scholarly journals Stress relaxation of porcine tendon under simulated biological environment: experiment and modeling

2021 ◽  
Vol 23 (1) ◽  
Author(s):  
Sylwia D. Łagan ◽  
Aneta Liber-Kneć
Keyword(s):  
Stress Relaxation ◽  
Viscoelastic Model ◽  
Model Fitting ◽  
Viscoelastic Behavior ◽  
Strain Range ◽  
Viscoelastic Response ◽  
Physiological Strain ◽  
Linear Viscoelastic ◽  
Biological Environment ◽  
Environment Experiment

Purpose: The aim of the study was to investigate the viscoelastic response in the low and high physiological strain with the use of experimental and modeling approach. Methods: Viscoelastic response in the low, transition and high physiologic strain (3, 6 and 9%) with consideration of simulated biological environment (0.9% saline solution, 37 °C) was measured in relaxation tests. Preconditioning of tendons was considered in the testing protocol and the applied range of load was obtained from tensile testing. The quasi-linear viscoelasticity theory was used to fit experimental data to obtain constants (moduli and times of relaxation), which can be used for description of the viscoelastic behavior of tendons. The exponential non-linear elastic representation of the stress response in ramp strain was also estimated. Results: Differences between stress relaxation process can be seen between tendons stretched to the physiological strain range (3%) and exceeding this range (6 and 9%). The strains of 6% and 9% showed a similar stress relaxation trend displaying relatively rapid relaxation for the first 70 seconds, whereas the lowest strain of 3% displayed relatively slow relaxation. Conclusions: Results of the model fitting showed that the quasi-linear viscoelastic model gives the best fit in the range of low physiological strain level.

Quasi-Linear Viscoelastic Theory is Insufficient to Comprehensively Describe the Time-Dependent Behavior of Human Cervical Spine Ligaments

2010 ◽  
Author(s):  
Kevin L. Troyer ◽  
Christian M. Puttlitz
Keyword(s):  
Cervical Spine ◽  
Stress Relaxation ◽  
Strain Range ◽  
Relaxation Curve ◽  
Physiological Strain ◽  
Dependent Behavior ◽  
Linear Viscoelastic ◽  
Viscoelastic Theory ◽  
Relaxation Experiments ◽  
Linear Viscoelastic Theory

Stress relaxation experiments were conducted on cervical spine ligaments at multiple strain magnitudes to determine the validity and applicability of the quasi-linear viscoelastic (QLV) theory to model their dynamic behavior. The results indicate that the shape of the stress relaxation curve is dependent upon the magnitude of the applied strain. Thus, a more general, nonlinear formulation is required to model these ligaments within the physiological strain range.

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 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.

Viscoelastic Behavior of Carbon Nanotube Yarns and Twisted Coils

2018 ◽  
Author(s):  
Pouria Khanbolouki ◽  
Mehran Tehrani
Keyword(s):  
Carbon Nanotube ◽  
Viscoelastic Model ◽  
Viscoelastic Behavior ◽  
Energy Harvesters ◽  
Linear Behavior ◽  
Non Linear ◽  
Stretchable Conductors ◽  
Linear Viscoelastic Behavior ◽  
Linear Viscoelastic ◽  
Development And Validation

Coiled structures made from polymer and Carbon Nanotube (CNT) yarns are used as artificial muscles, stretchable conductors, and energy harvesters. The purpose of this work is to present our latest understanding of the mechanical behavior of these CNT-based structures. CNT yarns are fabricated by inserting twists in sheets spun from CNT forests. Over twisting the CNT yarns results in coiled CNT yarns, similar to a spring where the spring radius is comparable to the diameter of the CNT yarn. In this study, we explain the development and validation of a viscoelastic model, to capture damping and hysteresis in CNT yarns under quasi-static and dynamic loads. Confirmation of linear viscoelastic behavior of CNT yarns can lead us to the development of a model for coiled CNT yarns. Coiled CNT yarns, on the other hand, show a complex non-linear viscoelastic behavior. Possible mechanisms responsible for this non-linear behavior are discussed.

scholarly journals Constitutive Modeling of Time-Dependent Response of Human Plantar Aponeurosis

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
P. G. Pavan ◽  
P. Pachera ◽  
C. Stecco ◽  
A. N. Natali
Keyword(s):  
Experimental Data ◽  
Stress Relaxation ◽  
Constitutive Model ◽  
Transverse Isotropy ◽  
Model Fitting ◽  
Viscoelastic Behavior ◽  
Time Dependent ◽  
Plantar Aponeurosis ◽  
Structural Conformation ◽  
Dependent Behavior

The attention is focused on the viscoelastic behavior of human plantar aponeurosis tissue. At this purpose, stress relaxation tests were developed on samples taken from the plantar aponeurosis of frozen adult donors with age ranging from 67 to 78 years, imposing three levels of strain in the physiological range (4%, 6%, and 8%) and observing stress decay for 240 s. A viscohyperelastic fiber-reinforced constitutive model with transverse isotropy was assumed to describe the time-dependent behavior of the aponeurotic tissue. This model is consistent with the structural conformation of the tissue where collagen fibers are mainly aligned with the proximal-distal direction. Constitutive model fitting to experimental data was made by implementing a stochastic-deterministic procedure. The stress relaxation was found close to 40%, independently of the level of strain applied. The agreement between experimental data and numerical results confirms the suitability of the constitutive model to describe the viscoelastic behaviour of the plantar aponeurosis.

Analysis of Fabric Deformation in a Roll-Making Operation Part III: Effect of Viscoelasticity

1992 ◽  
Vol 62 (11) ◽  
pp. 669-676 ◽  
Author(s):  
T. K. Ghosh ◽  
H. Peng ◽  
P. Banks-Lee
Keyword(s):  
Stress State ◽  
Stress Relaxation ◽  
Continuum Model ◽  
Present Model ◽  
Viscoelastic Model ◽  
Viscoelastic Behavior ◽  
Plane Stress State ◽  
Numerical Examples ◽  
Fabric Deformation ◽  
The Relationship

The relationship between various parameters of roll making, fabric properties, and the resultant stresses developed within a fabric roll has been discussed in Parts I and II of this series. A discrete continuum model was used to describe fabric deformation during roll making. In the present model, the fabric is assumed to be in plane stress state and the effect in the filling direction is entirely neglected. The fabric is considered as anisotropic in warp and thickness directions. The effect of fabric viscoelasticity in the warp direction is also considered. A simple two-term Maxwell viscoelastic model is used to describe the fabric viscoelastic behavior. The stress relaxation process within fabric rolls during and after roll formation is discussed through numerical examples.

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 Straightforward Procedure to Characterize Nonlinear Viscoelastic Response of Asphalt Concrete at High Temperatures

2018 ◽  
Vol 2672 (28) ◽  
pp. 481-492 ◽  
Author(s):  
Mohammad Bazzaz ◽  
Masoud K. Darabi ◽  
Dallas N. Little ◽  
Navneet Garg
Keyword(s):  
Asphalt Concrete ◽  
Viscoelastic Model ◽  
Viscoelastic Behavior ◽  
Deviatoric Stress ◽  
Creep Recovery ◽  
Viscoelastic Response ◽  
Nonlinear Viscoelastic ◽  
Wide Range ◽  
Stress Levels ◽  
Concrete Materials

This paper proposes a straightforward procedure to characterize the nonlinear viscoelastic response of asphalt concrete materials. Furthermore, a model is proposed to estimate the nonlinear viscoelastic parameters as a function of the triaxiality ratio, which accounts for both confinement and deviatoric stress levels. The simplified procedure allows for easy characterization of linear viscoelastic (LVE) and nonlinear viscoelastic (NVE) responses. First, Schapery’s nonlinear viscoelastic model is used to represent the viscoelastic behavior. Dynamic modulus tests are performed to calibrate LVE properties. Repeated creep-recovery tests at variable deviatoric stress levels (RCRT-VS) were designed and conducted to calibrate the nonlinear viscoelastic properties of four types of mixtures used in the Federal Aviation Administration’s National Airport Pavement and Materials Research Center test sections. The RCRT-VS were conducted at 55°C, 140 kPa initial confinement pressure, and wide range of deviatoric stress levels; mimicking the stress levels induced in a pavement structure under traffic. Once calibrated, the model was validated by comparing the model predictions and experimental measurements at different deviatoric stress levels. The predictions indicate that the proposed method is capable of characterizing NVE response of asphalt concrete materials.

Characterizing Gum Elastomers by Fourier Transform Rheometry

2003 ◽  
Vol 76 (4) ◽  
pp. 979-1000 ◽  
Author(s):  
Jean L. Leblanc ◽  
Christophe de la Chapelle
Keyword(s):  
Fourier Transform ◽  
High Strain ◽  
Dynamic Testing ◽  
Harmonic Component ◽  
Viscoelastic Behavior ◽  
Strain Range ◽  
Polymer Materials ◽  
Range Data ◽  
Non Linear ◽  
Linear Viscoelastic

Abstract Fourier transform (FT) rheometry is an emerging new technique that allows the linear and non-linear viscoelastic behavior of polymer materials to be accurately investigated. Basically samples are submitted to torsional harmonic strain at fixed frequency and temperature in order to capture strain and torque signals. A commercial instrument, i.e. the Rubber Process Analyzer RPA 2000® (Alpha Technologies), was suitably modified, essentially in using a fast electronic analogic-digital conversion card to record and treat torque and strain signals using purposely written software. Details of such modifications were previously published and the work presented is a sequel of this development. The quality of the applied strain is first precisely documented through FT and found excellent, particularly in the high strain range. Three gum EPDM with different macromolecular characteristics (MWD and long chain branching) were analyzed either using standard dynamic testing, i.e. essentially in the linear viscoelastic range, or using the Fourier transform rheometry approach, by considering data gathered in the far non-linear viscoelastic range. Data obtained are considered with respect to know features of the samples. A series of SBR 1500 samples, collected from various manufacturers, were first analyzed using standard methods; as expected very small differences were seen. Then FT was used to consider torque signals at very high strain (up to 400% at 1 Hz). Using a simple 4-parameter model to treat the variation upon increasing strain of the relative third harmonic component of the torque signal, differences are clearly detected that are discussed with respect to available polymer manufacturing information.

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