Properties ◽  
Spherical Inclusions ◽  
Periodic Microstructures ◽  
Crack Profile

ABSTRACTMacroscopic strength of the rock depends on the behavior of the micro constituents, that is, the minerals, pores and crack profile. It is important to determine the effect of these constituents on the overall behavior of the rock. This study seeks to estimate the effective elastic properties of granite using the finite element method. A representative volume element (RVE) of suitable size with spherical inclusions of different distribution is subjected to loading and the effective elastic properties determined. The results are compared to those obtained from analytical methods. The elastic properties are obtained in both the axial and transverse direction to account for anisotropy. It is observed that there is congruence in the results obtained both analytically and numerically. The method of periodic microstructures exhibits close agreement with the numerical results.

The effect of anisotropic vesiculation on the porous-permeable evolution in magmatic foams

2021 ◽  
Author(s):  
Jenny Schauroth ◽  
Joshua Weaver ◽  
Jackie E. Kendrick ◽  
Anthony Lamur ◽  
Yan Lavallée
Keyword(s):  
Percolation Threshold ◽  
Gas Flow ◽  
Gas Permeability ◽  
Dominant Mode ◽  
Porous Network ◽  
Near Surface ◽  
Shape Distribution ◽  
Aspect Ratios ◽  
Anisotropic Expansion ◽  
The Impact

<p>Volcanoes can undergo rapid transitions between effusive and explosive eruptions that are often dependant on the melt’s ability to devolatilise and outgas. Eruptive products show widely contrasting permeability values for a given porosity owing to the fact that magma properties evolve over time and space, hence porosity and permeability vary depending on transport and deformation history, scale and orientation. The vesicularity that enables bubble coalescence and permeability development, termed the percolation threshold, is experimentally determined to be at ~30-80 %, depending on the microstructure of magma (i.e. bubble size and shape distribution, crystal content, dominant mode of rheological deformation during vesiculation and flow). During ascent of magma pressure decreases and the magma adapts to these new conditions by vesiculating and expanding against wall rocks. Friction between the vesicular magma and the conduit wall encourages shear, which modifies the architecture of the vesicular network. The geometrical constriction associated with conduits, dykes or fractures which host magma thus prevents or limits the isotropic growth of vesicles; we hypothesise that geometrical constraints instead lead to different ratios of isotropic to anisotropic expansion, which impacts vesicle coalescence and the onset and development of permeable gas flow in magma. We present experimental results detailing the impact of constricting geometry on the development of a permeable porous network, by combining various diameter basalt crucibles with different sized cylindrical cores of aphyric rhyolitic glass (0.12 wt.% H<sub>2</sub>O). We vesiculate the samples in a furnace at 1009 °C for different isothermal dwell increments, before cooling our sample assembly and determining porosity, strain and gas permeability. The vesiculated rhyolites host an impervious glass rind (due to near-surface bubble resorption via diffusion) surrounding a vesicular core; as such, we measure gas permeability of the assembly after cutting the upper and lower glassy rind, to expose the permeability of the internal porous network developed experimentally. The findings indicate that increasing anisotropy, caused by minimising the extent of isotropic vesiculation and maximising vesiculation under constricted conditions, lowers the porosity at which the percolation threshold occurs by ~30 %. We postulate that pure and simple shear, developed parallel to the constricting walls, increase bubble aspect ratios and enhance coalescence. This suggests magmatic foams form connected networks at lower porosities when they vesiculate in constricted conduits, dykes and fractures, thus impacting outgassing efficiency. This implies that the physico-chemical evolution of vesiculating magma may be more strongly linked to structural and rheological controls than previously anticipated, with important implications on ascending magma evolution and eruptive processes, such as degassing, outgassing and fragmentation.</p>

Measurement of Scattering Coefficients

2011 ◽  
Author(s):  
Dale Chimenti ◽  
Stanislav Rokhlin ◽  
Peter Nagy
Keyword(s):  
Wave Propagation ◽  
Reflection Coefficient ◽  
Transmission Coefficient ◽  
Elastic Properties ◽  
Volume Fraction ◽  
Ultrasonic Field ◽  
Guided Wave ◽  
Scattering Coefficient ◽  
Elastic Behavior ◽  
Scattering Coefficients

In the previous chapters, we saw how waves in composites behaved under various circumstances, depending on material anisotropy and wave propagation direction. The most important function that describes guided wave propagation, and the plate elastic behavior on which propagation depends, is the reflection coefficient (RC) or transmission coefficient (TC). More generally, we can call either one simply, the scattering coefficient (SC). It is clear that the elastic properties of the composite are closely tied to the SC, and in turn the scattering coefficient determines the dispersion spectrum of the composite plate. Measuring the SC provides a route to the inference of the elastic properties. To measure the SC, we need only observe the reflected or transmitted ultrasonic field of the incident acoustic energy. In doing so, however, the scattered ultrasonic field is influenced by several factors, both intrinsic and extrinsic. Clearly, the scattered ultrasonic field of an incident acoustic beam falling on the plate from a surrounding or contacting fluid will be strongly influenced by the RC or TC of the plate material. The scattering coefficients are in turn dependent on the plate elastic properties and structural composition: fiber and matrix properties, fiber volume fraction, layup geometry, and perhaps other factors. These elements are not, however, the only ones to determine the amplitude and spatial distribution of energy in the scattered ultrasonic field. Extrinsic factors such as the finite transmitting and receiving transducers, their focal lengths, and their placement with respect to the sample under study can make contributions to the signal as important as the SC itself. Therefore, a systematic study of the role of the transducer is essential for a complete understanding and correct interpretation of acoustic signals in the scattered field. The interpretation of these signals leads ultimately to the inference of composite elastic properties. As we pointed out in Chapter 5, the near coincidence under some conditions of guided plate wave modes with the zeroes of the reflection coefficient (or peaks in the transmission coefficient) has been exploited many times to reveal the plate’s guided wave mode spectrum.

Elastic characteristics of the lung perivascular interstitial space

1983 ◽  
Vol 54 (6) ◽  
pp. 1717-1725 ◽  
Author(s):  
J. C. Smith ◽  
W. Mitzner
Keyword(s):  
Elastic Properties ◽  
Lung Volume ◽  
Interstitial Space ◽  
Elastic Behavior ◽  
Published Data ◽  
Fluid Accumulation ◽  
Recoil Pressure ◽  
Vascular Walls ◽  
Isolated Lung ◽  
Volume History

An analysis of the elastic behavior of the lung perivascular interstitial space during interstitial fluid accumulation is presented. Fluid accumulation must deform the lung parenchyma and vascular walls that form the interstitial space boundaries. The deformations of these boundaries are predicted from previously published data on the elastic properties of the boundary materials. The analysis gives the relationships among the elastic properties of the boundaries, the compliance of the interstitium, the lung volume, and the lung elastic recoil pressure. Values of the interstitial compliance are predicted to decrease with increasing lung recoil pressure and are dependent on the lung pressure-volume history. At low recoil pressures over 70% of the interstitial compliance results from deformation of the parenchyma. As the recoil pressure increases, either with increasing lung volume or due to the lung pressure-volume history, the contributions of the parenchymal and vascular wall deformations become similar. The predictions are generally consistent with published data on interstitial compliance obtained from measurements of isolated lung weight gain during vascular fluid transudation. This correlation suggests that the elastic behavior of the interstitial space can be accounted for by the known elastic properties of the boundary materials.

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