scholarly journals Generalised viscoelastic fibre at small strain

2021 ◽  
Vol 127 (1) ◽  
Author(s):  
Kostas P. Soldatos
Keyword(s):  
Energy Dissipation ◽  
Small Strain ◽  
Elastic Fibre ◽  
Viscoelastic Deformation ◽  
One Dimensional ◽  
Fibre Strain ◽  
Combined Action ◽  
The One ◽  
Elastic Spring

AbstractA straight elastic fibre is usually perceived as a one-dimensional structural component, and its similarity with a cylindrical rod makes its concept analogous, if not equivalent with the concept of an elastic spring. This analogy enables this communication to match the one-dimensional response of a relevant viscoelastic fibre with that of a viscoelastic spring and, hence, to describe its one-dimensional behaviour in the light of a new, generalised viscoelastic spring model. The model shares simultaneously properties of an elastic spring and an inelastic damper (dashpot) and this communication is interested on its applicability at small strain only. However, the form of its constitutive equation, which is based on the combined action of an internal energy function and a viscous flow potential, is non-linear as well as differential and, also, implicit in the stress. The model enables a posteriori determination of (i) the manner that the elastic and the inelastic parts of the fibre strain are assembled and form the observed total deformation, (ii) the part of stress that creates recoverable work and the part of stress wasted in energy dissipation, and (iii) the amount of work stored in the material as well as the amount of energy dissipation during the fibre deformation. A detailed analysis is presented for the case that small-strain, steady viscoelastic deformation takes place in a spatially homogeneous manner. This includes a complete relevant solution of the problem of interest and is accompanied by an adequate set of corresponding qualitative numerical results.

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.

Numerical study of the one-dimensional Hubbard model in determination of trans-polyacetylene properties

2001 ◽  
Vol 296 (4) ◽  
pp. 377-387 ◽  
Author(s):  
S. Goumri-Said ◽  
R. Moussa ◽  
J.P. DuFour ◽  
L. Salomon ◽  
H. Aourag
Keyword(s):  
Hubbard Model ◽  
Numerical Study ◽  
One Dimensional ◽  
The One

Integration of one-dimensional equations of motions

2020 ◽  
pp. 79-90
Author(s):  
Gleb L. Kotkin ◽  
Valeriy G. Serbo
Keyword(s):  
Potential Energy ◽  
Field Change ◽  
One Dimensional ◽  
System A ◽  
Small Correction ◽  
The Law ◽  
The One ◽  
The Given ◽  
Equations Of Motions

If the potential energy is independent of time, the energy of the system remains constant during the motion of a closed system. A system with one degree of freedom allows for the determination of the law of motion in quadrature. In this chapter, the authors consider motion of the particles in the one-dimensional fields. They discuss also how the law and the period of a particle moving in the potential field change due to adding to the given field a small correction.

Structural determination of the group K capsular polysaccharide of Neisseriameningitidis: a 2D-NMR analysis

1985 ◽  
Vol 63 (10) ◽  
pp. 2781-2786 ◽  
Author(s):  
Francis Michon ◽  
Jean Robert Brisson ◽  
René Roy ◽  
Harold J. Jennings ◽  
Fraser E. Ashton
Keyword(s):  
Capsular Polysaccharide ◽  
2D Nmr ◽  
Ion Exchange Chromatography ◽  
Exchange Chromatography ◽  
Electronic Effects ◽  
Nmr Studies ◽  
Polysaccharide Antigen ◽  
One Dimensional ◽  
The One

The capsular polysaccharide antigen of Neisseriameningitidis group K was isolated by Cetavlon precipitation and purified by ion-exchange chromatography. The structure of the K polysaccharide was determined to a large extent by comprehensive proton and carbon-13 nuclear magnetic resonance (nmr) studies. In these studies one-dimensional and two-dimensional experiments were carried out directly on the K polysaccharide. The K polysaccharide is composed of the following repeating unit: -4)β-D-ManpNAcA(1→3) [4-OAc]β-D-ManpNAcA(1→. Except for the one-bond couplings between their anomeric carbons and protons [Formula: see text], all the nmr spectroscopic evidence was consistent with both 2-acetamido-2-deoxy-D-mannopyranosyluronic acid residues adopting the 4C1 (D) conformation and having the β-D-configuration. This ambiguity in [Formula: see text] is probably due to through-space electronic effects generated by the presence of contiguous carboxylated sugar residues in the K polysaccharide. The O-acetyl substituents of the K polysaccharide are essential for its antigenicity to group K polysaccharide-specific antibodies.

scholarly journals On a direct method for the determination of an exact invariant for the time-dependent harmonic oscillator

1977 ◽  
Vol 20 (1) ◽  
pp. 97-105 ◽  
Author(s):  
P. G. L. Leach
Keyword(s):  
Direct Method ◽  
Dynamical Symmetry ◽  
Time Dependent ◽  
Symmetry Groups ◽  
New Approach ◽  
One Dimensional ◽  
The One ◽  
A Direct Method ◽  
Exact Invariant

AbstractAn exact invariant is found for the one-dimensional oscillator with equation of motion . The method used is that of linear canonical transformations with time-dependent coeffcients. This is a new approach to the problem and has the advantage of simplicity. When f(t) and g(t) are zero, the invariant is related to the well-known Lewis invariant. The significance of extension to higher dimension of these results is indicated, in particular for the existence of non-invariance dynamical symmetry groups.

Determination of Optimum Profile of One-Dimensional Cooling Fins

1983 ◽  
Vol 105 (3) ◽  
pp. 317-320 ◽  
Author(s):  
S. K. Hati ◽  
S. S. Rao
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Boundary Conditions ◽  
Minimum Principle ◽  
Problem Formulation ◽  
One Dimensional ◽  
A New Technique ◽  
The One ◽  
Optimum Profile

The optimum design of an one-dimensional cooling fin is considered by including all modes of heat transfer in the problem formulation. The minimum principle of Pontryagin is applied to determine the optimum profile. A new technique is used to solve the reduced differential equations with split boundary conditions. The optimum profile found is compared with the one obtained by considering only conduction and convection.

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