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.

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.

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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