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.

Stresses at the Intersection of Sphere and Cylinder by a Variant Finite-Difference Method

1974 ◽  
Vol 41 (3) ◽  
pp. 744-752 ◽  
Author(s):  
Mustafa Hassan Fayed
Keyword(s):  
Finite Difference ◽  
The Body ◽  
Simultaneous Equations ◽  
Discrete Problem ◽  
Internal Point ◽  
Governing Equations ◽  
Finite Difference Technique ◽  
Taylor Series Expansions ◽  
Continuous Problem

The aim of this paper is the determination of stresses at the intersection of cylinder with the sphere using a variant finite-difference technique. Mesh lines are drawn on the cross section of the body which are roughly parallel and perpendicular to the boundary, and which the author calls natural meshes. Discretization of the governing differential equations must be carried out to reduce the continuous problem to a discrete problem, this discretization converts the problem into a set of linear simultaneous equations for the functions under consideration at a set of mesh points. The derivatives to be inserted in the governing equations and boundary conditions are found by writing Taylor series expansions at a point in terms of five neighboring points in the case where the point is an internal point (four for a boundary point). By an elimination process the derivatives can be eliminated for each point, and we are left with the unknown functions only.

Modeling of Ductile Damage and Fracture Behavior Based on Different Micromechanisms

2010 ◽  
Vol 20 (4) ◽  
pp. 558-577 ◽  
Author(s):  
Michael Brünig ◽  
Daniel Albrecht ◽  
Steffen Gerke
Keyword(s):  
Continuum Model ◽  
Failure Modes ◽  
Three Dimensional ◽  
Stress Triaxiality ◽  
Yield Condition ◽  
Lode Parameter ◽  
Material Parameters ◽  
Damage And Failure ◽  
Damage And Fracture ◽  
The Continuum

The article deals with the effect of stress triaxiality on the inelastic deformation behavior of aluminum alloys. The proposed continuum model takes into account stress triaxiality dependence of the yield condition as well as of the damage criterion and the fracture condition with different branches corresponding to various damage and failure modes depending on the stress triaxiality and the Lode parameter. Results of numerical cell simulations on the microscale are presented and corresponding identification of micromechanically motivated material parameters is discussed. Furthermore, numerical results of three-dimensional macromechanical finite element analyses are compared with experimental data obtained from smooth and pre-notched tension specimens. The analyses allow verification of the continuum model and identification of further material parameters.

Computer Simulation of the Response of Amperometric Biosensors in Stirred and non Stirred Solution

2003 ◽  
Vol 8 (1) ◽  
pp. 3-18 ◽  
Author(s):  
R. Baronas ◽  
F. Ivanauskas ◽  
J. Kulys
Keyword(s):  
Mathematical Model ◽  
Computer Simulation ◽  
Finite Difference ◽  
Mass Transport ◽  
Enzyme Reaction ◽  
Analyte Concentration ◽  
Amperometric Biosensors ◽  
Finite Difference Technique ◽  
Enzyme Layer ◽  
Biosensor Response

A mathematical model of amperometric biosensors has been developed to simulate the biosensor response in stirred as well as non stirred solution. The model involves three regions: the enzyme layer where enzyme reaction as well as mass transport by diffusion takes place, a diffusion limiting region where only the diffusion takes place, and a convective region, where the analyte concentration is maintained constant. Using computer simulation the influence of the thickness of the enzyme layer as well the diffusion one on the biosensor response was investigated. The computer simulation was carried out using the finite difference technique.

Modelling of Moisture Movement in Wood during Outdoor Storage

2001 ◽  
Vol 6 (2) ◽  
pp. 3-14 ◽  
Author(s):  
R. Baronas ◽  
F. Ivanauskas ◽  
I. Juodeikienė ◽  
A. Kajalavičius
Keyword(s):  
Experimental Data ◽  
Finite Difference ◽  
Climatic Conditions ◽  
Two Dimensional ◽  
Moisture Movement ◽  
Finite Difference Technique ◽  
Long Term Storage ◽  
Space Formulation ◽  
Term Storage

A model of moisture movement in wood is presented in this paper in a two-dimensional-in-space formulation. The finite-difference technique has been used in order to obtain the solution of the problem. The model was applied to predict the moisture content in sawn boards from pine during long term storage under outdoor climatic conditions. The satisfactory agreement between the numerical solution and experimental data was obtained.

scholarly journals Hierarchical modeling of mechano-chemical dynamics of epithelial sheets across cells and tissue

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Yoshifumi Asakura ◽  
Yohei Kondo ◽  
Kazuhiro Aoki ◽  
Honda Naoki
Keyword(s):  
Wound Healing ◽  
Cell Migration ◽  
Continuum Model ◽  
Tissue Level ◽  
Chemical Signals ◽  
Cellular Level ◽  
Mathematical Framework ◽  
Collective Cell Migration ◽  
The Continuum ◽  
Cell Cell

AbstractCollective cell migration is a fundamental process in embryonic development and tissue homeostasis. This is a macroscopic population-level phenomenon that emerges across hierarchy from microscopic cell-cell interactions; however, the underlying mechanism remains unclear. Here, we addressed this issue by focusing on epithelial collective cell migration, driven by the mechanical force regulated by chemical signals of traveling ERK activation waves, observed in wound healing. We propose a hierarchical mathematical framework for understanding how cells are orchestrated through mechanochemical cell-cell interaction. In this framework, we mathematically transformed a particle-based model at the cellular level into a continuum model at the tissue level. The continuum model described relationships between cell migration and mechanochemical variables, namely, ERK activity gradients, cell density, and velocity field, which could be compared with live-cell imaging data. Through numerical simulations, the continuum model recapitulated the ERK wave-induced collective cell migration in wound healing. We also numerically confirmed a consistency between these two models. Thus, our hierarchical approach offers a new theoretical platform to reveal a causality between macroscopic tissue-level and microscopic cellular-level phenomena. Furthermore, our model is also capable of deriving a theoretical insight on both of mechanical and chemical signals, in the causality of tissue and cellular dynamics.

Thermal Modeling of Unlooped and Looped Pulsating Heat Pipes

2001 ◽  
Vol 123 (6) ◽  
pp. 1159-1172 ◽  
Author(s):  
Mohammad B. Shafii ◽  
Amir Faghri ◽  
Yuwen Zhang
Keyword(s):  
Heat Transfer ◽  
Finite Difference ◽  
Heat Pipes ◽  
Analytical Models ◽  
Charge Ratio ◽  
Sensible Heat ◽  
Governing Equations ◽  
Heating Wall ◽  
Heat Mode ◽  
Explicit Finite Difference

Analytical models for both unlooped and looped Pulsating Heat Pipes (PHPs) with multiple liquid slugs and vapor plugs are presented in this study. The governing equations are solved using an explicit finite difference scheme to predict the behavior of vapor plugs and liquid slugs. The results show that the effect of gravity on the performance of top heat mode unlooped PHP is insignificant. The effects of diameter, charge ratio, and heating wall temperature on the performance of looped and unlooped PHPs are also investigated. The results also show that heat transfer in both looped and unlooped PHPs is due mainly to the exchange of sensible heat.

scholarly journals Formulation of 2D Graphene Deformation Based on Chiral-Tube Base Vectors

2010 ◽  
Vol 2010 ◽  
pp. 1-7
Author(s):  
Bohua Sun
Keyword(s):  
Molecular Dynamics ◽  
Shell Model ◽  
Continuum Model ◽  
Real Space ◽  
Honeycomb Lattice ◽  
Mechanical Behaviors ◽  
Future Studies ◽  
Physical Components ◽  
Intrinsic Feature ◽  
The Continuum

The intrinsic feature of graphene honeycomb lattice is defined by its chiral index (n,m), which can be taken into account when using molecular dynamics. However, how to introduce the index into the continuum model of graphene is still an open problem. The present manuscript adopts the continuum shell model with single director to describe the mechanical behaviors of graphene. In order to consider the intrinsic features of the graphene honeycomb lattice—chiral index (n,m), the chiral-tube vectors of graphene in real space have been used for construction of reference unit base vectors of the shell model; therefore, the formulations will contain the chiral index automatically, or in an explicit form in physical components. The results are quite useful for future studies of graphene mechanics.

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