Numerical calculation of storage and loss modulus from stress relaxation data for linear viscoelastic materials

1971 ◽  
Vol 10 (2) ◽  
pp. 165-173 ◽  
Author(s):  
F. R. Schwarzl
Keyword(s):  
Numerical Calculation ◽  
Stress Relaxation ◽  
Loss Modulus ◽  
Viscoelastic Materials ◽  
Relaxation Data ◽  
Linear Viscoelastic

Prediction of Creep Behavior from Stress Relaxation Data for Nonlinearly Viscoelastic Materials

1978 ◽  
Vol 51 (1) ◽  
pp. 117-125 ◽  
Author(s):  
L. M. Wu ◽  
E. A. Meinecke ◽  
B. C. Tsai
Keyword(s):  
Stress Relaxation ◽  
Creep Behavior ◽  
Strain Curve ◽  
Relaxation Modulus ◽  
Polymeric Materials ◽  
Viscoelastic Materials ◽  
Relaxation Data ◽  
Stress Strain ◽  
Straight Line ◽  
Simple Fashion

Abstract The stress relaxation behavior of many polymeric materials can be expressed in a very simple fashion, because the logarithm of nominal stress fi(t) (based upon the undeformed cross-sectional area of the sample) plotted against the logarithm of time, t, is a straight line. Furthermore, these lines are often parallel, and with linearly viscoelastic materials, one obtains a straight line for the stress-relaxation modulus E(t)=fi(t)/εi, independent of the strain level. Thus, the linear stress-relaxation modulus can be expressed as: Ei(t)=Ei0·t−m, with Ei0 the modulus at t=1 s and m the slope of the straight line in the double logarithmic plot. Most polymers are, of course, nonlinearly viscoelastic (except for infinitesimal deformations); that is, the stress-relaxation modulus is a function of both time and strain. These time and strain effects can be factored out, if the log fi(t) versus log t curves are parallel: Ei(t,εi)=Ei0·t−mϕ(ε), where ϕ(ε), the strain function, is a measure of the nonlinearity of the viscoelastic response. It has been shown elsewhere that Ei0/ϕ(ε) is approximately identical to the modulus observed in the stress-strain measurement. With many polymers, creep experiments also yield approximately straight lines of slope n, when the logarithm of strain εi(t) is plotted against the logarithm of time. With nonlinearly viscoelastic materials, one generally does not obtain a set of parallel lines, when the stress fi, is changed. Therefore, it is not possible to separate the influence of time and stress on the creep compliance Di(t)=εi(t)/fi, as was the case for stress relaxation. It has been shown previously that the creep behavior can be predicted from stress-relaxation data with the help of the convolution integral. The numerical method involved is very laborious, however. It has been shown that the rate of creep may be predicted from the slope of stress-relaxation curves and the shape of the stress-strain curve. The purpose of this paper is to present a method by which the creep behavior of nonlinearly viscoelastic materials can be predicted in a simple fashion from stress-relaxation data. The theoretical predictions have been tested with the stress-relaxation and creep data of a block copolymer.

The Bending and Recovery of Fabrics under Conditions of Changing Temperature and Relative Humidity

1976 ◽  
Vol 46 (2) ◽  
pp. 113-122 ◽  
Author(s):  
B. M. Chapman
Keyword(s):  
Stress Relaxation ◽  
Relative Humidity ◽  
Relaxation Behavior ◽  
Bending Stress ◽  
Relaxation Data ◽  
Viscoelastic Parameter ◽  
Stress Relaxation Behavior ◽  
Recovery Behavior ◽  
Linear Viscoelastic ◽  
Viscoelastic Element

The bending stress relaxation and recovery behavior of fabrics under conditions of changing temperature and humidity has been investigated. The fabric recovery is successfully predicted, from its stress relaxation behavior and a frictional parameter, using a previously presented model consisting of a generalized linear viscoelastic element in parallel with a frictional element. Furthermore, a viscoelastic parameter, simply obtainable from the relaxation data, together with the frictional parameter, have been shown to correlate well with observed recovery and may be useful as convenient indicators of fabric wrinkle performance.

scholarly journals A discrete spectral analysis for determining quasi-linear viscoelastic properties of biological materials

2015 ◽  
Vol 12 (113) ◽  
pp. 20150707 ◽  
Author(s):  
Behzad Babaei ◽  
Steven D. Abramowitch ◽  
Elliot L. Elson ◽  
Stavros Thomopoulos ◽  
Guy M. Genin
Keyword(s):  
Stress Relaxation ◽  
Relaxation Spectrum ◽  
Model Identification ◽  
Biological Materials ◽  
Relaxation Data ◽  
Collateral Ligament ◽  
Time Constants ◽  
Discrete Approach ◽  
Standard Tool ◽  
Linear Viscoelastic

The viscoelastic behaviour of a biological material is central to its functioning and is an indicator of its health. The Fung quasi-linear viscoelastic (QLV) model, a standard tool for characterizing biological materials, provides excellent fits to most stress–relaxation data by imposing a simple form upon a material's temporal relaxation spectrum. However, model identification is challenging because the Fung QLV model's ‘box’-shaped relaxation spectrum, predominant in biomechanics applications, can provide an excellent fit even when it is not a reasonable representation of a material's relaxation spectrum. Here, we present a robust and simple discrete approach for identifying a material's temporal relaxation spectrum from stress–relaxation data in an unbiased way. Our ‘discrete QLV’ (DQLV) approach identifies ranges of time constants over which the Fung QLV model's typical box spectrum provides an accurate representation of a particular material's temporal relaxation spectrum, and is effective at providing a fit to this model. The DQLV spectrum also reveals when other forms or discrete time constants are more suitable than a box spectrum. After validating the approach against idealized and noisy data, we applied the methods to analyse medial collateral ligament stress–relaxation data and identify the strengths and weaknesses of an optimal Fung QLV fit.

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