Heat-Induced Changes in the Finite Strain Viscoelastic Behavior of a Collaagenous Tissue

2005 ◽  
Vol 127 (4) ◽  
pp. 580-586 ◽  
Author(s):  
S. Baek ◽  
P. B. Wells ◽  
K. R. Rajagopal ◽  
J. D. Humphrey
Keyword(s):  
Stress Relaxation ◽  
Thermal Damage ◽  
Finite Strain ◽  
Viscoelastic Model ◽  
Viscoelastic Behavior ◽  
Elastic Response ◽  
Collagenous Tissue ◽  
Before And After ◽  
Damage Process ◽  
Soft Tissue Diseases

Supra-physiological temperatures are increasingly being used to treat many different soft tissue diseases and injuries. To identify improved clinical treatments, however, there is a need for better information on the effect of the mechanics on the thermal damage process as well as the effect of the incurred damage on the subsequent mechanical properties. In this paper, we report the first biaxial data on the stress relaxation behavior of a collagenous tissue before and after thermal damage. Based on a two-dimensional finite strain viscoelastic model, which incorporates an exponential elastic response, it is shown that the thermal damage can significantly decrease the characteristic time for stress relaxation and the stress residual.

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.

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.

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.

scholarly journals A Nonlinear Constituent Based Viscoelastic Model for Articular Cartilage and Analysis of Tissue Remodeling Due to Altered Glycosaminoglycan-Collagen Interactions

2009 ◽  
Vol 131 (10) ◽  
Author(s):  
Gregory C. Thomas ◽  
Anna Asanbaeva ◽  
Pasquale Vena ◽  
Robert L. Sah ◽  
Stephen M. Klisch
Keyword(s):  
Articular Cartilage ◽  
Viscoelastic Model ◽  
Viscoelastic Behavior ◽  
Relaxation Data ◽  
Volumetric Expansion ◽  
Nonlinear Viscoelastic ◽  
Developmental Growth ◽  
Before And After ◽  
Nonlinear Viscoelastic Behavior ◽  
Comparison Of The Results

A constituent based nonlinear viscoelastic (VE) model was modified from a previous study (Vena, et al., 2006, “A Constituent-Based Model for the Nonlinear Viscoelastic Behavior of Ligaments,” J. Biomech. Eng., 128, pp. 449–457) to incorporate a glycosaminoglycan (GAG)-collagen (COL) stress balance using compressible elastic stress constitutive equations specific to articular cartilage (AC). For uniaxial loading of a mixture of quasilinear VE constituents, time constant and relaxation ratio equations are derived to highlight how a mixture of constituents with distinct quasilinear VE properties is one mechanism that produces a nonlinear VE tissue. Uniaxial tension experiments were performed with newborn bovine AC specimens before and after ∼55% and ∼85% GAG depletion treatment with guanidine. Experimental tissue VE parameters were calculated directly from stress relaxation data, while intrinsic COL VE parameters were calculated by curve fitting the data with the nonlinear VE model with intrinsic GAG viscoelasticity neglected. Select tissue and intrinsic COL VE parameters were significantly different from control and experimental groups and correlated with GAG content, suggesting that GAG-COL interactions exist to modulate tissue and COL mechanical properties. Comparison of the results from this and other studies that subjected more mature AC tissue to GAG depletion treatment suggests that the GAGs interact with the COL network in a manner that may be beneficial for rapid volumetric expansion during developmental growth while protecting cells from excessive matrix strains. Furthermore, the underlying GAG-COL interactions appear to diminish as the tissue matures, indicating a distinctive remodeling response during developmental growth.

Effect of Thermal Damage and Biaxial Loading on the Optical Properties of a Collagenous Tissue

2003 ◽  
Vol 125 (4) ◽  
pp. 540-548 ◽  
Author(s):  
J.-H. Jun ◽  
J. L. Harris ◽  
J. D. Humphrey ◽  
S. Rastegar
Keyword(s):  
Optical Properties ◽  
Thermal Damage ◽  
Biaxial Loading ◽  
Mechanical Load ◽  
Integrating Sphere ◽  
Biaxial Testing ◽  
Scattering Coefficients ◽  
Collagenous Tissue ◽  
Before And After ◽  
Diagnostic Applications

Thermal denaturation can induce marked changes in the optical and mechanical properties of collagenous tissues. The optical properties are important in both therapeutic and diagnostic applications of lasers in medicine. Although mechanical stress can be caused by collagen shrinkage in laser-based therapies, how the mechanical loading state affects the optical properties is not well understood. We used a new computer-controlled biaxial testing system to subject bovine epicardium to various loading conditions both before and after multiple levels of thermal damage. An integrating sphere technique was used to measure transmittance and diffuse reflectance, from which absorption and scattering coefficients were calculated using a Monte Carlo method. Results showed that the scattering coefficient increased with increasing mechanical load but decreased as the degree of thermal damage increased. There was no significant change in the absorption coefficient due to thermal damage over the ranges studied.

A Single Integral Finite Strain Viscoelastic Model of Ligaments and Tendons

1996 ◽  
Vol 118 (2) ◽  
pp. 221-226 ◽  
Author(s):  
G. A. Johnson ◽  
G. A. Livesay ◽  
S. L-Y. Woo ◽  
K. R. Rajagopal
Keyword(s):  
Finite Strain ◽  
Viscoelastic Model ◽  
Three Dimensional ◽  
Uniaxial Extension ◽  
Viscoelastic Behavior ◽  
Nonlinear Behavior ◽  
Biological Tissues ◽  
Model Parameters ◽  
Three Dimensional Model ◽  
Single Integral

A general continuum model for the nonlinear viscoelastic behavior of soft biological tissues was formulated. This single integral finite strain (SIFS) model describes finite deformation of a nonlinearly viscoelastic material within the context of a three-dimensional model. The specific form describing uniaxial extension was obtained, and the idea of conversion from one material to another (at a microscopic level) was then introduced to model the nonlinear behavior of ligaments and tendons. Conversion allowed different constitutive equations to be used for describing a single ligament or tendon at different strain levels. The model was applied to data from uniaxial extension of younger and older human patellar tendons and canine medial collateral ligaments. Model parameters were determined from curve-fitting stress-strain and stress-relaxation data and used to predict the time-dependent stress generated by cyclic extensions.

The Temperature-Dependent Viscoelastic Behavior of Dielectric Elastomers

2015 ◽  
Vol 82 (9) ◽  
Author(s):  
Jingkai Guo ◽  
Rui Xiao ◽  
Harold S. Park ◽  
Thao D. Nguyen
Keyword(s):  
Stress Relaxation ◽  
Master Curve ◽  
Viscoelastic Model ◽  
Viscoelastic Behavior ◽  
Thermomechanical Analysis ◽  
Quantitative Agreement ◽  
Dielectric Elastomers ◽  
Time To Failure ◽  
Temperature Dependent ◽  
Viscoelastic Creep

In this paper, we investigated the temperature-dependent viscoelastic behavior of dielectric elastomers (DEs) and the effects of viscoelasticity on the electro-actuation behavior. We performed dynamic thermomechanical analysis to measure the master curve of the stress relaxation function and the temperature dependence of the relaxation time of VHB 4905, a commonly used DE. The master curve was applied to calculate the viscoelastic spectrum for a discrete multiprocess finite deformation viscoelastic model. In addition, we performed uniaxial creep and stress relaxation experiments and electrical actuation experiments under different prestretch conditions. The measured spectrum was applied to predict the experimental results. Generally, the model produced good quantitative agreement with both the viscoelastic and electro-actuation experiments, which shows the necessity of using a multiprocess relaxation model to accurately capture the viscoelastic response for VHB. However, the model underpredicted the electro-actuated creep strain for high voltages near the pull-in instability. We attributed the discrepancies to the complex boundary conditions that were not taken into account in the simulation. We also investigated the failure of VHB membrane caused by viscoelastic creep when prestretched and subjected to constant voltage loading. The experimental time to failure for the specimens decreased exponentially with voltage, which agreed well with the predictions of the model.

Structural and Elastic Response of Mo/Ni Multilayers to Ion Irradiation

2000 ◽  
Vol 615 ◽  
Author(s):  
Jérôme Pacaud ◽  
Franck Martin ◽  
Anny Michel ◽  
Christiane Jaouen ◽  
Philippe Djemia ◽  
...  
Keyword(s):  
Light Scattering ◽  
Stress Relaxation ◽  
Ion Irradiation ◽  
Growth Direction ◽  
Interplanar Distance ◽  
Elastic Response ◽  
X Ray Diffraction ◽  
X Ray ◽  
Induced Stress ◽  
Before And After

ABSTRACTMo/Ni multilayers are investigated by x-ray diffraction and Brillouin light scattering before and after ion induced stress relaxation and mixing. Study of the evolution of interplanar distances in both layers as a function of the period exhibits a strong anomaly of the Mo (110) distance (in the growth direction) that can be correlated with the elastic anomaly. The very low interplanar distance in the molybdenum layers found after stress relaxation seems to favor an explanation of this behavior based on the diffusion of Ni in the Mo layers during the growth.

scholarly journals Characterizing the hyper-viscoelastic behavior of adhesive films

2021 ◽  
Vol 37 ◽  
pp. 446-453
Author(s):  
Hao-Hsun Hsu ◽  
Jia-Lin Tsai
Keyword(s):  
Experimental Data ◽  
Stress Relaxation ◽  
Constitutive Model ◽  
Viscoelastic Model ◽  
Viscoelastic Behavior ◽  
Tensile Tests ◽  
Single Step ◽  
Material Parameters ◽  
Reduced Gradient Method ◽  
Viscoelastic Constitutive Model

Abstract In this study, the hyper-viscoelastic behavior of adhesive films was characterized. A constitutive model was developed by combining the Mooney–Rivlin hyperelastic model and a viscoelastic model expressed in terms of the Prony series to describe the constitutive behavior of the adhesive films. The material parameters of the developed constitutive model were determined through single-step stress relaxation tests conducted for 30 min at four strain levels: 100%, 200%, 300% and 400%. Based on the reduced gradient method, the optimized material parameters were then evaluated by curve fitting the experimental data. To validate the proposed constitutive model, we performed the tensile tests at different strain rates from 5 × 10−4 to 5 × 10−1 s−1 and the multistep stress relaxation tests on the adhesive films. The model predictions and experimental data were in good agreement. Thus, the proposed hyper-viscoelastic constitutive model with parameters determined through single-step stress relaxation tests is effective in characterizing the mechanical behavior of adhesive films.

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