The Thickness of Steady Plane Shear Flows of Circular Disks Driven by Identical Boundaries

1988 ◽  
Vol 55 (4) ◽  
pp. 969-974 ◽  
Author(s):  
D. M. Hanes ◽  
J. T. Jenkins ◽  
M. W. Richman
Keyword(s):  
Relative Motion ◽  
Constitutive Relations ◽  
Balance Laws ◽  
Plane Shear ◽  
Normal Traction ◽  
Steady Solutions ◽  
Steady Shearing ◽  
Steady Plane ◽  
Steady Motions ◽  
Circular Disks

We employ balance laws and constitutive relations for rapid, dense, plane flows of identical circular disks together with boundary conditions at a bumpy wall to analyse steady shearing flows maintained by the relative motion of two identical, parallel walls. The disks and the walls are assumed to be frictionless and nearly elastic. Given the properties of the flowing disks, those of the boundary, and the ratio of the tangential and normal tractions applied to the boundary, we determine what the distance between the walls must be for a steady solution to be possible. For these steady solutions we relate the velocity of the walls to the normal and tangential tractions applied to them. We find that in certain circumstances steady motions may be maintained even when the ratio of tangential to normal traction is much less than its value in a homogeneous simple shear. In the Appendix, the corresponding results for spheres are outlined.

Balance Laws and Constitutive Relations for Plane Flows of a Dense, Binary Mixture of Smooth, Nearly Elastic, Circular Disks

1987 ◽  
Vol 54 (1) ◽  
pp. 27-34 ◽  
Author(s):  
J. T. Jenkins ◽  
F. Mancini
Keyword(s):  
Distribution Function ◽  
Binary Mixture ◽  
Pair Distribution Function ◽  
Constitutive Relations ◽  
Balance Laws ◽  
Focus Attention ◽  
Circular Disks

We derive balance laws and constitutive relations for plane flows of a dense, binary mixture of smooth, nearly elastic, circular disks. The disks may differ in size and mass and in the coefficients of restitution characterizing the energy lost in collisions between like and unlike pairs. We focus attention on those parts of the fluxes and sources of momentum and energy that are due to collisions. To calculate them, we suppose that the complete pair distribution function for two colliding disks is the product of Maxwellian velocity distributions for each disk and a factor that incorporates the effects of excluded area and collisional shielding. In an Appendix we provide constitutive relations calculated in a similar way for a dense, binary mixture of smooth, nearly elastic, spheres.

Response of Honeycombs Subjected to In-Plane Shear

2016 ◽  
Vol 83 (6) ◽  
Author(s):  
Youming Chen ◽  
Raj Das ◽  
Mark Battley
Keyword(s):  
Shear Stress ◽  
Shear Strength ◽  
Young’S Modulus ◽  
Cell Walls ◽  
Young's Modulus ◽  
Constitutive Relations ◽  
Length Ratio ◽  
Plane Shear ◽  
Base Materials ◽  
Vertical Cell

Study on the response of honeycombs subjected to in-plane shear helps establish the constitutive relations for honeycombs and shed light on the mechanics of cellular materials. The present study explores the nonlinear elastic response of honeycombs under in-plane shear by analyzing the large deflection of cell walls in a unit cell. Governing equations are established which relate the macroscopic response of honeycombs to the deflection of cell walls. Solving these equations, the behavior of regular honeycombs under in-plane shear along horizontal (X) and vertical (Y) directions was investigated. It is found that the response of regular honeycombs under in-plane shear depends on the nondimensional shear stress which is a parameter combining the thickness-to-length ratio of cell walls, the Young's modulus of base materials, and macroscopic shear stress. Lateral shrinking is a distinctive characteristic for honeycombs under in-plane shear, which should be taken into account when establishing constitutive relations and performing simple shear experiments. Expressions for predicting the shear strength of honeycombs are formulated in this paper. It is noted that the normalized shear strength of regular honeycombs depends on two ratios: the thickness-to-length ratio of cell walls and the ratio of Young's modulus to yield strength of base materials, and the former has a dominant effect. By comparing honeycombs with cell walls of uniform thickness against honeycombs with vertical cell walls of double thickness, it is found that doubling the thickness of vertical cell walls of honeycombs increases their shear strength along horizontal (X) direction nearly twice, but does not improve the shear strength that much along the vertical (Y) direction.

Nonlinear Elastic Constitutive Relations of Auxetic Honeycombs

2009 ◽  
Author(s):  
Jaehyung Ju ◽  
Joshua D. Summers ◽  
John Ziegert ◽  
Georges Fadel
Keyword(s):  
Cell Walls ◽  
Strain Energy ◽  
Constitutive Relations ◽  
Effective Strain ◽  
Strain Energy Function ◽  
Periodic Boundary Conditions ◽  
Plane Shear ◽  
Local Cell ◽  
Nonlinear Elastic ◽  
Nonlinear Constitutive Relation

When designing a flexible structure consisting of cellular materials, it is important to find the maximum effective strain of the cellular material resulting from the deformed cellular geometry and not leading to local cell wall failure. In this paper, a finite in-plane shear deformation of auxtic honeycombs having effective negative Poisson’s ratio is investigated over the base material’s elastic range. An analytical model of the inplane plastic failure of the cell walls is refined with finite element (FE) micromechanical analysis using periodic boundary conditions. A nonlinear constitutive relation of honeycombs is obtained from the FE micromechanics simulation and is used to define the coefficients of a hyperelastic strain energy function. Auxetic honeycombs show high shear flexibility without a severe geometric nonlinearity when compared to their regular counterparts.

Cyclic Energy Loss of Honeycombs Under In-Plane Shear Loading

2009 ◽  
Author(s):  
Jaehyung Ju ◽  
Joshua D. Summers ◽  
John Ziegert ◽  
George Fadel
Keyword(s):  
Energy Loss ◽  
Structural Design ◽  
Energy Efficient ◽  
Fe Simulation ◽  
Numerical Study ◽  
Constitutive Relations ◽  
Shear Loading ◽  
Prony Series ◽  
Plane Shear ◽  
Hysteretic Energy

In an effort to develop an elastomer-like material with low hysteretic energy loss associated with an energy efficient structural design, a cyclic energy loss model of honeycombs is investigated. In-plane viscoelastic constitutive relations of a honeycomb are developed based on honeycomb geometries and a base material’s viscoelastic properties. Using Prony series parameters for the stress-relaxation of a material, a numerical study on hysteretic energy dissipation is conducted for regular and auxetic honeycombs. Finite element (FE) simulation is carried out to validate the numerical study. Preferred cell geometries of honeycombs are also discussed in terms of minimizing the hysteretic energy loss.

Non-Steady, Plane, One-Dimensional and Isothermal Flows

1994 ◽  
Vol 144 ◽  
pp. 467-471
Author(s):  
O. T. Matsuura
Keyword(s):  
Observational Data ◽  
Isothermal Flow ◽  
Self Similarity ◽  
One Dimensional ◽  
First Approximation ◽  
Isothermal Flows ◽  
Steady Solutions ◽  
Steady Plane ◽  
Transient Plasma

AbstractUsing the Sedov’s (1959) method of self-similarity, non-steady solutions were obtained for a plane, one-dimensional and isothermal flow in presence of gravity. Although simple, such a flow seems to be suitable for describing, in a first approximation, the transient plasma ejections along thecoronal rays. The topology of the solutions shows that the ejections through such structures can be classified in two distinct types. The observable properties for each type are discussed in an attempt to establish a preliminary framework for the strategy of future observations, as well as for the analysis of the existing observational data.

scholarly journals Flows of cohesive granular media

2021 ◽  
Vol 249 ◽  
pp. 01001
Author(s):  
Sandip Mandal ◽  
Adrien Gans ◽  
Maxime Nicolas ◽  
Olivier Pouliquen
Keyword(s):  
Granular Media ◽  
Flow Behavior ◽  
Constitutive Relations ◽  
Shear Banding ◽  
Plane Shear ◽  
Simple Method ◽  
Plastic Properties ◽  
Shear Cell ◽  
Numerical Studies ◽  
Long Time

Cohesive granular media have broad applications in industries. However, our understanding of their flow behavior is still limited compared to dry granular media, although rich knowledge about their static and plastic properties has been gained. In this paper, we provide some insights into the flow behavior of cohesive granular media from our recent numerical studies using an inclined plane and a plane shear cell. We evidence that the cohesive nature of flows is significantly affected by material properties of the particles like stiffness and inelasticity in addition to the inter-particle adhesion and introduce the concept of “effective” adhesion, which incorporates the effects of these three variables. We propose constitutive relations involving dimensionless inertial number and “effective” cohesion number, based on the “effective” adhesion to describe the rheology. We also show that increasing adhesion increases the hysteresis in granular media, evidencing the existence of a prominent shear weakening branch in the friction coefficient versus inertial number rheological curve. Moreover, we reveal that this increasing hysteresis gives rise to the increasing occurrence of shear banding instability, pointing to the increasing possibility of jamming in cohesive granular media. Finally, we present a promising experimental approach to investigate the flow behavior of cohesive granular materials, based on a simple method of preparing a long time stable medium with a controlled adhesion between particles.

Linear piezoelectricity

2020 ◽  
pp. 327-354
Author(s):  
Lallit Anand ◽  
Sanjay Govindjee
Keyword(s):  
Energy Balance ◽  
Energy Transport ◽  
Constitutive Relations ◽  
Electric Displacement ◽  
Balance Laws ◽  
Third Order ◽  
Static Limit ◽  
Electrical Boundary Conditions ◽  
Linear Piezoelectricity ◽  
Electromechanical Energy

This chapter presents the elements of linear piezoelectricity including mechanical and electrostatic balance laws and coupled mechanical electrical constitutive relations. The thermodynamically consistent constitutive relations are determined from a coupled electromechanical energy balance argument and expressions are given alternately considering the electric field and the electric displacement as independent fields. Appropriate electrical boundary conditions are also discussed. The theory is also specialized to poled piezoceramics. A chapter appendix provides a brief discussion of Maxwell’s equations for electromagnetics and energy transport in the quasi-static limit. A second chapter appendix discusses the properties of third order tensors.

The restoration of blurred electron micrographs

1986 ◽  
Vol 44 ◽  
pp. 180-181
Author(s):  
Bridget Carragher ◽  
David A. Bluemke ◽  
Michael J. Potel ◽  
Robert Josephs
Keyword(s):  
Cross Section ◽  
Electron Micrographs ◽  
Relative Motion ◽  
Finite Thickness ◽  
Image Plane ◽  
Helical Axis ◽  
Thin Sections ◽  
Structural Details

We have investigated the feasibility of restoring blurred electron micrographs. Two related problems have been considered; the restoration of images blurred as a result of relative motion between the specimen and the image plane, and the restoration of images which are rotationally blurred about an axis. Micrographs taken while the specimen is drifting result in images which are blurred in the direction of motion. An example of rotational blurring arises in micrographs of thin sections of helical particles viewed in cross section. The twist of the particle within the finite thickness of the section causes the image to appear rotationally blurred about the helical axis. As a result, structural details, particularly at large distances from the helical axis, will be obscured.

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