Strength Homogenization of Double-Porosity Cohesive-Frictional Solids

2013 ◽  
Vol 80 (2) ◽  
Author(s):  
J. Alberto Ortega ◽  
Franz-Josef Ulm
Keyword(s):  
Effective Stress ◽  
Double Porosity ◽  
Second Order ◽  
Porous Solids ◽  
Strength Development ◽  
Strength Criteria ◽  
Model Predictions ◽  
Strength Behavior ◽  
Homogenization Model ◽  
The Mean

The strength homogenization of cohesive-frictional solids influenced by the presence of two pressurized pore spaces of different characteristic sizes is addressed in this study. A two-scale homogenization model is developed based on limit analysis and the second-order method (SOM) in linear comparison composite theory, which resolves the nonlinear strength behavior through the use of linear comparison composites with optimally chosen properties. For the scale of the classical configuration of a porous solid, the formulation employs a compressible thermoelastic comparison composite to deliver closed-form expressions of strength criteria. Comparisons with numerical results reveal that the proposed homogenization estimates for drained conditions are adequate except for high triaxialities in the mean compressive strength regime. At the macroscopic scale of the double-porosity material, the SOM results are in agreement with strength criteria predicted by alternative micromechanics solutions for materials with purely cohesive solid matrices and drained conditions. The model predictions for the cohesive-frictional case show that drained strength development in granularlike composites is affected by the partitioning of porosity between micro- and macropores. In contrast, the drained strength is virtually equivalent for single- and double-porosity materials with matrix-inclusion morphologies. Finally, the second-order linear comparison composite approach confirms the applicability of an effective stress concept, previously proposed in the literature of homogenization of cohesive-frictional porous solids, for double-porosity materials subjected to similar pressures in the two pore spaces. For dissimilar pore pressures, the model analytically resolves the complex interplays of microstructure, solid properties, and volume fractions of phases, which cannot be recapitulated by the effective stress concept.

Visualizing the Variance of a Random Variable

2011 ◽  
Vol 18 (01) ◽  
pp. 71-85
Author(s):  
Fabrizio Cacciafesta
Keyword(s):  
Stochastic Dominance ◽  
Mean Absolute Error ◽  
Random Variable ◽  
Absolute Error ◽  
Second Order ◽  
Taylor Formula ◽  
Order Stochastic Dominance ◽  
The Mean ◽  
Second Order Stochastic Dominance ◽  
Options Theory

We provide a simple way to visualize the variance and the mean absolute error of a random variable with finite mean. Some application to options theory and to second order stochastic dominance is given: we show, among other, that the "call-put parity" may be seen as a Taylor formula.

3D Numerical Simulation of Polydisperse Pressurized Gas-Solid Fluidized Bed

2011 ◽  
Author(s):  
P. Fede ◽  
O. Simonin ◽  
I. Ghouila
Keyword(s):  
Numerical Simulation ◽  
Fluidized Bed ◽  
Ethylene Polymerization ◽  
Solid Phase ◽  
Three Dimensional ◽  
Gas Velocity ◽  
Particle Segregation ◽  
3D Numerical Simulation ◽  
Model Predictions ◽  
The Mean

Three dimensional unsteady numerical simulations of dense pressurized polydisperse fluidized bed have been carried out. The geometry is a medium-scale industrial pilot for ethylene polymerization. The numerical simulation have been performed with a polydisperse collision model. The consistency of the polydisperse model predictions with the monodisperse ones is shown. The results show that the pressure distribution and the mean vertical gas velocity are not modified by polydispersion of the solid phase. In contrast, the solid particle species are not identically distributed in the fluidized bed indicating the presence of particle segregation.

Drift Forces on a Floating Body of Simple Geometry Due to Second Order Interactions Between Pairs of Harmonics With Different Frequencies

2009 ◽  
Author(s):  
Joa˜o Pessoa ◽  
Nuno Fonseca ◽  
C. Guedes Soares
Keyword(s):  
Vertical Cylinder ◽  
Vertical Axis ◽  
Second Order ◽  
The Body ◽  
Floating Body ◽  
Order Problem ◽  
Simple Geometry ◽  
The Mean ◽  
Order Quantities ◽  
Drift Forces

The paper presents an investigation of the slowly varying second order drift forces on a floating body of simple geometry. The body is axis-symmetric about the vertical axis, like a vertical cylinder with a rounded bottom and a ratio of diameter to draft of 3.25. The hydrodynamic problem is solved with a second order boundary element method. The second order problem is due to interactions between pairs of incident harmonic waves with different frequencies, therefore the calculations are carried out for several difference frequencies with the mean frequency covering the whole frequency range of interest. Results include the surge drift force and pitch drift moment. The results are presented in several stages in order to assess the influence of different phenomena contributing to the global second order responses. Firstly the body is restrained and secondly it is free to move at the wave frequency. The second order results include the contribution associated with quadratic products of first order quantities, the total second order force, and the contribution associated to the free surface forcing.

scholarly journals Experimental Investigation of Fully Plastic Contact of a Sphere Against a Hard Flat

2005 ◽  
Vol 128 (2) ◽  
pp. 230-235 ◽  
Author(s):  
J. Jamari ◽  
D. J. Schipper
Keyword(s):  
Experimental Investigation ◽  
Contact Pressure ◽  
Contact Area ◽  
Measurement Method ◽  
Contact Load ◽  
Model Predictions ◽  
The Mean

In this paper we report the experimental investigation to evaluate the published models for the contact of a deformable sphere against a hard flat in the fully plastic contact regime. A new measurement method has been used to measure the contact area. The behavior of the mean contact pressure and the contact area as a function of the contact load are presented. Substantial differences are found between the measurements and the model predictions. A constant value of the mean contact pressure as the load increases is observed, however, the value is lower than the hardness, as often reported. The contact area is found to be a simple truncation of the sphere by a hard flat.

scholarly journals Validation of a Second-Order Slip Model for Transition-Regime, Gaseous Flows

2004 ◽  
Author(s):  
Nicolas G. Hadjiconstantinou
Keyword(s):  
Second Order ◽  
Stress Fields ◽  
Gas Flows ◽  
Transition Regime ◽  
Slip Model ◽  
Dilute Gas ◽  
Transient Problems ◽  
Model Predictions ◽  
Gaseous Flows ◽  
Related Stress

We discuss and validate a recently proposed second-order slip model for dilute gas flows. Our discussion focuses on the importance of quantitatively accounting for the effect of Knudsen layers close to the walls. This is important, not only for obtaining an accurate slip model but also for interpreting the results of the latter since in transition-regime flows the Knudsen layers penetrate large parts of the flow. Our extensive validation illustrates the above points by comparing direct Monte Carlo solutions to the slip model predictions for an unsteady flow. Excellent agreement is found between simulation and the slip model predictions up to Kn = 0.4, for both the velocity profile and stress at the wall. This demonstrates that the proposed second-order slip model reliably describes arbitrary flowfields (and related stress fields) in a predictive manner at least up to Kn = 0.4 for both steady and transient problems.

scholarly journals Natural convection of Bingham fluids in rectangular cross-sectional cylindrical annuli with differentially heated vertical walls

2019 ◽  
Vol 29 (1) ◽  
pp. 43-77 ◽  
Author(s):  
Sahin Yigit ◽  
Nilanjan Chakraborty
Keyword(s):  
Boundary Condition ◽  
Nusselt Number ◽  
Natural Convection ◽  
Yield Stress ◽  
Thermal Transport ◽  
Second Order ◽  
Bingham Fluids ◽  
Cross Sectional ◽  
Content Type ◽  
The Mean

PurposeThis paper aims to numerically analyse natural convection of yield stress fluids in rectangular cross-sectional cylindrical annular enclosures. The laminar steady-state simulations have been conducted for a range of different values of normalised internal radius (ri/L1/8 to 16, whereLis the difference between outer and inner radii); aspect ratio (AR=H/Lfrom 1/8 to 8 whereHis the enclosure height); and nominal Rayleigh number (Rafrom 103to 106) for a single representative value of Prandtl number (Pris 500).Design/methodology/approachThe Bingham model has been used to mimic the yield stress fluid motion, and numerical simulations have been conducted for both constant wall temperature (CWT) and constant wall heat flux (CWHF) boundary conditions for the vertical side walls. The conservation equations of mass, momentum and energy have been solved in a coupled manner using the finite volume method where a second-order central differencing scheme is used for the diffusive terms and a second-order up-wind scheme is used for the convective terms. The well-known semi-implicit method for pressure-linked equations algorithm is used for the coupling of the pressure and velocity.FindingsIt is found that the mean Nusselt number based on the inner peripheryNu¯iincreases (decreases) with an increase inRa(Bn) due to augmented buoyancy (viscous) forces irrespective of the boundary condition. The ratio of convective to diffusive thermal transport increases with increasingri/Lfor both Newtonian (i.e.Bn= 0) and Bingham fluids regardless of the boundary condition. Moreover, the mean Nusselt numberNu¯inormalised by the corresponding Nusselt number due to pure conductive transport (i.e.Nu¯i/(Nu¯i)cond) shows a non-monotonic trend with increasingARin the CWT configuration for a given set of values ofRa,Pr,Lifor both Newtonian (i.e.Bn= 0) and Bingham fluids, whereasNu¯i/(Nu¯i)condincreases monotonically with increasingARin the CWHF configuration. The influences of convective thermal transport strengthen while thermal diffusive transport weakens with increasingAR, and these competing effects are responsible for the non-monotonicNu¯i/(Nu¯i)condvariation withARin the CWT configuration.Originality/valueDetailed scaling analysis is utilised to explain the observed influences ofRa,BN,ri/LandAR, which along with the simulation data has been used to propose correlations forNu¯i.

scholarly journals Glacier Sliding Down an Inclined Wavy Bed

1976 ◽  
Vol 17 (77) ◽  
pp. 447-462 ◽  
Author(s):  
L. W. Morland
Keyword(s):  
Order Term ◽  
High Viscosity ◽  
Second Order ◽  
Temperature Fields ◽  
Surface Velocity ◽  
Flow Equations ◽  
Basal Sliding ◽  
Pressure Melting ◽  
The Mean ◽  
Bed Slope

The treatments by Nye and Kamb of glacier sliding over a wavy bed with small slope, which assume the ice to be approximated by a Newtonian fluid of high viscosity, are complemented by the inclusion of the glacier depth and the inclination of the bed to the horizontal. The driving force of the motion, gravity, is therefore present in the flow equations and defines immediately the mean drag on the bed. A geothermal heal flux is also included in order to estimate its possible effect on the flow. A complex variable method is used to determine the velocity and temperature fields to second order in the bed slope. These fields satisfy the zero shear traction and pressure-melting-regelation conditions to the same order on the actual bed profile. It is the balance of the second-order term which determines explicitly the (zero order) basal-sliding velocity and surface velocity in terms of the geometry and physical properties of both ice and bed. An explicit solution is illustrated for a sinusoidal bed. and a simple criterion for the onset of cavitation is obtained.

Drying response and effective stress in a double porosity aggregated soil

2009 ◽  
Vol 105 (1-2) ◽  
pp. 44-50 ◽  
Author(s):  
A.R. Bagherieh ◽  
N. Khalili ◽  
G. Habibagahi ◽  
A. Ghahramani
Keyword(s):  
Effective Stress ◽  
Double Porosity

Mean-Square Response of a Second-Order System to Nonstationary, Random Excitation

1970 ◽  
Vol 37 (3) ◽  
pp. 612-616 ◽  
Author(s):  
L. L. Bucciarelli ◽  
C. Kuo
Keyword(s):  
Narrow Band ◽  
Random Excitation ◽  
Second Order ◽  
Envelope Function ◽  
Order System ◽  
Mean Square ◽  
Forcing Function ◽  
Mean Square Response ◽  
Noise Function ◽  
The Mean

The mean-square response of a lightly damped, second-order system to a type of non-stationary random excitation is determined. The forcing function on the system is taken in the form of a product of a well-defined, slowly varying envelope function and a noise function. The latter is assumed to be white or correlated as a narrow band process. Taking advantage of the slow variation of the envelope function and the small damping of the system, relatively simple integrals are obtained which approximate the mean-square response. Upper bounds on the mean-square response are also obtained.

The Second-Order Master Equation

2019 ◽  
pp. 128-158
Author(s):  
Pierre Cardaliaguet ◽  
François Delarue ◽  
Jean-Michel Lasry ◽  
Pierre-Louis Lions
Keyword(s):  
Master Equation ◽  
Mean Field ◽  
Second Order ◽  
Well Posedness ◽  
Mean Field Game ◽  
First Order ◽  
Common Noise ◽  
System P ◽  
The Mean

This chapter investigates the second-order master equation with common noise, which requires the well-posedness of the mean field game (MFG) system. It also defines and analyzes the solution of the master equation. The chapter explains the forward component of the MFG system that is recognized as the characteristics of the master equation. The regularity of the solution of the master equation is explored through the tangent process that solves the linearized MFG system. It also analyzes first-order differentiability and second-order differentiability in the direction of the measure on the same model as for the first-order derivatives. This chapter concludes with further description of the derivation of the master equation and well-posedness of the stochastic MFG system.

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