Coulomb–Mohr Granular Materials: Quasi-static Flows and the Highly Frictional Limit

2008 ◽  
Vol 61 (6) ◽  
Author(s):  
Grant M. Cox ◽  
Ngamta Thamwattana ◽  
Scott W. McCue ◽  
James M. Hill
Keyword(s):  
Granular Materials ◽  
Soil Mechanics ◽  
Yield Condition ◽  
Stress Fields ◽  
Flow Rule ◽  
Axially Symmetric ◽  
Governing Equations ◽  
Frictional Materials ◽  
Good Agreement ◽  
Strong Agreement

One approach to modeling fully developed shear flow of frictional granular materials is to use a yield condition and a flow rule, in an analogous way to that commonly employed in the fields of metal plasticity and soil mechanics. Typically, the yield condition of choice for granular materials is the Coulomb–Mohr criterion, as this constraint is relatively simple to apply but at the same time is also known to predict stresses that are in good agreement with experimental observations. On the other hand, there is no strong agreement within the engineering and applied mechanics community as to which flow rule is most appropriate, and this subject is still very much open to debate. This paper provides a review of the governing equations used to describe the flow of granular materials subject to the Coulomb–Mohr yield condition, concentrating on the coaxial and double-shearing flow rules in both plane strain and axially symmetric geometries. Emphasis is given to highly frictional materials, which are defined as those granular materials that possess angles of internal friction whose trigonometric sine is close in value to unity. Furthermore, a discussion is provided on the practical problems of determining the stress and velocity distributions in a gravity flow hopper, as well as the stress fields beneath a standing stockpile and within a stable rat-hole.

Some axially symmetric flows of Mohr–Coulomb compressible granular materials

1992 ◽  
Vol 438 (1902) ◽  
pp. 67-93 ◽  
Keyword(s):  
Granular Material ◽  
Granular Materials ◽  
Yield Condition ◽  
Polar Coordinates ◽  
Flow Rule ◽  
Physical Parameters ◽  
Alternative Theory ◽  
Axially Symmetric ◽  
Special Cases ◽  
Associated Flow Rule

In this paper we consider a number of axially symmetric flows of compressible granular materials obeying the Coulomb–Mohr yield condition and the associated flow rule. We pay particular attention to those plastic régimes and flows not included in the seminal work of Cox, Eason & Hopkins (1961). For certain plastic régimes, the velocity equations uncouple from the stress equations and the flow is said to be kinematically determined. We present a number of kinematically determined flows and the development given follows the known solutions applicable to the so-called ‘double-shearing’ model of granular materials which assumes incompressibility and for which the governing equations are almost the same. Similarly, for certain other plastic régimes the stresses may be completely determined without reference to the velocity equations and these are referred to as statically determined flows. In the latter sections of the paper we examine statically determined flows arising from the assumption that the shear stress in either cylindrical or spherical polar coordinates is zero. In the final section we present a numerical solution, which incorporates gravitational effects, for the flow of a granular material in a converging hopper. In addition, we examine the Butterfield & Harkness (1972) modification of the double-shearing model of granular materials which formally includes both the double-shearing theory and the Coulomb–Mohr flow rule theory as special cases. Moreover, for kinematically determined régimes, the velocity equations are the same apart from a different constant, while for statically determined régimes the governing velocity equations are slightly more complicated, involving another constant which is a different combination of the basic physical parameters. Thus some of the solutions presented here can be immediately extended to this alternative theory of granular material behaviour and therefore the prospect arises of devising experiments which might validate or otherwise one theory or the other.

Axially Symmetric Radial Flow of Rigid/Linear-Hardening Materials

1979 ◽  
Vol 46 (2) ◽  
pp. 322-328 ◽  
Author(s):  
D. Durban
Keyword(s):  
Radial Flow ◽  
Closed Form Solution ◽  
Wire Drawing ◽  
Form Solution ◽  
Flow Rule ◽  
Axially Symmetric ◽  
Linear Hardening ◽  
Stress Components ◽  
Von Mises ◽  
Good Agreement

A closed-form solution has been discovered for axially symmetric radial flow of rigid/linear-hardening materials. It is assumed that the materials obey the von Mises flow rule and that the flow field is in steady state. Explicit expressions for the stress components and the radial velocity are given. The applicability of the solution to wire drawing or extrusion is discussed. Some approximate formulas are derived and shown to be in good agreement, within their range of validity, with experimental results for drawing.

Transient Thermal Stresses in Elasto-Plastic Discs

1969 ◽  
Vol 11 (4) ◽  
pp. 384-391 ◽  
Author(s):  
H. Odenö
Keyword(s):  
Temperature Distribution ◽  
Thermal Stresses ◽  
Plastic Material ◽  
Yield Condition ◽  
Transient Temperature ◽  
Flow Rule ◽  
Axially Symmetric ◽  
Exterior Surface ◽  
Tresca Yield Condition ◽  
Perfectly Plastic

A thin circular disc of elastic-perfectly plastic material, subjected to an axially symmetric transient temperature distribution, is treated analytically. All material parameters are assumed to be independent of the temperature. Poisson's ratio is taken to be one-half. The Tresca yield condition with associated flow rule is employed. The temperature distribution is that which appears when the outer rim surface of the disc receives a rapid temperature increase and it is solved approximately by the collocation method. The analysis shows that under certain circumstances, plastic deformation will occur in a moving annular region. This region starts to develop at the exterior surface and moves inward, while changing its width. After a certain finite time its width shrinks to zero. Except for a residual constant state of strain, the strain field is then again elastic. An application to the method of separating the ring and the shaft in a shrink-fit is carried out numerically. The residual stresses in the ring are calculated.

scholarly journals Finite Element Simulations of an Elasto-Viscoplastic Model for Clay

Geosciences ◽  
2019 ◽  
Vol 9 (3) ◽  
pp. 145 ◽  
Author(s):  
Mohammad N. Islam ◽  
Carthigesu T. Gnanendran ◽  
Mehrdad Massoudi
Keyword(s):  
Finite Element ◽  
San Francisco ◽  
Critical State ◽  
Soil Mechanics ◽  
Flow Rule ◽  
Compression Index ◽  
Mechanics Model ◽  
Associated Flow Rule ◽  
Marine Deposit ◽  
Good Agreement

In this paper, we develop an elasto-viscoplastic (EVP) model for clay using the non-associated flow rule. This is accomplished by using a modified form of the Perzyna’s overstressed EVP theory, the critical state soil mechanics, and the multi-surface theory. The new model includes six parameters, five of which are identical to those in the critical state soil mechanics model. The other parameter is the generalized nonlinear secondary compression index. The EVP model was implemented in a nonlinear coupled consolidated code using a finite-element numerical algorithm (AFENA). We then tested the model for different clays, such as the Osaka clay, the San Francisco Bay Mud clay, the Kaolin clay, and the Hong Kong Marine Deposit clay. The numerical results show good agreement with the experimental data.

scholarly journals The Stationary Concentrated Vortex Model

Climate ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 39
Author(s):  
Oleg Onishchenko ◽  
Viktor Fedun ◽  
Wendell Horton ◽  
Oleg Pokhotelov ◽  
Natalia Astafieva ◽  
...  
Keyword(s):  
Vortex Structure ◽  
Radial Direction ◽  
Symmetry Axis ◽  
Outer Part ◽  
Vertical Direction ◽  
Axially Symmetric ◽  
New Model ◽  
Vortex Model ◽  
Axis Of Symmetry ◽  
Good Agreement

A new model of an axially-symmetric stationary concentrated vortex for an inviscid incompressible flow is presented as an exact solution of the Euler equations. In this new model, the vortex is exponentially localised, not only in the radial direction, but also in height. This new model of stationary concentrated vortex arises when the radial flow, which concentrates vorticity in a narrow column around the axis of symmetry, is balanced by vortex advection along the symmetry axis. Unlike previous models, vortex velocity, vorticity and pressure are characterised not only by a characteristic vortex radius, but also by a characteristic vortex height. The vortex structure in the radial direction has two distinct regions defined by the internal and external parts: in the inner part the vortex flow is directed upward, and in the outer part it is downward. The vortex structure in the vertical direction can be divided into the bottom and top regions. At the bottom of the vortex the flow is centripetal and at the top it is centrifugal. Furthermore, at the top of the vortex the previously ascending fluid starts to descend. It is shown that this new model of a vortex is in good agreement with the results of field observations of dust vortices in the Earth’s atmosphere.

On the Motion of Granular Materials Due to Shear

2000 ◽  
Author(s):  
Mehrdad Massoudi ◽  
Tran X. Phuoc
Keyword(s):  
Finite Difference ◽  
Granular Materials ◽  
Continuum Model ◽  
Theory Model ◽  
Governing Equations ◽  
Flat Plates ◽  
Material Parameters ◽  
Finite Difference Technique ◽  
Linear Differential ◽  
The Continuum

Abstract In this paper we study the flow of granular materials between two horisontal flat plates where the top plate is moving with a constant speed. The constitutive relation used for the stress is based on the continuum model proposed by Rajagopal and Massoudi (1990), where the material parameters are derived using the kinetic theory model proposed by Boyle and Massoudi (1990). The governing equations are non-dimensionalized and the resulting system of non-linear differential equations is solved numerically using finite difference technique.

An analytical model of an I-cored coil located above a conductive material with a hole

2018 ◽  
Vol 82 (2) ◽  
pp. 21001
Author(s):  
Grzegorz Tytko ◽  
Leszek Dziczkowski
Keyword(s):  
Test Object ◽  
Middle Layer ◽  
Axially Symmetric ◽  
The Finite Element Method ◽  
Cylindrical Coordinate ◽  
Air Space ◽  
Through Hole ◽  
Tree Method ◽  
Good Agreement ◽  
Made In

The paper examines the problem of an axially symmetric I-cored coil located above a three-layered plate with a hole in the middle layer. A cylindrical coordinate system was applied, wherein the solution domain was truncated in the radial direction. The employment of the truncated region eigenfunction expansion (TREE) method resulted in deriving the final formulas for the change of the coil impedance with regard to the air space, and also pertaining to the test object without a flaw. Formulas for various configurations of the test object, among others for a surface hole, a subsurface hole and a through hole, have been presented. For the purpose of defectoscopy, the influence of the hole in the plate on the impedance components was investigated. The calculations were made in Matlab for frequencies from 100 Hz to 50 kHz. The obtained results were verified using the finite element method (FEM) in Comsol Multiphysics package. A very good agreement was observed in the case of both the resistance and reactance.

An Application of Incremental Plasticity Theory to Fatigue Life Prediction of Steels

1991 ◽  
Vol 113 (4) ◽  
pp. 404-410 ◽  
Author(s):  
W. R. Chen ◽  
L. M. Keer
Keyword(s):  
Fatigue Life ◽  
Life Prediction ◽  
Kinematic Hardening ◽  
Yield Condition ◽  
Strain Curve ◽  
Fatigue Life Prediction ◽  
304 Stainless Steel ◽  
Flow Rule ◽  
Stress Strain ◽  
Von Mises

An incremental plasticity model is proposed based on the von-Mises yield condition, associated flow rule, and nonlinear kinematic hardening rule. In the present model, fatigue life prediction requires only the uniaxial cycle stress-strain curve and the uniaxial fatigue test results on smooth specimens. Experimental data of 304 stainless steel and 1045 carbon steel were used to validate this analytical model. It is shown that a reasonable description of steady-state hysteresis stress-strain loops and prediction of fatigue lives under various combined axial-torsional loadings are given by this model

scholarly journals The influence of pavement degradation caused by cyclic loading on its failure mechanisms

2016 ◽  
Vol 11 (3) ◽  
pp. 179-187 ◽  
Author(s):  
Marcin Gajewski ◽  
Stanisław Jemioło
Keyword(s):  
Yield Condition ◽  
Limit Load ◽  
Flow Rule ◽  
Smooth Approximation ◽  
Simple Method ◽  
Plastic Properties ◽  
The Road ◽  
Plastic Materials ◽  
Number Of Cycles ◽  
Elastic Plastic Materials

In this paper, a simple method is proposed to estimate capacity of multilayered road structure including the degradation of the elastic and plastic properties of the constituent materials. In the study boundary value problem modeling interaction of wheels with road surface layer in the frame of large deformation theory for elastic-plastic materials was formulated. Plastic properties of the material were described by the flow rule un-associated with yield condition. The Coulomb-Mohr yield condition was assumed and the potential for plasticity is its smooth approximation. In addition, in constitutive modeling the dependence of the Young’s modulus and cohesion of the material from the number of cycles is taken into account. This paper presents qualitative findings in relation to mechanical behavior of the road structure, i.e., for example, the development of plastic zones with increasing load for un-degraded and degraded materials. In addition, a parametric study of the influence of the degradation ratio of the elasticity and plasticity properties for road structure failure mechanism (limit load value) was made.

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