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.

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.

An Experimental and Analytical Evaluation of the Nonlinear Viscoelastic Properties of the Healing Medial Collateral Ligament in a Goat Model

2003 ◽  
Author(s):  
S. D. Abramowitch ◽  
T. D. Clineff ◽  
R. E. Debski ◽  
S. L.-Y. Woo
Keyword(s):  
Stress Relaxation ◽  
Medial Collateral Ligament ◽  
Viscoelastic Properties ◽  
Soft Tissues ◽  
Viscoelastic Behavior ◽  
Collateral Ligament ◽  
Relaxation Experiment ◽  
Nonlinear Viscoelastic ◽  
Linear Viscoelastic Behavior ◽  
Linear Viscoelastic

The medial collateral ligament (MCL) is one of the most frequently injured ligaments in the knee. Although it can heal spontaneously after rupture, laboratory studies have shown that the mechanical properties of the healing MCL remain inferior to normal for up to two years after injury (1). Additionally, the healing MCL has been shown to display increased amounts of stress relaxation and creep (2). In order to more completely describe the viscoelastic properties of healing ligaments, we propose to use the Quasi-Linear Viscoelastic (QLV) theory formulated by Fung (1972). This theory has been used to successfully describe the viscoelastic properties of many soft-tissues (3). Recently, our research center has developed an improved approach to determine the constants describing the QLV theory based on data collected from a stress relaxation experiment that utilizes a slow strain rate during loading. This approach allows for experimental errors that commonly result from fast strain rates to be avoided (ex. overshoot) (4). Therefore, the objective of this study were to use this new approach to determine the constants describing the quasi-linear viscoelastic behavior of the healing goat MCL at 12 weeks after injury.

Methods for Quasi-Linear Viscoelastic Modeling of Soft Tissue: Application to Incremental Stress-Relaxation Experiments

2003 ◽  
Vol 125 (5) ◽  
pp. 754-758 ◽  
Author(s):  
Joseph J. Sarver ◽  
Paul S. Robinson ◽  
Dawn M. Elliott
Keyword(s):  
Soft Tissue ◽  
Stress Relaxation ◽  
Normalization Method ◽  
Time Constants ◽  
Future Studies ◽  
Linear Viscoelastic ◽  
Relaxation Experiments ◽  
Different Strains ◽  
Viscoelastic Modeling ◽  
Strain Dependent

The quasi-linear viscoelastic (QLV) model was applied to incremental stress-relaxation tests and an expression for the stress was derived for each step. This expression was used to compare two methods for normalizing stress data prior to estimating QLV parameters. The first and commonly used normalization method was shown to be strain-dependent. Thus, a second normalization method was proposed and shown to be strain-independent and more sensitive to QLV time constants. These analytical results agreed with representative tendon data. Therefore, this method for normalizing stress data was proposed for future studies of incremental stress-relaxation, or whenever comparing stress-relaxation at different strains.

STRESS RELAXATION OF MAGNETORHEOLOGICAL FLUIDS

2002 ◽  
Vol 16 (17n18) ◽  
pp. 2655-2661
Author(s):  
W. H. LI ◽  
G. CHEN ◽  
S. H. YEO ◽  
H. DU
Keyword(s):  
Stress Relaxation ◽  
Viscoelastic Model ◽  
Relaxation Modulus ◽  
Damping Function ◽  
Mr Fluids ◽  
Large Step ◽  
Linear Viscoelastic ◽  
Predicted Values ◽  
Two Parameters ◽  
Step Strain

In this paper, the experimental and modeling study and analysis of the stress relaxation characteristics of magnetorheological (MR) fluids under step shear are presented. The experiments are carried out using a rheometer with parallel-plate geometry. The applied strain varies from 0.01% to 100%, covering both the pre-yield and post-yield regimes. The effects of step strain, field strength, and temperature on the stress modulus are addressed. For small step strain ranges, the stress relaxation modulus G(t,γ) is independent of step strain, where MR fluids behave as linear viscoelastic solids. For large step strain ranges, the stress relaxation modulus decreases gradually with increasing step strain. Morever, the stress relaxation modulus G(t,γ) was found to obey time-strain factorability. That is, G(t,γ) can be represented as the product of a linear stress relaxation G(t) and a strain-dependent damping function h(γ). The linear stress relaxation modulus is represented as a three-parameter solid viscoelastic model, and the damping function h(γ) has a sigmoidal form with two parameters. The comparison between the experimental results and the model-predicted values indicates that this model can accurately describe the relaxation behavior of MR fluids under step strains.

Evaluation of the Viscoelastic Properties of the Intact Medial Collateral Ligament in a Goat Model

1999 ◽  
Author(s):  
Theodore D. Clineff ◽  
Richard E. Debski ◽  
Sven U. Scheffler ◽  
John D. Withrow ◽  
Savio L.-Y. Woo
Keyword(s):  
Medial Collateral Ligament ◽  
Viscoelastic Properties ◽  
Analytical Approach ◽  
Cruciate Ligament ◽  
Collateral Ligament ◽  
Future Studies ◽  
Linear Viscoelastic ◽  
Viscoelastic Theory ◽  
Anterior Cruciate ◽  
Linear Viscoelastic Theory

Abstract The time and history dependent viscoelastic properties have been determined for the normal medial collateral ligament (MCL) of canine (Woo, 1981), porcine anterior cruciate ligament (Kwan, 1993), and human patellar tendon in a cadaver model (Johnson, 1994). The objective of this study was to use a combined experimental and analytical approach to quantify the viscoelastic properties of the intact MCL in a goat model. A thorough understanding of the viscoelastic properties at low strain levels is necessary to future studies of the healing MCL. The quasi-linear viscoelastic theory (QLV) (Fung, 1972) was used to characterize the properties of the MCL during stress relaxation.

Bulk Moduli from Physical Aging and Stress Relaxation Data

1998 ◽  
pp. 447-448
Author(s):  
J. Vernel ◽  
M. J. Kubát ◽  
R. W. Rychwalski ◽  
J. Kubat
Keyword(s):  
Stress Relaxation ◽  
Physical Aging ◽  
Relaxation Data
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