Comparison of a Novel Nonlinear Viscoelastic Finite Ramp Time Correction Method to a Heaviside Step Assumption

2011 ◽  
Author(s):  
Kevin L. Troyer ◽  
Christian M. Puttlitz
Keyword(s):  
Stress Relaxation ◽  
Soft Tissues ◽  
Viscoelastic Behavior ◽  
Relaxation Modulus ◽  
Correction Method ◽  
Nonlinear Viscoelastic ◽  
Instantaneous Strain ◽  
Relaxation Experiments ◽  
Time Correction

Connective soft tissues exhibit time-dependent, or viscoelastic, behavior. In order to characterize this behavior, stress relaxation experiments can be performed to determine the tissue’s relaxation modulus. Theoretically, the relaxation modulus describes the stress relaxation behavior of the tissue in response to an instantaneous (step) application of strain. However, a step increase in strain is experimentally impossible and a pure ramp load is intractable due to the inertial limitations of the testing device. Even small deviations from an instantaneous strain application may cause significant errors in the determination of the tissue’s relaxation modulus.

Study on Nonlinear Viscoelastic Properties of Asphalt Mixture Based on Stress Relaxation Test

2014 ◽  
Vol 563 ◽  
pp. 48-52
Author(s):  
Lei Chen ◽  
Zhi Xin Yu ◽  
Wei Ping Cui ◽  
Li Juan Qin
Keyword(s):  
Stress Relaxation ◽  
Asphalt Mixture ◽  
Viscoelastic Behavior ◽  
Exponential Model ◽  
Relaxation Test ◽  
Asphalt Binders ◽  
Stress Relaxation Test ◽  
Nonlinear Viscoelastic ◽  
Low Temperature Cracking ◽  
Relaxation Experiments

Development of normal stress in the direction perpendicular to the asphalt mixture is an important feature of the nonlinear viscoelastic behavior of asphalt binders. In this paper, this phenomenon was studied with the help of stress-relaxation experiments in torsion.  Results indicate that stress relaxation test by controlling strain could be used to evaluate the stress relaxation ability of asphalt mixture. With the aging degree of asphalt mixtures increased, the low temperature cracking resistance got worse; the higher the temperature is, the faster the stress relaxed; the smaller the initial strain, the worse the stress relaxation ability also. The viscoelasticity of asphalt mixture could be simulated by exponential model fractional and the experiments well supported the modeling results.

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.

A Direct Experimental Determination of the Elastic Contribution of Chain Entangling in a Tightly Crosslinked Elastomer

1982 ◽  
Vol 55 (1) ◽  
pp. 62-65
Author(s):  
W. Batsberg ◽  
O. Kramer
Keyword(s):  
Stress Relaxation ◽  
Elastic Equilibrium ◽  
Relaxation Modulus ◽  
Chain Scission ◽  
Experimental Result ◽  
Strained State ◽  
Equilibrium Stress ◽  
Linear Chains ◽  
Network Methods

Abstract The experimental result, that the equilibrium force is nearly equal to the pseudoequilibrium force immediately prior to quenching and irradiation, allows the following conclusions: (1) Chain scission during crosslinking is not a serious problem. (2) The network of highly entangled linear chains is effectively at elastic equilibrium immediately prior to crosslinking in the strained state. This would not be the case if the entangled structure remained untrapped. (3) The effect of chain entangling in tightly crosslinked elastomers is large, also at elastic equilibrium. In fact, it is almost quantitatively equal to the pseudo-equilibrium stress relaxation modulus of the uncrosslinked linear polymer. This result is in agreement with the results from the Langley and the two-network methods.

An Improved Method to Analyze the Stress Relaxation of Ligaments Following a Finite Ramp Time Based on the Quasi-Linear Viscoelastic Theory

2004 ◽  
Vol 126 (1) ◽  
pp. 92-97 ◽  
Author(s):  
Steven D. Abramowitch ◽  
Savio L.-Y. Woo
Keyword(s):  
Stress Relaxation ◽  
Soft Tissues ◽  
Viscoelastic Behavior ◽  
Cyclic Stress ◽  
Elastic Response ◽  
Curve Fit ◽  
Order Of Magnitude ◽  
Linear Viscoelastic ◽  
Linear Viscoelastic Theory ◽  
Experimental Values

The quasi-linear viscoelastic (QLV) theory proposed by Fung (1972) has been frequently used to model the nonlinear time- and history-dependent viscoelastic behavior of many soft tissues. It is common to use five constants to describe the instantaneous elastic response (constants A and B) and reduced relaxation function (constants C, τ1, and τ2) on experiments with finite ramp times followed by stress relaxation to equilibrium. However, a limitation is that the theory is based on a step change in strain which is not possible to perform experimentally. Accounting for this limitation may result in regression algorithms that converge poorly and yield nonunique solutions with highly variable constants, especially for long ramp times (Kwan et al. 1993). The goal of the present study was to introduce an improved approach to obtain the constants for QLV theory that converges to a unique solution with minimal variability. Six goat femur-medial collateral ligament-tibia complexes were subjected to a uniaxial tension test (ramp time of 18.4 s) followed by one hour of stress relaxation. The convoluted QLV constitutive equation was simultaneously curve-fit to the ramping and relaxation portions of the data r2>0.99. Confidence intervals of the constants were generated from a bootstrapping analysis and revealed that constants were distributed within 1% of their median values. For validation, the determined constants were used to predict peak stresses from a separate cyclic stress relaxation test with averaged errors across all specimens measuring less than 6.3±6.0% of the experimental values. For comparison, an analysis that assumed an instantaneous ramp time was also performed and the constants obtained for the two approaches were compared. Significant differences were observed for constants B, C, τ1, and τ2, with τ1 differing by an order of magnitude. By taking into account the ramping phase of the experiment, the approach allows for viscoelastic properties to be determined independent of the strain rate applied. Thus, the results obtained from different laboratories and from different tissues may be compared.

Nonlinear Viscoelastic Behavior of Active Fiber Composites

2014 ◽  
Vol 136 (2) ◽  
Author(s):  
Vahid Tajeddini ◽  
Hassene Ben Atitallah ◽  
Anastasia Muliana ◽  
Zoubeida Ounaies
Keyword(s):  
Stress Relaxation ◽  
Creep Deformation ◽  
Fiber Composite ◽  
Viscoelastic Behavior ◽  
Longitudinal Axis ◽  
Viscoelastic Response ◽  
Active Fiber ◽  
Nonlinear Viscoelastic ◽  
Nonlinear Viscoelastic Behavior ◽  
Analytical Approaches

In the present study, viscoelastic response of an active fiber composite (AFC) is investigated by conducting stress relaxation and creep deformation tests, and the quasi-linear viscoelastic (QLV) constitutive model is used to describe the viscoelastic response of the AFC. The AFC under study consists of unidirectional long piezoelectric ceramic fibers embedded in an epoxy polymer, encapsulated between two Kapton layers with interdigitated surface electrodes. The relaxation and creep experiments are performed by loading the AFC samples along the longitudinal axis of the fibers, under several strain and stress levels at three temperatures, namely 25 °C, 50 °C, and 75 °C. The experimental results reveal the nonlinear viscoelastic behavior of the composite. Next, simulation and prediction of the viscoelastic response, including stress relaxation and creep deformation of the material, are done by using semi-analytical QLV model in which a relaxation time-dependent function is used, which also depends on strain and temperature. The results from the model are compared with those from the experiments. In general, the experimental and simulation results are in good agreement, except in the case of some of the creep responses, where considerable discrepancies are seen between the experimental and analytical approaches. Possible reasons for these differences are discussed in details.

A Nonlinear Viscoelastic Model for the Relaxation Behavior of Tendon

2012 ◽  
Author(s):  
Frances M. Davis ◽  
Raffaella De Vita
Keyword(s):  
Stress Relaxation ◽  
Relaxation Function ◽  
Viscoelastic Model ◽  
Viscoelastic Behavior ◽  
Relaxation Behavior ◽  
Successful Model ◽  
Viscoelastic Models ◽  
Nonlinear Viscoelastic ◽  
Linear Viscoelastic ◽  
Nonlinear Viscoelastic Model

Tendons are viscoelastic materials which undergo stress relaxation when held at a constant strain. The most successful model used to describe the viscoelastic behavior of tendons is the quasi-linear viscoelastic (QLV) model [1]. In the QLV model, the relaxation function is assumed to be a separable function of time and strain. Recently, this assumption has been shown to be invalid for tendons [2] thus suggesting the need for new nonlinear viscoelastic models.

Stress Relaxation of Articular Cartilage in Unconfined Compression

2012 ◽  
Author(s):  
Patrick Smyth ◽  
Itzhak Green ◽  
Robert Jackson ◽  
R. Reid Hanson
Keyword(s):  
Articular Cartilage ◽  
Stress Relaxation ◽  
Mechanical Response ◽  
Viscoelastic Behavior ◽  
Osteoarthritic Cartilage ◽  
Healthy Cartilage ◽  
Storage And Loss Moduli ◽  
Relaxation Experiments ◽  
Insight Into

The articular cartilage function is to allow the bones in a joint to move without causing excess friction and damage. When this cartilage becomes damaged, the supportive and lubricating mechanisms break down, leading to injuries which can be permanent or take extended periods of time for recovery. Because of its importance in general health and body mobility, the unique lubricating properties of cartilage have been studied for many decades. Many current theories exist to characterize the biphasic and triphasic nature of cartilage; however, an important reason that cartilage is so effective is its viscoelastic nature, which allows elastic and dissipative mechanisms to exist simultaneously. It is desired to derive the material properties of cartilage in order to better understand its mechanical effectiveness. Utilizing a CETR-UMT-3 Tribometer, stress relaxation experiments will be performed on freshly harvested equine cartilage plugs that remain hydrated in a fluid bath. Viscoelastic models, such as the Prony series and fractional derivative, are applied to the experimental data to determine the storage and loss moduli of the sample explants. The storage and loss information characterizes the mechanical response of cartilage, and provides insight into the effectiveness and longevity of biological joints. A comparison will be made between joints that experience similar loads, but undergo different relative motions, to determine if the mechanical properties of cartilage are tailored to joint function. Osteoarthritic cartilage will also be explored for deviations in viscoelastic behavior compared to healthy cartilage. Ultimately, it is hoped that a viscoelastic characterization of articular cartilage will lead to insight into the precursors of osteoarthritis, more advanced prosthetics, and biomimetric applications such as the integration of flexible surfaces in mechanical systems.

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