scholarly journals Closure to “Discussion of ‘A Mathematical Model Depicting the Stress-Strain Diagram and the Hysteresis Loop’” (1959, ASME J. Appl. Mech., 26, pp. 692–693)

1959 ◽  
Vol 26 (4) ◽  
pp. 693
Author(s):  
I. R. Whiteman
Keyword(s):  
Mathematical Model ◽  
Hysteresis Loop ◽  
Strain Diagram ◽  
Stress Strain

A Mathematical Model Depicting the Stress-Strain Diagram and the Hysteresis Loop

1959 ◽  
Vol 26 (1) ◽  
pp. 95-100
Author(s):  
I. R. Whiteman
Keyword(s):  
Mathematical Model ◽  
Hysteresis Loop ◽  
Yield Stress ◽  
Frequency Distribution ◽  
Elastic Region ◽  
Tangent Modulus ◽  
Strain Diagram ◽  
Cumulative Frequency ◽  
Cumulative Frequency Distribution ◽  
Stress Strain

Abstract A model is made up of elastoplastic elements, all of which have the same value of Young’s modulus E, but which have different values of yield stress. It is shown that the dimensionless tangent modulus graph Et/E represents the cumulative frequency distribution of those elements which are in the elastic region. From the frequency distribution, the equations for the stress-strain diagram and the hysteresis loop can be written.

A New Look at Measurements of Network Density

1986 ◽  
Vol 59 (1) ◽  
pp. 138-141 ◽  
Author(s):  
Robert A. Hayes
Keyword(s):  
Hysteresis Loop ◽  
Interaction Parameters ◽  
Network Density ◽  
Stress Strain ◽  
Solvent Interaction ◽  
Solvent Method ◽  
Strain Data ◽  
Good Agreement ◽  
Polymer Solvent ◽  
New Look

Abstract A two-solvent method for determining the polymer-solvent interaction parameters independently of stress-strain data is described. The values obtained are much lower than those reported previously. Network densities calculated from swelling data and these interaction parameters are in good agreement with those calculated from the return portion of a hysteresis loop at high elongations.

scholarly journals Hysteresis in Muscle

2017 ◽  
Vol 27 (01) ◽  
pp. 1730003 ◽  
Author(s):  
Jorgelina Ramos ◽  
Stephen Lynch ◽  
David Jones ◽  
Hans Degens
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Hysteresis Loop ◽  
Mechanical Systems ◽  
Single Fibre ◽  
Scientific Disciplines ◽  
Main Components ◽  
First Time ◽  
Muscle Models ◽  
Clockwise Hysteresis

This paper presents examples of hysteresis from a broad range of scientific disciplines and demonstrates a variety of forms including clockwise, counterclockwise, butterfly, pinched and kiss-and-go, respectively. These examples include mechanical systems made up of springs and dampers which have been the main components of muscle models for nearly one hundred years. For the first time, as far as the authors are aware, hysteresis is demonstrated in single fibre muscle when subjected to both lengthening and shortening periodic contractions. The hysteresis observed in the experiments is of two forms. Without any relaxation at the end of lengthening or shortening, the hysteresis loop is a convex clockwise loop, whereas a concave clockwise hysteresis loop (labeled as kiss-and-go) is formed when the muscle is relaxed at the end of lengthening and shortening. This paper also presents a mathematical model which reproduces the hysteresis curves in the same form as the experimental data.

scholarly journals Mathematical Models and Evaluation Software for Stress-Strain State of the Earth’s Lithosphere

2019 ◽  
pp. 51-66
Author(s):  
Alexander O. Faddeev ◽  
Svetlana A. Pavlova ◽  
Tatiana M. Nevdakh
Keyword(s):  
Mathematical Model ◽  
Strain State ◽  
Uniform Grid ◽  
Shear Stresses ◽  
Stress Strain ◽  
Gravitation Field ◽  
Vertical Movements ◽  
Stress Strain State ◽  
The Earth ◽  
Viscous Shear

Introduction. For the purposes of this article, geodeformation processes mean processes associated with deformations arising from the movement of species and blocks of the lithosphere at various depths, including surfaces. The objective is to reconstruct geodynamic stress fields, which cause modern shifts and deformations in the Lithosphere. A mathematical model and software for estimating the stress-strain state of the Earth Lithosphere are considered. Materials and Methods.For mathematical modeling of stresses, isostatically reduced data on abnormal gravitation field were used. The methods of continuum mechanics and methods of the theory of differential equations were used to design a model for estimating the stressstrain state of the Earth Lithosphere. For processing input, intermediate and outcoming data, the Fourier transform method of spectral analysis for constructing grid functions and spectral-temporal method were used. To model for the stress-strain state of the Lithosphere globally, stress calculation was corrected on the basis of sputnik-derived velocity data at the surface of the earth crust. The data on the rates of horizontal and vertical movements at the surface of the Earth crust were processed to obtain a distribution of velocities in the uniform grid embracing longitudes and latitudes. The processing procedure was carried out on the basis of the Kraiging method. The software was developed in Borland Delphi 7.0 programming environment. Results. Based on the data on the abnormal gravitation field in isostatic reduction and information on the distribution of velocities of horizontal motions on the surface of the Earth crust, a mathematical model of the stress-strain state of the Lithosphere was constructed. With the help of the obtained mathematical model and software complex, the stress-strain state of the Lithosphere was calculated at various depth using elastic and elastic-viscous models, and maps of equipotential distribution of shear elastic-viscous deformations in the lithosphere at the depth of 10 km were constructed. Discussion and Conclusion. The presented mathematical model and software allow restoring fields of both elastic and elastic-viscous deformations that is fundamental for quantification of elastic-viscous shear stresses deep in the Earth Lithosphere.

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