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.

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.

Time Dependent Nonlinear Viscoelastic Behavior of Polymer Fluids—A Review of Current Understanding

1981 ◽  
Vol 54 (3) ◽  
pp. 641-661 ◽  
Author(s):  
David S. Soong
Keyword(s):  
Viscoelastic Behavior ◽  
Time Dependent ◽  
Polymer Dynamics ◽  
Industrial Processes ◽  
Future Research ◽  
Transient Flows ◽  
Nonlinear Viscoelastic ◽  
Transient Data ◽  
Nonlinear Viscoelastic Behavior ◽  
Active Investigation

Abstract The behavior of concentrated polymer solutions and melts in transient flows has been under active investigation in recent years. This research interest stems from the realization that a better understanding of these time dependent phenomena has the potential to greatly improve existing industrial processes and to provide new insights to polymer dynamics. In this article, various aspects of the transient viscoelastic properties are discussed. Special emphases are placed on some important considerations in acquiring reliable transient data. Several promising network theories capable of interpreting these experimental results are reviewed. Future research challenges, such as the design of more complicated and stringent rheological tests for the established models, have also been identified.

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.

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.

Constitutive Modeling of High-Elongation Solid Propellants

1992 ◽  
Vol 114 (1) ◽  
pp. 111-115 ◽  
Author(s):  
S¸. O¨zu¨pek ◽  
E. B. Becker
Keyword(s):  
Viscoelastic Model ◽  
Three Dimensional ◽  
Viscoelastic Behavior ◽  
Phenomenological Approach ◽  
Solid Propellants ◽  
Softening Function ◽  
Nonlinear Viscoelastic ◽  
Stress Strain Relation ◽  
High Elongation ◽  
Nonlinear Viscoelastic Behavior

A phenomenological approach is used to represent the nonlinear viscoelastic behavior of solid propellants. A three-dimensional finite strain viscoelastic model, modified by a strain softening function that accounts for damage effects, is considered in the research. Some of the significant aspects of high-elongation propellants are incorporated into the constitutive model. The resulting stress-strain relation is applied to a particular high-elongation propellant by means of the related material characterization. The response predicted by the model is compared with the experimental data for different loading conditions. The model predicts the propellant behavior quite well at uniaxial strain magnitudes up to 50 percent. Numerical analysis of very general geometries and loadings are possible, since a fully general model is calibrated.

Constitutive Equations and Finite Element Implementation of Isochronous Nonlinear Viscoelastic Behavior

2018 ◽  
Vol 140 (4) ◽  
Author(s):  
Hossein Sepiani ◽  
Maria Anna Polak ◽  
Alexander Penlidis
Keyword(s):  
Finite Element ◽  
Material Properties ◽  
Constitutive Relations ◽  
Viscoelastic Behavior ◽  
Material Behavior ◽  
Constitutive Law ◽  
Nonlinear Viscoelastic ◽  
Nonlinear Viscoelastic Behavior ◽  
Stress Dependent

We present a phenomenological three-dimensional (3D) nonlinear viscoelastic constitutive model for time-dependent analysis. Based on Schapery's single integral constitutive law, a solution procedure has been provided to solve nonlinear viscoelastic behavior. This procedure is applicable to 3D problems and uses time- and stress-dependent material properties to characterize the nonlinear behavior of material. The equations describing material behavior are chosen based on the measured material properties in a short test time frame. This estimation process uses the Prony series material parameters, and the constitutive relations are based on the nonseparable form of equations. Material properties are then modified to include the long-term response of material. The presented model is suitable for the development of a unified computer code that can handle both linear and nonlinear viscoelastic material behavior. The proposed viscoelastic model is implemented in a user-defined material algorithm in abaqus (UMAT), and the model validity is assessed by comparison with experimental observations on polyethylene for three uniaxial loading cases, namely short-term loading, long-term loading, and step loading. A part of the experimental results have been conducted by (Liu, 2007, “Material Modelling for Structural Analysis of Polyethylene,” M.Sc. thesis, University of Waterloo, Waterloo, ON Canada), while the rest are provided by an industrial partner. The research shows that the proposed finite element model can reproduce the experimental strain–time curves accurately and concludes that with proper material properties to reflect the deformation involved in the mechanical tests, the deformation behavior observed experimentally can be accurately predicted using the finite element simulation.

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.

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