Homogenization of Composites with Extended General interfaces: Comprehensive Review and Unified Modeling

2021 ◽  
Author(s):  
Soheil Firooz ◽  
Paul Steinmann ◽  
Ali Javili
Keyword(s):  
Numerical Study ◽  
Finite Thickness ◽  
Heterogeneous Materials ◽  
Interface Model ◽  
Interface Position ◽  
Unified Modeling ◽  
Interface Models ◽  
Universal Interface ◽  
Underlying Mechanisms ◽  
Interface Parameters

Abstract Interphase regions that form in heterogeneous materials through various underlying mechanisms such as poor mechanical or chemical adherence, roughness, and coating, play a crucial role in the response of the medium. A well- established strategy to capture a finite-thickness interphase behavior is to replace it with a zero-thickness interface model characterized by its own displacement and/or traction jumps, resulting in different interface models. The contributions to date dealing with interfaces commonly assume that the interface is located in the middle of its corresponding interphase. We revisit this assumption and introduce a universal interface model, wherein a unifying approach to the homogenization of heterogeneous materials embedding interfaces between their constituents is developed. The proposed novel interface model is universal in the sense that it can recover any of the classical interface models. Next, via incorporating this universal interface model into homogenization, we develop bounds and estimates for the overall moduli of fiber-reinforced and particle-reinforced composites as functions of the interface position and properties. Furthermore, we elaborate on the computational implications of this interface model. Finally, we carry out a comprehensive numerical study to highlight the influence of interface position, stiffness ratio and interface parameters on the overall properties of composites, where an excellent agreement between the analytical and computational results is observed. The developed interface-enhanced homogenization framework also successfully captures size effects, which are immediately relevant to emerging applications of nano-composites due their pronounced interface effects at small scales.

scholarly journals A Comparison of Interface Growth Models Applied to Rayleigh–Taylor and Richtmyer–Meshkov Instabilities

2020 ◽  
Vol 142 (12) ◽  
Author(s):  
J. Canfield ◽  
N. Denissen ◽  
M. Francois ◽  
R. Gore ◽  
R. Rauenzahn ◽  
...  
Keyword(s):  
Compressible Flow ◽  
Numerical Models ◽  
Transition To Turbulence ◽  
Analytical Models ◽  
Fluid Interfaces ◽  
Interface Model ◽  
Interface Position ◽  
Flow Solver ◽  
Interface Models ◽  
Interface Growth

Abstract Sophisticated numerical models that contain fluid interfaces rely upon interface evolution models to approximate the transition to turbulence near interfaces, in the presence of Rayleigh–Taylor (RTI) or Richtmyer–Meshkov (RMI) instability. Semi-analytical models have been developed in recent decades to predict the interface growth from an initial state into the nonlinear regime. Two of these models are considered in this study. They are the Goncharov and the z-models. Both of these interface models have strengths and weaknesses, which are examined here. Both of them have been implemented in the xRAGE compressible flow solver, which models fluid interfaces. The flow solver provides the fluids acceleration as a body force to the interface model. The purpose of such interface model is to evolve the early times of interface position as a subgrid model within a compressible flow simulation in order to then initialize a turbulence model. In this work, the interface models are assessed and compared for their evolution of RTI and RMI. The z-model performed better than the Goncharov model for all cases that were explored.

Detailed Numerical Study of the Main Sources of Loss and Flow Behavior in Low Pressure Steam Turbine Exhaust Hoods

2017 ◽  
Author(s):  
Dickson Munyoki ◽  
Markus Schatz ◽  
Damian M. Vogt
Keyword(s):  
Steam Turbine ◽  
Numerical Study ◽  
Flow Behavior ◽  
Low Pressure ◽  
Operating Conditions ◽  
Pressure Recovery ◽  
Exhaust Hood ◽  
Recovery Coefficient ◽  
Pressure Steam ◽  
Underlying Mechanisms

The performance of the axial-radial diffuser downstream of the last low-pressure steam turbine stages and the losses occurring subsequently within the exhaust hood directly influences the overall efficiency of a steam power plant. It is estimated that an improvement of the pressure recovery in the diffuser and exhaust hood by 10% translates into 1% of last stage efficiency [11]. While the design of axial-radial diffusers has been the object of quite many studies, the flow phenomena occurring within the exhaust hood have not received much attention in recent years. However, major losses occur due to dissipation within vortices and inability of the hood to properly diffuse the flow. Flow turning from radial to downward flow towards the condenser, especially at the upper part of the hood is essentially the main cause for this. This paper presents a detailed analysis of the losses within the exhaust hood flow for two operating conditions based on numerical results. In order to identify the underlying mechanisms and the locations where dissipation mainly occurs, an approach was followed, whereby the diffuser inflow is divided into different sectors and pressure recovery, dissipation and finally residual kinetic energy of the flow originating from these sectors is calculated at different locations within the hood. Based on this method, the flow from the topmost sectors at the diffuser inlet is found to cause the highest dissipation for both investigated cases. Upon hitting the exhaust hood walls, the flow on the upper part of the diffuser is deflected, forming complex vortices which are stretching into the condenser and interacting with flow originating from other sectors, thereby causing further swirling and generating additional losses. The detailed study of the flow behavior in the exhaust hood and the associated dissipation presents an opportunity for future investigations of efficient geometrical features to be introduced within the hood to improve the flow and hence the overall pressure recovery coefficient.

Numerical Study on the Interfacial Modification Effects of Soy Protein on Poly(Vinylidene Fluoride)

2019 ◽  
Author(s):  
Zhuoyuan Zheng ◽  
Chen Xin ◽  
Yumeng Li
Keyword(s):  
High Temperature ◽  
Soy Protein ◽  
Disulfide Bonds ◽  
Vinylidene Fluoride ◽  
Numerical Study ◽  
Protein Molecule ◽  
Heat Denaturation ◽  
Β Phase ◽  
Poly Vinylidene Fluoride ◽  
Underlying Mechanisms

Abstract The application of bio-degradable green materials is a rising global trend during the past decades for the sake of environment protection and sustainable development. Soy protein-based biomaterial is a promising candidate to replace the petroleum-based synthetic materials and was proved to be an effective functional modifier for polymers from our previous studies. Molecular dynamic (MD) simulation is implemented in this study to provide insights in understanding the underlying mechanisms. 11S molecule is chosen as a representative of soy protein, and three different denaturation processes are applied, including heat denaturation at two temperatures and the breaking of disulfide bonds. It is observed that by controlling the denaturation conditions, the hydrophobicity of the protein molecule is manipulated: high temperature denaturation can increase the exposed area of hydrophilic residues; whereas, by breaking the disulfide bonds, the hydrophobic residues of the molecules can be largely exposed. Besides, the mechanisms of using protein as functional modifier to tune the structures of the hydrophobic Poly(vinylidene fluoride) (PVDF) polymer (amorphous and β-crystal phases) are studied. S-S debond protein is found to favor the formation of amorphous PVDF; whereas, high temperature denatured one has stronger interactions with β phase.

Persistence Probability for a Class of Gaussian Processes Related to Random Interface Models

2015 ◽  
Vol 47 (1) ◽  
pp. 146-163 ◽  
Author(s):  
Hironobu Sakagawa
Keyword(s):  
Gaussian Processes ◽  
Interface Model ◽  
Persistence Probability ◽  
Random Interface ◽  
Interface Models ◽  
Fixed Level

We consider a class of Gaussian processes which are obtained as height processes of some (d + 1)-dimensional dynamic random interface model on ℤd. We give an estimate of persistence probability, namely, large T asymptotics of the probability that the process does not exceed a fixed level up to time T. The interaction of the model affects the persistence probability and its asymptotics changes depending on the dimension d.

A numerical study of the flow in the wake of a plate of finite thickness

1999 ◽  
Vol 10 (2) ◽  
pp. 151-159
Author(s):  
K. B. Murashkin ◽  
V. M. Paskonov ◽  
S. V. Fortova
Keyword(s):  
Numerical Study ◽  
Finite Thickness

The shear strength of soils containing undulating shear zones—a numerical study

1988 ◽  
Vol 25 (3) ◽  
pp. 550-558 ◽  
Author(s):  
George T. Dounias ◽  
David M. Potts ◽  
Peter R. Vaughan
Keyword(s):  
Strain Softening ◽  
Numerical Study ◽  
Finite Thickness ◽  
Shear Zones ◽  
Shear Surface ◽  
Weak Zone ◽  
Surface Finite Elements ◽  
Soil Block ◽  
Strength And Deformation ◽  
Intact Soil

This paper investigates the behaviour of a clay layer containing an undulating shear surface, when sheared across the undulations. A relatively long soil block containing an undulating weak zone of finite thickness is assumed. A finite element study is undertaken, examining the effect of the thickness and the amplitude of the weak zone on the overall strength and deformation of the block. Also examined is the behaviour of the block when either only the weak zone or both the weak zone and the intact soil are strain softening. Key words: undulating shear surface, finite elements, strain softening.

Natural Convection in a Partitioned Vertical Enclosure Heated With a Uniform Heat Flux

2006 ◽  
Vol 129 (6) ◽  
pp. 717-726 ◽  
Author(s):  
Kamil Kahveci
Keyword(s):  
Heat Flux ◽  
Nusselt Number ◽  
Natural Convection ◽  
Thermal Resistance ◽  
Average Nusselt Number ◽  
Numerical Study ◽  
Finite Thickness ◽  
Vertical Wall ◽  
Uniform Heat Flux ◽  
Uniform Heat

This numerical study looks at laminar natural convection in an enclosure divided by a partition with a finite thickness and conductivity. The enclosure is assumed to be heated using a uniform heat flux on a vertical wall, and cooled to a constant temperature on the opposite wall. The governing equations in the vorticity-stream function formulation are solved by employing a polynomial-based differential quadrature method. The results show that the presence of a vertical partition has a considerable effect on the circulation intensity, and therefore, the heat transfer characteristics across the enclosure. The average Nusselt number decreases with an increase of the distance between the hot wall and the partition. With a decrease in the thermal resistance of the partition, the average Nusselt number shows an increasing trend and a peak point is detected. If the thermal resistance of the partition further declines, the average Nusselt number begins to decrease asymptotically to a constant value. The partition thickness has little effect on the average Nusselt number.

scholarly journals A note on traction continuity across an interface in a geometrically non-linear framework

2018 ◽  
Vol 24 (8) ◽  
pp. 2478-2496 ◽  
Author(s):  
Ali Javili
Keyword(s):  
Spatial Configuration ◽  
Three Dimensional ◽  
Interface Model ◽  
Cohesive Interface ◽  
Interface Models ◽  
Linear Framework ◽  
Non Linear ◽  
Spatial Configurations ◽  
Elastic Interface ◽  
General Interface

The objective of this contribution is to elaborate on the notion of “traction continuity” across an interface at finite deformations. The term interface corresponds to a zero-thickness model representing the interphase between different constituents in a material. Commonly accepted interface models are the cohesive interface model and the elastic interface model. Both the cohesive and elastic interface models are the limit cases of a generalized interface model. This contribution aims to rigorously analyze the concept of the traction jump for the general interface model. The governing equations of the general interface model in the material as well as spatial configurations are derived and the traction jump across the interface for each configuration is highlighted. It is clearly shown that the elastic interface model undergoes a traction jump in both the material and spatial configurations according to a generalized Young–Laplace equation. For the cohesive interface model, however, while the traction field remains continuous in the material configuration, it can suffer a jump in the spatial configuration. This finding is particularly important since the cohesive interface model is based on the assumption of traction continuity across the interface and that the term “traction” often refers to the spatial configuration and not the material one. Thus, additional care should be taken when formulating an interface model in a geometrically non-linear framework. The theoretical findings for various interface models are carefully illustrated via a series of two-dimensional and three-dimensional numerical examples using the finite element method.

scholarly journals A numerical study for inward solidification of a liquid contained in cylindrical and spherical vessel

2010 ◽  
Vol 14 (2) ◽  
pp. 365-372 ◽  
Author(s):  
Kirby Rajeev ◽  
Subir Das
Keyword(s):  
Numerical Study ◽  
Operational Matrix ◽  
Interface Condition ◽  
Initial Value ◽  
Spherical Vessel ◽  
Interface Position ◽  
Operational Matrix Of Integration ◽  
Fixed Interface ◽  
Vector Matrix ◽  
Change Material

This study presents a numerical solution of inward solidification of phase change material contained in cylinder/sphere. Here, constant thermal property is assumed throughout the analysis for the liquid, which is initially at fusion temperature. The governing dimensionless equations of the above problem and boundary conditions are converted to initial value problem of vector matrix form. The time function is approximated by Chebyshev series and the operational matrix of integration is applied. The solution is utilized iteratively in the interface condition to determine the time taken to attain a fixed interface position.

A Numerical Study of Natural Convective Heat Transfer From Two-Sided Inclined Square Plates Having a Finite Thickness

2019 ◽  
Author(s):  
Rafiq Manna ◽  
Patrick H. Oosthuizen
Keyword(s):  
Heat Transfer ◽  
Convective Heat Transfer ◽  
Convective Heat ◽  
Numerical Study ◽  
Finite Thickness ◽  
Plate Thickness ◽  
Side Surface ◽  
Bottom Surface ◽  
Study Results ◽  
Inclination Angles

Abstract Simultaneous natural convective heat transfer from the top, bottom and side surfaces of two-sided inclined square plates having various thicknesses has been numerically investigated. The aim of this work is to determine whether the plate thickness has a significant influence on the heat transfer rates from the plate surfaces when the plate is inclined to the horizontal and to determine how the heat transfer rate varies with this angle of inclination. The upper, lower and side surfaces of the plate have been assumed to be isothermal and at the same temperature which is higher than that of the surrounding fluid. The range of conditions considered is such that laminar, transitional, and turbulent flow occur over the plate. The numerical solution has been obtained using the commercial CFD solver ANSYS FLUENT©. In this study, results have only been obtained for the case where the plate is exposed to air. Inclination angles of between 0 and 40 degrees from the horizontal and plate dimensionless thicknesses (thickness-to-side length ratios) of between 0 and 0.3 have been considered. Variations of the mean Nusselt number with Rayleigh number for the top surface, bottom surface, side surface and that averaged over all heated surfaces of the plate for various inclination angles and for various plate dimensionless thicknesses have been obtained.

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