Extrinsic viscous anisotropy in two-phase aggregates, fabric parametrisation and application to mantle convection

2020 ◽  
Author(s):  
Albert de Montserrat Navarro ◽  
Manuele Faccenda
Keyword(s):  
Volume Fraction ◽  
Three Dimensional ◽  
Two Phase ◽  
Mantle Dynamics ◽  
Mineral Phases ◽  
Viscosity Contrast ◽  
The Matrix ◽  
Order Of Magnitude ◽  
Convection Patterns ◽  
Strong Inclusion

<p>Earth's mantle rocks are poly-aggregates where different mineral phases coexist.  These rocks may often be approximated as two-phase aggregates with a dominant phase and less abundant one (e.g. bridgmanite-ferropericlase aggregates in the lower mantle). Severe shearing of these rocks leads to a non-homogeneous partitioning of the strain between the different phases. The resulting bulk rock is mechanically not isotropic, and the elastic and the viscous tensor depend on the volume fraction and viscosity contrast between the mineral phases and the fabric.</p><p>Here we employ three-dimensional mechanical models to reproduce and parametrise fabrics typical of mantle rocks and quantify the evolution of the viscous tensor. These fabrics are produced by shearing a mechanically heterogeneous medium comprised by randomly distributed isotropic inclusions embedded in: i) a weak inclusion-strong matrix aggregate where strain is mainly accommodated by the weak phase, that flattens and yields a penetrative foliation; and, ii) a strong inclusion-weak matrix where strain is mainly accommodated by the matrix, in this case, the strong phase deforms primarily parallel to the direction of the flow, producing cigar-shaped inclusions.</p><p>Finally, we combine the fabric parametrisation of a two-phase aggregate with the Differential Effective Medium (DEM) theory to study the evolution of the viscous tensor and its effects in mantle dynamics. The results of two-dimensional models of thermal convection show that a viscosity contrast of one order of magnitude between the two mineral phases is enough to deflect mantle plumes and produce convection patterns that differ considerably from the ideal isotropic media.</p>

scholarly journals COMPUTATIONAL MICROSTRUCTURE-BASED ANALYSIS OF RESIDUAL STRESS EVOLUTION IN METAL-MATRIX COMPOSITE MATERIALS DURING THERMOMECHANICAL LOADING

2021 ◽  
Vol 19 (2) ◽  
pp. 241
Author(s):  
Ruslan Balokhonov ◽  
Varvara Romanova ◽  
Eugen Schwab ◽  
Aleksandr Zemlianov ◽  
Eugene Evtushenko
Keyword(s):  
Residual Stress ◽  
Metal Matrix ◽  
Spatial Scales ◽  
Three Dimensional ◽  
Matrix Composites ◽  
Two Phase ◽  
Irregular Shapes ◽  
The Matrix ◽  
Stress Formation ◽  
Mechanical Fragmentation

A technique for computer simulation of three-dimensional structures of materials with reinforcing particles of complex irregular shapes observed in the experiments is proposed, which assumes scale invariance of the natural mechanical fragmentation. Two-phase structures of metal-matrix composites and coatings of different spatial scales are created, with the particles randomly distributed over the matrix and coating computational domains. Using the titanium carbide reinforcing particle embedded into the aluminum as an example, plastic strain localization and residual stress formation along the matrix-particle interface are numerically investigated during cooling followed by compression or tension of the composite. A detailed analysis is performed to evaluate the residual stress concentration in local regions of bulk tension formed under all-round and uniaxial compression of the composite due to the concave and convex interfacial asperities.

Droplet Formation in a Microchannel T-Junction With Different Step Structure Position

2020 ◽  
Vol 143 (7) ◽  
Author(s):  
Mohammad Yaghoub Abdollahzadeh Jamalabadi ◽  
Rasoul Kazemi ◽  
Mohammad Ghalandari
Keyword(s):  
Nusselt Number ◽  
Volume Fraction ◽  
Three Dimensional ◽  
Droplet Formation ◽  
Continuous Phase ◽  
Flow Path ◽  
The Other ◽  
Two Phase ◽  
Fluid Behavior ◽  
Discrete Phase

Abstract In this study, numerical simulation of formation of droplet within T-shaped microchannel is investigated. Three-dimensional, transient and two-phase numerical solution for four different microchannels with different stepping positions in the flow path was performed. Various parameters such as volume fraction, Nusselt number, pressure, Reynolds number, and temperature are discussed. The results show that the location of stepped barriers in the flow path affects the process of droplet formation, its number and size in the microchannel and should be considered as an important factor in determining the fluid behavior in the microchannel. It was observed that by placing half of the step at the entrance and the other half after the entrance, the continuous phase (S3 mode) was formed in 37.5 s compared to the other modes. The droplets were also smaller in size and more in numbers. It was also observed that the maximum value for the Nusselt number was obtained for the S2 mode where the step was located just above the discrete-phase entrance. In addition, the pressure at the inlet was higher and the flow velocity increased after the step and its pressure decreased, and continued to decrease due to frictional path.

Vortex Simulation for Behavior of Solid Particles Falling in Air

2011 ◽  
Author(s):  
Hisanori Yagami ◽  
Tomomi Uchiyama
Keyword(s):  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Air Flow ◽  
Three Dimensional ◽  
Particle Diameter ◽  
Vortex Method ◽  
Solid Particles ◽  
Particle Volume ◽  
Two Phase ◽  
Spherical Region

The behavior of small solid particles falling in an unbounded air is simulated. The particles, initially arranged within a spherical region in a quiescent air, are made to fall, and their fall induces the air flow around them, resulting in the gas-particle two-phase flow. The particle diameter and density are 1 mm and 7.7 kg/m3 respectively. A three-dimensional vortex method proposed by one of the authors is applied. The simulation demonstrates that the particles are accelerated by the induced downward air flow just after the commencement of their fall. It also highlights that the particles are whirled up by a vortex ring produced around the downward air flow after the acceleration. The effect of the particle volume fraction at the commencement of the fall is also explored.

The 3-D Finite Element Analysis on Elastic-Plastic Micromechanical Response of the Particle Volume Fraction

2019 ◽  
Vol 962 ◽  
pp. 210-217
Author(s):  
Yong Ming Guo ◽  
Nozomi Fukae
Keyword(s):  
Volume Fraction ◽  
Particle Volume Fraction ◽  
Three Dimensional ◽  
Particle Volume ◽  
Two Phase ◽  
Element Analysis ◽  
Elastic Plastic ◽  
Microstructural Parameters ◽  
Commercial Software Package ◽  
Properties Of Materials

It is well known that the properties of materials are a function of their microstructural parameters. The FEM is a good selection for studies of three-dimensional microstructure-property relationships. In this research, the elastic-plastic micromechanical response of the particle volume fraction of two-phase materials have been calculated using a commercial software package of the FEM, some new knowledges on the microstructure-property relationships have obtained.

Comparison of Two Approaches to Model Cure-Induced Microcracking in Three-Dimensional Woven Composites

2012 ◽  
Author(s):  
Igor Tsukrov ◽  
Michael Giovinazzo ◽  
Kateryna Vyshenska ◽  
Harun Bayraktar ◽  
Jon Goering ◽  
...  
Keyword(s):  
Finite Element ◽  
Residual Stresses ◽  
Volume Fraction ◽  
Three Dimensional ◽  
Woven Composites ◽  
Finite Element Models ◽  
The Matrix ◽  
3D Woven Composites ◽  
The Difference ◽  
Resin Curing

Finite element models of 3D woven composites are developed to predict possible microcracking of the matrix during curing. A specific ply-to-ply weave architecture for carbon fiber reinforced epoxy is chosen as a benchmark case. Two approaches to defining the geometry of reinforcement are considered. One is based on the nominal description of composite, and the second involves fabric mechanics simulations. Finite element models utilizing these approaches are used to calculate the overall elastic properties of the composite, and predict residual stresses due to resin curing. It is shown that for the same volume fraction of reinforcement, the difference in the predicted overall in-plane stiffness is on the order of 10%. Numerical model utilizing the fabric mechanics simulations predicts lower level of residual stresses due to curing, as compared to nominal geometry models.

Complete Bandgap in Three-Dimensional Holey Phononic Crystals With Resonators

2013 ◽  
Vol 135 (4) ◽  
Author(s):  
Yan-Feng Wang ◽  
Yue-Sheng Wang
Keyword(s):  
Three Dimensional ◽  
Phononic Crystals ◽  
Vibration Modes ◽  
The Finite Element Method ◽  
Local Resonance ◽  
The Matrix ◽  
Order Of Magnitude ◽  
Complete Bandgap ◽  
Careful Design ◽  
Shape And Size

In this paper, the bandgap properties of three-dimensional holey phononic crystals with resonators are investigated by using the finite element method. The resonators are periodically arranged cubic lumps in the cubic holes connected to the matrix by narrow connectors. The influence of the geometry parameters of the resonators on the bandgap is discussed. In contrast to a system with cubic or spherical holes, which has no bandgaps, systems with resonators can exhibit complete bandgaps. The bandgaps are significantly dependent upon the geometry of the resonators. By the careful design of the shape and size of the resonator, a bandgap that is lower by an order of magnitude than the Bragg bandgap can be obtained. The vibration modes at the band edges of the lowest bandgaps are analyzed in order to understand the mechanism of the bandgap generation. It is found that the emergence of the bandgap is due to the local resonance of the resonators. Spring-mass models or spring-pendulum models are developed in order to evaluate the frequencies of the bandgap edges. The study in this paper is relevant to the optimal design of the bandgaps in light porous materials.

A Methodology for Synthesizing High-Performance Robots Fabricated With Optimally Tailored Composite Laminates

1987 ◽  
Vol 109 (1) ◽  
pp. 74-86 ◽  
Author(s):  
C. K. Sung ◽  
B. S. Thompson
Keyword(s):  
Composite Laminates ◽  
High Performance ◽  
Volume Fraction ◽  
Three Dimensional ◽  
High Strength ◽  
Fiber Volume ◽  
Cross Sectional ◽  
Fiber Properties ◽  
Robot Arms ◽  
The Matrix

An essential ingredient of the next generation of robotic manipulators will be high-strength lightweight arms which promise high-performance characteristics. Currently, a design methodology for optimally synthesizing these essential robotic components does not exist. Herein, an approach is developed for addressing this void in the technology-base by integrating state-of-the-art techniques in both the science of composite materials and also the science of flexible robotic systems. This approach is based on the proposition that optimal performance can be achieved by fabricating robot arms with optimal cross-sectional geometries fabricated with optimally tailored composite laminates. A methodology is developed herein which synthesizes the manufacturing specification for laminates which are specifically tailored for robotic applications in which both high-strength, high-stiffness robot arms are required which also possess high material damping. The parameters in the manufacturing specification include the fiber-volume fraction, the matrix properties, the fiber properties, the ply layups, the stacking sequence and the ply thicknesses. This capability is then integrated within a finite-element methodology for analyzing the dynamic response of flexible robots. An illustrative example demonstrates the approach by simulating the three-dimensional elastodynamic response of a robot subjected to a prescribed spatial maneuver.

Numerical Analysis of Erosive Wear on the Guide Vanes of a Francis Turbine

2015 ◽  
Vol 741 ◽  
pp. 531-535
Author(s):  
Hong Ming Zhang ◽  
Li Xiang Zhang
Keyword(s):  
Numerical Analysis ◽  
Volume Fraction ◽  
Three Dimensional ◽  
Erosive Wear ◽  
Francis Turbine ◽  
Two Phase ◽  
Guide Vanes ◽  
Flow Equations ◽  
Sand Erosion ◽  
Volume Method

The paper presents the numerical analysis of erosive wear on the guide vanes of a Francis turbine using CFD code. The 3-D turbulent particulate-liquid two-phase flow equations are employed in this study. The computing domain is discretized with a full three-dimensional mesh system of unstructured tetrahedral shapes. The finite volume method is used to solve the governing equations and the pressure-velocity coupling is handled via a Pressure Implicit with Splitting of Operators (PISO) procedure. Simulation results have shown that the volume fraction of sand at the top of the guide vanes is higher than others and the maximum of volume fraction of sand is at same location with the maximum of sand erosion rate density. The erosive wear is more serious at the top of the guide vanes.

Modelling mechanically stable muscle architectures

1992 ◽  
Vol 336 (1277) ◽  
pp. 275-292 ◽  
Keyword(s):  
Pressure Distribution ◽  
Volume Fraction ◽  
Experimental Studies ◽  
Three Dimensional ◽  
Muscle Fibres ◽  
Pressure Measurements ◽  
Muscle Belly ◽  
Longitudinal Plane ◽  
Order Of Magnitude ◽  
Volume Problem

This paper presents a planar architectural model for an activated skeletal muscle, with mechanical equilibrium throughout the muscle belly. The model can predict the shape of the muscle fibres and tendinous sheets as well as the internal pressure distribution in the central longitudinal plane (perpendicular to the tendinous sheets) of uni- and bipennate muscle bellies. Mechanically stable solutions for muscle architectures were calculated by equating the pressure developed by curved muscle fibres with the pressure under a curved tendinous sheet. The pressure distribution under a tendinous sheet is determined by its tension, its curvature and the tensile stress of the attached muscle fibres. Dissections showed a good resemblance of the architecture of embalmed muscles with those from our simulations. Calculated maximum pressures are in the same order of magnitude as pressure measurements from the literature. Our model predicts that intramuscular blood flow can be blocked during sustained contraction, as several experimental studies have indeed demonstrated. The volume fractions of muscle fibres and interfibre space in the muscle belly were also calculated. The planar models predict a too low volume fraction for the muscle fibres (about 45% for the bipennate models with a straight central aponeurosis, and about 60% for the simulated unipennate muscle). It is discussed how, in a real muscle, this volume problem can be solved by a special three-dimensional arrangement of muscle fibres in combination with varying widths of the tendinous sheets.

A generalized Archie’s law for n phases

Geophysics ◽  
2010 ◽  
Vol 75 (6) ◽  
pp. E247-E265 ◽  
Author(s):  
Paul W. J. Glover
Keyword(s):  
Volume Fraction ◽  
Three Dimensional ◽  
Three Dimensions ◽  
Reservoir Rock ◽  
Archie’S Law ◽  
Phase Volume Fraction ◽  
General Law ◽  
Special Cases ◽  
The Matrix ◽  
Definition Of

Archie’s law has been the standard method for relating the conductivity of a clean reservoir rock to its porosity and the conductivity of its pore fluid for more than [Formula: see text]. However, it is applicable only when the matrix is nonconducting. A modified version that allows a conductive matrix was published in 2000. A generalized form of Archie’s law is studied for any number of phases for which the classical Archie’s law and modified Archie’s law for two phases are special cases. The generalized Archie’s law contains a phase conductivity, a phase volume fraction, and phase exponent for each of its [Formula: see text] phases. The connectedness of each of the phases is considered, and the principle of conservation of connectedness in a three-dimensional multiphase mixture is introduced. It is confirmed that the general law is formally the same as the classical Archie’s law and modified Archie’s law for one and two conducting phases, respectively. The classical second Archie’s law is compared with the generalized law, which leads to the definition of a saturation exponent for each phase. This process has enabled the derivation of relationships between the phase exponents and saturation exponents for each phase. The relationship between percolation theory and the generalized model is also considered. The generalized law is examined in detail for two and three phases and semiquantitatively for four phases. Unfortunately, the law in its most general form is very difficult to prove experimentally. Instead, numerical modeling in three dimensions is carried out to demonstrate that it behaves well for a system consisting of four interacting conducting phases.

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