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.

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.

Viscoelastic Models for Ligaments and Tendons

1994 ◽  
Vol 47 (6S) ◽  
pp. S282-S286 ◽  
Author(s):  
S. L.-Y. Woo ◽  
G. A. Johnson ◽  
R. E. Levine ◽  
K. R. Rajagopal
Keyword(s):  
Constitutive Modeling ◽  
Finite Strain ◽  
Experimental Studies ◽  
Viscoelastic Behavior ◽  
Microstructural Change ◽  
Viscoelastic Models ◽  
Dependent Behavior ◽  
Recent Approach ◽  
Single Integral ◽  
Strain Model

Ligaments and tendons serve a variety of important functions in the human body. Many experimental studies have focused on understanding their mechanical behavior, mathematical modeling has also contributed important information. This paper presents a brief review of viscoelastic models that have been proposed to describe the nonlinear and time-dependent behavior of ligaments and tendons. Specific attention is devoted to quasi-linear viscoelasticity (QLV) and to our most recent approach, the single integral finite strain model (SIFS) which incorporates constitutive modeling of microstructural change. An example is given in which the SIFS model is used to describe the viscoelastic behavior of a human patellar tendon.

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.

Parameter Estimation of Nonlinear Biomedical Systems Using Extended Kalman Filter Algorithm

2017 ◽  
pp. 76-99 ◽  
Author(s):  
Kamalanand Krishnamurthy
Keyword(s):  
Parameter Estimation ◽  
Kalman Filter ◽  
Extended Kalman Filter ◽  
Computational Models ◽  
Three Dimensional ◽  
Model Parameters ◽  
State Variables ◽  
Three Dimensional Model ◽  
Biomedical Systems ◽  
Estimation Of Model Parameters

Parameter estimation is a central issue in mathematical modelling of biomedical systems and for the development of patient specific models. The technique of estimating parameters helps in obtaining diagnostic information from computational models of biological systems. However, in most of the biomedical systems, the estimation of model parameters is a challenging task due to the nonlinearity of mathematical models. In this chapter, the method of estimation of nonlinear model parameters from measurements of state variables, using the extended Kalman filter, is extensively explained using an example of the three-dimensional model of the HIV/AIDS system.

Mechanics of Angioplasty: Wall, Balloon and Stent

2000 ◽  
Author(s):  
Gerhard A. Holzapfel ◽  
Christian A. J. Schulze-Bauer ◽  
Michael Stadler
Keyword(s):  
Solid Mechanics ◽  
Three Dimensional ◽  
Element Model ◽  
Biological Tissues ◽  
Interventional Treatment ◽  
Strong Nonlinearity ◽  
Three Dimensional Model ◽  
Plaque Disruption ◽  
Geometrical Data ◽  
Elastoplastic Constitutive Model

Abstract Studying the solid mechanics of angioplasty provides essential insight in the mechanisms of angioplasty such as overstretching the disease-free tissue, plaque disruption or dissection, redistribution inside the wall and lipid extrusion etc. We desribe our current understanding of the mechanics of angioplasty based on the example of a human iliac artery with an eccentric stenosis. We outline a new approach which has the potential to improve interventional treatment planning, to predict the balloon and stent-induced wall stresses as well as the dilation success. In particular, we use MRI to obtain accurate geometrical data for the vessel wall and plaque architecture and to identify their different types of soft (biological) tissues and calcifications. One issue is to characterize the quasistatic stress-strain response of these components in both axial and circumferential directions. We present new experimental results showing strong nonlinearity and anisotropy. Another issue is to identify predominant directions of each component by analyzing orientations of cellular nuclei. The morphological and mechanical information is used for the elastoplastic constitutive model designed to capture the finite strains of the stenotic artery during angioplasty. The three-dimensional model is fitted to the experimental data. Associated material parameters, corresponding to the different tissues of the stenosis, are presented. The numerical part outlines briefly the concept of the finite element model and, based on a computational structural analysis, discusses the mechanism of angioplasty for the considered type of stenosis.

scholarly journals Glassy dynamics in three-dimensional embryonic tissues

2013 ◽  
Vol 10 (89) ◽  
pp. 20130726 ◽  
Author(s):  
Eva-Maria Schötz ◽  
Marcos Lanio ◽  
Jared A. Talbot ◽  
M. Lisa Manning
Keyword(s):  
Pattern Formation ◽  
Mechanical Response ◽  
Three Dimensional ◽  
Biological Tissues ◽  
Model Parameters ◽  
Elastic Solids ◽  
Cell Dynamics ◽  
Cell Parameters ◽  
Embryonic Tissues ◽  
Long Timescales

Many biological tissues are viscoelastic, behaving as elastic solids on short timescales and fluids on long timescales. This collective mechanical behaviour enables and helps to guide pattern formation and tissue layering. Here, we investigate the mechanical properties of three-dimensional tissue explants from zebrafish embryos by analysing individual cell tracks and macroscopic mechanical response. We find that the cell dynamics inside the tissue exhibit features of supercooled fluids, including subdiffusive trajectories and signatures of caging behaviour. We develop a minimal, three-parameter mechanical model for these dynamics, which we calibrate using only information about cell tracks. This model generates predictions about the macroscopic bulk response of the tissue (with no fit parameters) that are verified experimentally, providing a strong validation of the model. The best-fit model parameters indicate that although the tissue is fluid-like, it is close to a glass transition, suggesting that small changes to single-cell parameters could generate a significant change in the viscoelastic properties of the tissue. These results provide a robust framework for quantifying and modelling mechanically driven pattern formation in tissues.

Three-Dimensional Viscoelastic Interactions of a Center of Dilatation with a Penny-Shaped Interfacial Crack

2011 ◽  
Vol 117-119 ◽  
pp. 471-475 ◽  
Author(s):  
Yu Zhou Sun ◽  
Ya Dong Bian ◽  
Zhong Guo Zhang
Keyword(s):  
Rock Fracture ◽  
Auxiliary Problem ◽  
Viscoelastic Model ◽  
Three Dimensional ◽  
Interfacial Crack ◽  
Viscoelastic Behavior ◽  
Inverse Laplace Transform ◽  
Bimaterial Interface ◽  
Thermal Dilatation ◽  
The Time Domain

This paper presents a three-dimensional viscoelastic model to study the interactions of a penny-shaped interfacial crack and a center of dilatation in the infinite viscoelastic bimaterial, which can model the rock fracture subjected to stress and thermal dilatation during some engineering process. A distinct issue associated with the present work is the incorporation of viscoelastic behavior of bimaterial. The proposed problem is first transformed into the Laplace space, and the solution in the transform space is obtained by decomposing the original problem into two auxiliary problems: (I) a center of dilatation near a bimaterial interface (no crack); and (II) a penny-shaped interfacial crack subject to internal tractions that cancel out those induced in auxiliary problem (I). The mode I, II and III stress intensity factors (SIFs) in the time domain are obtained with the inverse Laplace transform.

Thermoacoustic Modeling of a Graphene-Based Actuator

2014 ◽  
Author(s):  
Jonghoon Bin ◽  
William S. Oates ◽  
Kunihiko Taira
Keyword(s):  
Three Dimensional ◽  
Three Dimensions ◽  
Model Parameters ◽  
Three Dimensional Model ◽  
Mcmc Algorithms ◽  
Flux Boundary Conditions ◽  
Model Parameter Uncertainty ◽  
The One ◽  
Different Characteristics ◽  
Surface Temperature Variation

A model for two-dimensional graphene-based thermoacoutic membranes is investigated analytically and validated numerically in this study. In one-dimension, the temperature and the pressure variables are analytically determined by decoupling the two variables in the governing equations due to the large disparity between length scales. We further extend the one-dimensional findings to three dimensions. The three-dimensional pressure fluctuation produced by the surface temperature variation is determined with the aid of the acoustic piston model. Through the one and three-dimensional model analysis, the dependence of acoustic pressure as a function of frequency is studied and the acoustic response with respect to the frequency shows different characteristics when assuming Dirichlet (temperature) or Neumann (heat flux) boundary conditions. The general thermoacoustic model is then applied to a graphene-on-paper sound device. Probabilistic Bayesian method coupled with Monte Carlo Markov Chain (MCMC) algorithms is used to optimize model parameters and to analyze model parameter uncertainty. Excellent correlations of thermoacoustic behavior is predicted by the model which provides insight into heat transport mechanisms associated with generating sound from thermally cycling graphene at high frequencies.

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.

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