One-Dimensional Softening With Localization

1986 ◽  
Vol 53 (4) ◽  
pp. 791-797 ◽  
Author(s):  
Howard L. Schreyer ◽  
Z. Chen
Keyword(s):  
Numerical Modeling ◽  
Constitutive Equation ◽  
Strain Gradient ◽  
Model Problem ◽  
One Dimension ◽  
One Dimensional ◽  
Limit Stress ◽  
The Relationship

The relationship between material softening and structural softening is investigated through the use of a model problem in one dimension. If the size of the softening zone is large the structural softening response is stable under displacement-prescribed loading. For a small size, the softening response is unstable and the loading regime is sensitive to imperfections in stiffness. A nonlocal constitutive equation in which the limit stress is a function of strain and strain gradient is introduced to provide an approach for simulating softening with localization. Implications for the numerical modeling of softening phenomena are given.

scholarly journals The meaning of an infinitely great velocity         

2021 ◽  
Author(s):  
Qing Li
Keyword(s):  
Constant Velocity ◽  
Dimensional Space ◽  
Two Dimensions ◽  
One Dimension ◽  
One Dimensional ◽  
Single Dimension ◽  
Principle Of Relativity ◽  
Definition Of ◽  
The Relationship ◽  
Inertial Systems

Abstract  An instantaneous velocity where a moment of the clock only corresponds to an arbitrary distance or position in space cannot be implied in Axiom 1, but it indicates that there is only one dimensional existence, space or time, where a certain moment only corresponds to itself specifically, not to any other time or any given length of space. Further , a definition of velocity that consists of two dimensions representing the relationship between space and time is not valid and there is only one-dimensional space or time that is independent of each other in Axiom 1. As a result, the principle of relativity and the principle of the constant velocity of light are replaced by the principle of an inertial system and the principle of universal invariant velocity in Axiom 1. Unlike two dimensions whose magnitude is determined by the ratio, the magnitude of a single dimension is determined by the unit values of one dimension, which indicates that an infinitely great velocity is meaningless. Further, if the two inertial systems are infinite versus finite in Axiom 3, then this extension of the infinitely great velocity can be defined as inextensible.

An Analytical Study on the Post-Peak Structural Response

2011 ◽  
Vol 78 (4) ◽  
Author(s):  
Hui-Hui Dai ◽  
Xiaowu Zhu ◽  
Zhen Chen
Keyword(s):  
Analytical Study ◽  
Model Problem ◽  
Constitutive Relations ◽  
Sufficient Conditions ◽  
Structural Response ◽  
Previous Literature ◽  
One Dimension ◽  
Necessary And Sufficient ◽  
The Relationship ◽  
Nonlinear Constitutive Relations

An analytical study is taken to investigate the relationship between material softening and structural softening through the use of a model problem in one dimension. General nonlinear constitutive relations are used. Compared with the bilinear assumptions in previous literature, we find that the nonlinear assumptions herein capture more details in the post-peak structural response. We manage to derive necessary and sufficient conditions for the occurrence of four important post-peak cases, which are often observed in experiments. In particular, our analysis reveals that the mechanism of the snap-through phenomenon is due to the convexity change in the constitutive curve of the softening part.

‘Each Song Was Just Like a Little Sermon’

2018 ◽  
Author(s):  
Isaac Land
Keyword(s):  
Nineteenth Century ◽  
Golden Age ◽  
Military Training ◽  
One Dimensional ◽  
National Pride ◽  
Recent Scholarship ◽  
The Relationship

This chapter is central to the volume’s chronological contentions, as its argument accounts for the specialized, one-dimensional Dibdin of ‘Tom Bowling’ that has endured into recent scholarship. Focusing on Dibdin’s posthumous reception, it examines the moral and rhetorical difficulties of repackaging Dibdin’s works for a Victorian sensibility; it explores the specifics of mid-century concert culture previously highlighted by Derek Scott and William Weber as central to changes in nineteenth-century taste and programming; and it develops the theme of nostalgia into a revelatory consideration of the relationship between new naval technologies, national pride, and military training, and the songs, people, and language of a remembered Napoleonic ‘golden age’—to which Dibdin proves to have been as central, in the Victorian imagination, as Nelson.

Effect of mechanical restraint on the rate of corrosion in concrete

1998 ◽  
Vol 25 (1) ◽  
pp. 81-86 ◽  
Author(s):  
N Hearn ◽  
J Aiello
Keyword(s):  
Mix Design ◽  
Concrete Repair ◽  
Accelerated Corrosion ◽  
One Dimensional ◽  
Mechanical Restraint ◽  
Corrosion Rates ◽  
Accelerated Corrosion Tests ◽  
The Matrix ◽  
The Relationship

Experimental work on prismatic concrete specimens was conducted to determine the relationship between mechanical restraint and the rate of corrosion. The current together with the changes in strain of the confining frame were monitored during the accelerated corrosion tests. The effect of mix design and cracking on the corrosion rates was also investigated. The results show that one-dimensional mechanical restraint retards the corrosion process, as indicated by the reduction in the steel loss. Improved quality of the matrix, with and without cracking, reduces the rate of steel loss. In the inferior quality concrete, the effect of cracking on the corrosion rate is minimal.Key words: corrosion, concrete, repair.

scholarly journals Assessing a Linear Nanosystem's Limiting Reliability from its Components

2008 ◽  
Vol 45 (03) ◽  
pp. 879-887 ◽  
Author(s):  
Nader Ebrahimi
Keyword(s):  
Present State ◽  
Size Range ◽  
Two Dimensions ◽  
The Other ◽  
One Dimension ◽  
Present Moment ◽  
One Dimensional ◽  
The One ◽  
Fixed Moment ◽  
Nanosized Systems

Nanosystems are devices that are in the size range of a billionth of a meter (1 x 10-9) and therefore are built necessarily from individual atoms. The one-dimensional nanosystems or linear nanosystems cover all the nanosized systems which possess one dimension that exceeds the other two dimensions, i.e. extension over one dimension is predominant over the other two dimensions. Here only two of the dimensions have to be on the nanoscale (less than 100 nanometers). In this paper we consider the structural relationship between a linear nanosystem and its atoms acting as components of the nanosystem. Using such information, we then assess the nanosystem's limiting reliability which is, of course, probabilistic in nature. We consider the linear nanosystem at a fixed moment of time, say the present moment, and we assume that the present state of the linear nanosystem depends only on the present states of its atoms.

scholarly journals AN ANALYTIC SOLUTION FOR ONE-DIMENSIONAL DISSIPATIONAL STRAIN-GRADIENT PLASTICITY

2009 ◽  
Vol 50 (3) ◽  
pp. 407-420
Author(s):  
ROGER YOUNG
Keyword(s):  
Boundary Condition ◽  
Strain Gradient ◽  
Analytic Solution ◽  
Strain Gradient Plasticity ◽  
Numerical Results ◽  
Gradient Plasticity ◽  
One Dimensional ◽  
Numerical Result ◽  
Formulation Analysis ◽  
The One

AbstractAn analytic solution is developed for the one-dimensional dissipational slip gradient equation first described by Gurtin [“On the plasticity of single crystals: free energy, microforces, plastic strain-gradients”, J. Mech. Phys. Solids48 (2000) 989–1036] and then investigated numerically by Anand et al. [“A one-dimensional theory of strain-gradient plasticity: formulation, analysis, numerical results”, J. Mech. Phys. Solids53 (2005) 1798–1826]. However we find that the analytic solution is incompatible with the zero-sliprate boundary condition (“clamped boundary condition”) postulated by these authors, and is in fact excluded by the theory. As a consequence the analytic solution agrees with the numerical results except near the boundary. The equation also admits a series of higher mode solutions where the numerical result corresponds to (a particular case of) the fundamental mode. Anand et al. also established that the one-dimensional dissipational gradients strengthen the material, but this proposition only holds if zero-sliprate boundary conditions can be imposed, which we have shown cannot be done. Hence the possibility remains open that dissipational gradient weakening may also occur.

DISCRETE COMPACTNESS FOR p AND hp 2D EDGE FINITE ELEMENTS

2003 ◽  
Vol 13 (11) ◽  
pp. 1673-1687 ◽  
Author(s):  
DANIELE BOFFI ◽  
LESZEK DEMKOWICZ ◽  
MARTIN COSTABEL
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Model Problem ◽  
Finite Element Approximation ◽  
Stability Estimate ◽  
Element Approximation ◽  
Dimensional Model ◽  
Compactness Property ◽  
One Dimensional ◽  
Discrete Compactness

In this paper we discuss the hp edge finite element approximation of the Maxwell cavity eigenproblem. We address the main arguments for the proof of the discrete compactness property. The proof is based on a conjectured L2 stability estimate for the involved polynomial spaces which has been verified numerically for p≤15 and illustrated with the corresponding one dimensional model problem.

Investigation of the One-Dimensional Endochronic Constitutive Equation for Metals by the Rivlin Test

1984 ◽  
Vol 106 (3) ◽  
pp. 264-270 ◽  
Author(s):  
Han C. Wu ◽  
C. C. Yang
Keyword(s):  
Constitutive Equation ◽  
Strain Path ◽  
Small Strain ◽  
One Dimensional ◽  
Good For ◽  
The One ◽  
Cyclic Straining ◽  
Strain Cycling ◽  
Theory And Experiment

Two sets of experiments with and without strain cycling have been carried out to test the validity of an equation derived from the improved theory of endochronic plasticity. It has been found that for strain path not involving cyclic straining the agreement between theory and experiment is quite good. In the test with strain cycling, the agreement is not good for small strain amplitudes of cycling but the discrepancy diminishes with the increasing amplitude of the strain cycling.

Theoretical Modeling of Thermoelectricity in Bi Nanowires

1998 ◽  
Vol 545 ◽  
Author(s):  
X. Sun ◽  
Z. Zhang ◽  
G. Dresselhaus ◽  
M. S. Dresselhaus ◽  
J. Y. Ying ◽  
...  
Keyword(s):  
Numerical Modeling ◽  
Theoretical Model ◽  
Quantum Confinement ◽  
Figure Of Merit ◽  
Wire Diameter ◽  
Thermoelectric Figure Of Merit ◽  
Thermoelectric Figure ◽  
Crystalline Orientation ◽  
One Dimensional ◽  
Bismuth Nanowires

AbstractBismuth as a semimetal is not a good thermoelectric material in bulk form because of the approximate cancellation between the electron and hole contributions. However, quantum confinement can be introduced by making Bi nanowires to move the lowest conduction subband edge up and the highest valence subband edge down to get a one-dimensional (1D) semiconductor at some critical wire diameter dc. A theoretical model based on the basic band structure of bulk Bi is developed to predict the dependence of these quantities on wire diameter and on the crystalline orientation of the bismuth nanowires. Numerical modeling is performed for trigonal, binary and bisectrix crystal orientations. By carefully tailoring the Bi wire diameter and carrier concentration, substantial enhancement in the thermoelectric figure of merit is expected for small nanowire diameters.

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