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.

Identification of Nonlinear Viscoelastic Models of Flexible Polyurethane Foam From Uniaxial Compression Data

2016 ◽  
Vol 138 (2) ◽  
Author(s):  
Yousof Azizi ◽  
Patricia Davies ◽  
Anil K. Bajaj
Keyword(s):  
Uniaxial Compression ◽  
Viscoelastic Model ◽  
Viscoelastic Behavior ◽  
Model Parameters ◽  
Viscoelastic Models ◽  
Nonlinear Viscoelastic ◽  
Compression Data ◽  
Computationally Intensive ◽  
Nonlinear Viscoelastic Model ◽  
Flexible Polyurethane

Flexible polyethylene foam is used in many engineering applications. It exhibits nonlinear and viscoelastic behavior which makes it difficult to model. To date, several models have been developed to characterize the complex behavior of foams. These attempts include the computationally intensive microstructural models to continuum models that capture the macroscale behavior of the foam materials. In this research, a nonlinear viscoelastic model, which is an extension to previously developed models, is proposed and its ability to capture foam response in uniaxial compression is investigated. It is hypothesized that total stress can be decomposed into the sum of a nonlinear elastic component, modeled by a higher-order polynomial, and a nonlinear hereditary type viscoelastic component. System identification procedures were developed to estimate the model parameters using uniaxial cyclic compression data from experiments conducted at six different rates. The estimated model parameters for individual tests were used to develop a model with parameters that are a function of strain rates. The parameter estimation technique was modified to also develop a comprehensive model which captures the uniaxial behavior of all six tests. The performance of this model was compared to that of other nonlinear viscoelastic models.

Identification of Nonlinear Viscoelastic Models of Flexible Polyurethane Foam From Uniaxial Compression Data

2012 ◽  
Author(s):  
Yousof Azizi ◽  
Patricia Davies ◽  
Anil K. Bajaj
Keyword(s):  
Uniaxial Compression ◽  
Viscoelastic Model ◽  
Viscoelastic Behavior ◽  
Model Parameters ◽  
Viscoelastic Models ◽  
Nonlinear Viscoelastic ◽  
Compression Data ◽  
Computationally Intensive ◽  
Nonlinear Viscoelastic Model ◽  
Flexible Polyurethane

Flexible polyethylene foam, which is used in many engineering applications, exhibits nonlinear and viscoelastic behavior. To date, several models have been proposed to characterize the complex behavior of foams from the computationally intensive microstructural models to continuum models that capture the macroscale behavior of the foam materials. A nonlinear viscoelastic model, which is an extension of previously developed models, is proposed and its ability to capture foam response in uniaxial compression is investigated. It is assumed in the model that total stress is decomposed into the sum of a nonlinear elastic component, which is modeled by a higher order polynomial, and a nonlinear hereditary type viscoelastic component. System identification procedures are developed to estimate the model parameters using uniaxial compression data from experiments conducted at different rates. The performance of this model is compared to that of other nonlinear viscoelastic models.

A Constituent-Based Model for the Nonlinear Viscoelastic Behavior of Ligaments

2005 ◽  
Vol 128 (3) ◽  
pp. 449-457 ◽  
Author(s):  
P. Vena ◽  
D. Gastaldi ◽  
R. Contro
Keyword(s):  
Stress Relaxation ◽  
Viscoelastic Model ◽  
Viscoelastic Behavior ◽  
Biological Tissues ◽  
Relaxation Behavior ◽  
Constitutive Law ◽  
Time Dependent ◽  
Nonlinear Viscoelastic ◽  
Nonlinear Viscoelastic Behavior ◽  
Constitutive Parameters

This paper presents a constitutive model for predicting the nonlinear viscoelastic behavior of soft biological tissues and in particular of ligaments. The constitutive law is a generalization of the well-known quasi-linear viscoelastic theory (QLV) in which the elastic response of the tissue and the time-dependent properties are independently modeled and combined into a convolution time integral. The elastic behavior, based on the definition of anisotropic strain energy function, is extended to the time-dependent regime by means of a suitably developed time discretization scheme. The time-dependent constitutive law is based on the postulate that a constituent-based relaxation behavior may be defined through two different stress relaxation functions: one for the isotropic matrix and one for the reinforcing (collagen) fibers. The constitutive parameters of the viscoelastic model have been estimated by curve fitting the stress relaxation experiments conducted on medial collateral ligaments (MCLs) taken from the literature, whereas the predictive capability of the model was assessed by simulating experimental tests different from those used for the parameter estimation. In particular, creep tests at different maximum stresses have been successfully simulated. The proposed nonlinear viscoelastic model is able to predict the time-dependent response of ligaments described in experimental works (Bonifasi-Lista et al., 2005, J. Orthopaed. Res., 23, pp. 67–76;Hingorani et al., 2004, Ann. Biomed. Eng., 32, pp. 306–312;Provenzano et al., 2001, Ann. Biomed. Eng., 29, pp. 908–214;Weiss et al., 2002, J. Biomech., 35, pp. 943–950). In particular, the nonlinear viscoelastic response which implies different relaxation rates for different applied strains, as well as different creep rates for different applied stresses and direction-dependent relaxation behavior, can be described.

An Approach to Characterize Nonlinear Viscoelastic Material Behavior Using Dynamic Mechanical Tests and Analyses

1999 ◽  
Vol 66 (4) ◽  
pp. 872-878 ◽  
Author(s):  
H. J. Golden ◽  
T. W. Strganac ◽  
R. A. Schapery
Keyword(s):  
Viscoelastic Model ◽  
Dynamic Test ◽  
Mechanical Analysis ◽  
Mechanical Tests ◽  
Material Behavior ◽  
Dynamic Mechanical ◽  
Nonlinear Characterization ◽  
Nonlinear Viscoelastic ◽  
Linear Viscoelastic ◽  
Nonlinear Viscoelastic Model

Linear viscoelastic properties may be rapidly identified using dynamic mechanical analysis methods, yet these traditional methods do not properly identify nonlinear viscoelastic response. Herein, dynamic mechanical methodologies are extended to provide an approach for nonlinear characterization. The proposed method is based on Schapery's nonlinear viscoelastic model extended to dynamic mechanical theory. The oscillatory loading during a dynamic test is addressed within the nonlinear viscoelastic model. An experimental protocol is established. Analyses and experiments are performed for the characterization of thin-film polyethylene to validate the approach.

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.

Modeling Stress-Relaxation Behavior of the Periodontal Ligament During the Initial Phase of Orthodontic Treatment

2013 ◽  
Vol 135 (9) ◽  
Author(s):  
Dan L. Romanyk ◽  
Garrett W. Melenka ◽  
Jason P. Carey
Keyword(s):  
Stress Relaxation ◽  
Periodontal Ligament ◽  
Orthodontic Treatment ◽  
Viscoelastic Model ◽  
Relaxation Behavior ◽  
Stress Relaxation Behavior ◽  
Cubic Form ◽  
Viscoelastic Models ◽  
Applied Forces

The periodontal ligament is the tissue that provides early tooth motion as a result of applied forces during orthodontic treatment: a force-displacement behavior characterized by an instantaneous displacement followed by a creep phase and a stress relaxation phase. Stress relaxation behavior is that which provides the long-term loading to and causes remodelling of the alveolar bone, which is responsible for the long-term permanent displacement of the tooth. In this study, the objective was to assess six viscoelastic models to predict stress relaxation behavior of rabbit periodontal ligament (PDL). Using rabbit stress relaxation data found in the literature, it was found that the modified superposition theory (MST) model best predicts the rabbit PDL behavior as compared to nonstrain-dependent and strain-dependent versions of the Burgers four-parameter and the five-parameter viscoelastic models, as well as predictions by Schapery's viscoelastic model. Furthermore, it is established that using a quadratic form for MST strain dependency provides more stable solutions than the cubic form seen in previous studies.

Tensile Property Test Analysis of Double Protein Modified Fiber

2012 ◽  
Vol 535-537 ◽  
pp. 1433-1436
Author(s):  
Jin Zhong Zhu ◽  
Shi Hui Wang ◽  
Jun Rui Hu ◽  
Yun Li
Keyword(s):  
Stress Relaxation ◽  
Soybean Protein ◽  
Viscoelastic Model ◽  
Test Analysis ◽  
Elongation At Break ◽  
Nonlinear Viscoelastic ◽  
Initial Modulus ◽  
Protein Fiber ◽  
Mechanical Models ◽  
Nonlinear Viscoelastic Model

In order to study the tensile mechanical properties of the double protein modified fiber. Tensile breaking property and stress relaxation were analyzed and proper mechanical models were selected for fitting. The analysis shows that: in dry and wet, the straight tensile breaking tenacity of the double protein modified fiber is weaker than that of the modified soybean protein fiber, the elongation at break and initial modulus are near to those of the modified soybean protein fiber, the breaking tenacity of the double protein modified fiber increases slightly when wet while the elongation at break and initial modulus decline a little. In knotted and looped, the double protein modified fiber’s tensile breaking tenacity is weaker than that of the modified soybean protein and its tensile breaking strength and elongation at break decrease differently. The fitting reveals that the four element nonlinear viscoelastic model is the best to describe straight tensile. The two optimal models for knotted and looped tensile are the four element nonlinear viscoelastic model and the Improved Zurek model. In addition, the six element viscoelastic plasticity model is appropriate to simulate stress relaxation.

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.

Comparison Between a Quasilinear and a Nonlinear Viscoelastic Model for Brain Tissue

2000 ◽  
Author(s):  
Kurosh K. Darvish ◽  
Jeff R. Crandall
Keyword(s):  
Brain Tissue ◽  
Viscoelastic Model ◽  
Constitutive Models ◽  
Viscoelastic Behavior ◽  
Bovine Brain ◽  
Integral Model ◽  
Nonlinear Viscoelastic ◽  
Hereditary Integral ◽  
Nonlinear Constitutive Models ◽  
Nonlinear Viscoelastic Model

Abstract The nonlinearity of the viscoelastic behavior of brain tissue was studied. Two nonlinear constitutive models were developed using the experimental results of forced vibrations on bovine brain samples, namely a quasilinear viscoelastic model and a multiple hereditary integral model. The latter was found to be superior especially at higher frequencies (above 27 Hz).

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