Behavior of Viscoelastic Media Under Small Sinusoidal Oscillations Superposed on Finite Strain

1968 ◽  
Vol 35 (3) ◽  
pp. 433-440 ◽  
Author(s):  
W. Goldberg ◽  
G. Lianis
Keyword(s):  
Steady State ◽  
Finite Strain ◽  
Complex Modulus ◽  
Uniaxial Extension ◽  
Viscoelastic Behavior ◽  
Uniaxial Stress ◽  
Viscoelastic Media ◽  
Sinusoidal Oscillations ◽  
Fluid Theory ◽  
Finite Linear

In this paper, we examine the response of an incompressible elastomer when it is subjected to small, steady-state oscillations superposed on a large steady deformation. The material is assumed to be isotropic in its undeformed state, and its viscoelastic behavior is characterized by means of two different approximate theories: (a) Lianis’ approximation of the theory of finite linear viscoelasticity, and (b) Bernstein, Kearsley, Zapas’ elastic fluid theory, Signorini approximation. Theoretical expressions are developed for the uniaxial stress in a body subjected to steady-state sinusoidal oscillations superposed on a state of steady, finite, uniaxial extension, using both theories. A complex modulus is defined, which reduces to the complex modulus of infinitesimal viscoelasticity when the finite strain is zero. Experiments were performed on three different polymers and the observed response is compared with that predicted by both theories.

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.

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.

Damage and Thixotropy in Asphalt Mixture and Binder Fatigue Tests

2012 ◽  
Vol 2293 (1) ◽  
pp. 8-17 ◽  
Author(s):  
Félix Pérez-Jiménez ◽  
Ramon Botella ◽  
Rodrigo Miró
Keyword(s):  
Cyclic Loading ◽  
Strain Amplitude ◽  
Fatigue Testing ◽  
Complex Modulus ◽  
Asphalt Mixture ◽  
Viscoelastic Behavior ◽  
Fatigue Cracking ◽  
Asphalt Mixtures ◽  
Asphalt Binders ◽  
Irreversible Damage

Fatigue cracking is considered one of the main damage mechanisms in asphalt pavement design. Design methods use fatigue laws obtained by laboratory testing of the materials involved. Typically, these tests consist of subjecting the asphalt mixture to cyclic loading until failure occurs. However, failure is associated not with specimen fracture (which is unusual), but with a slight decrease in the mechanical properties of the material, usually in the complex modulus. As a consequence, it is important to differentiate between real damage to the material and changes in its viscoelastic behavior and thixotropy. It is also crucial to account for the healing that occurs in asphalt material after rest periods. The above considerations are important in the fatigue testing of asphalt binders because these materials show pronounced viscoelastic behavior and thixotropy, especially when subjected to cyclic loading. This paper demonstrates that in many cases what is taken for fatigue failure during testing (i.e., a decrease in the complex modulus below half of its initial value) is actually thixotropy. Thus, the complex modulus can be recovered by reducing the loading or, as in this study, the strain applied. In contrast, asphalt mixtures experience irreversible damage, and depending on the asphalt binder, the thixotropic effects are more or less pronounced. This paper analyzes the failure criteria currently used in the fatigue testing of asphalt mixtures and binders and evaluates the parameters chosen, namely, complex modulus (G*) and phase angle (δ) to characterize asphalt binders (G*sin δ). A cyclic uniaxial tension–compression test under strain-controlled conditions was performed. Three test modalities were used: time sweeps (constant strain amplitude until total failure), increasing strain sweeps (increase in strain amplitude every 5,000 cycles), and up-and-down strain sweeps (alternating increases and decreases in strain amplitude).

Nonlinear viscoelastic behavior of sedimentary rocks, Part I: Effect of frequency and strain amplitude

Geophysics ◽  
1998 ◽  
Vol 63 (1) ◽  
pp. 184-194 ◽  
Author(s):  
Azra N. Tutuncu ◽  
Augusto L. Podio ◽  
Alvin R. Gregory ◽  
Mukul M. Sharma
Keyword(s):  
Strain Amplitude ◽  
Sedimentary Rocks ◽  
Low Frequency ◽  
Viscoelastic Behavior ◽  
Uniaxial Stress ◽  
Companion Paper ◽  
Elastic Behavior ◽  
Amplitude Dependence ◽  
Frequency Measurements ◽  
Young’S Moduli

Sedimentary rocks display nonlinear elastic behavior. This nonlinearity is a strong function of frequency, strain amplitude, and the properties of the saturating fluid. Experimental observations and potential mechanisms that cause these nonlinearities are presented in this and a companion paper. Young’s moduli and Poisson’s ratios obtained from ultrasonic laboratory measurements (50 kHz, 100 kHz, 180kHz and 1 MHz), low‐frequency measurements (1–2000 Hz) and static measurements (0.001–0.05 Hz) show significant differences under identical stress conditions. A comparison of the laboratory‐measured quantities with log‐derived moduli measured at 20 kHz indicates that [Formula: see text]. This shows clearly that a wide variety of sandstones demonstrate frequency‐dependent elastic behavior (viscoelastic behavior) over a range of frequencies. Differences between static (low‐frequency, high‐strain amplitude) velocities and ultrasonic velocities can be explained partially by differences in frequency as predicted by grain contact models. Such models, however, do not explain the strain amplitude dependence observed in our data. A series of uniaxial stress cycling measurements were carried out to investigate the influence of strain amplitude on elastic moduli. These low‐frequency measurements (0.01 Hz) clearly show that the Young’s modulus decreases with strain amplitude for a wide variety of sandstones. Attenuation increases with strain amplitude. The strain amplitude dependence does not change when the rocks are saturated with brine although the rocks soften measureably.

Mechanical Vibration Filters With Nonlinear Characteristics

1960 ◽  
Vol 82 (4) ◽  
pp. 369-375
Author(s):  
Will J. Worley
Keyword(s):  
Steady State ◽  
Mechanical Vibration ◽  
Nonlinear Characteristics ◽  
Single Degree Of Freedom ◽  
Single Degree ◽  
Nonlinear Springs ◽  
Sinusoidal Oscillations ◽  
Single Mass ◽  
Linear And Nonlinear ◽  
Differential Analyzer

The behavior of a single degree of freedom system consisting of a single mass mounted on a spring and damper attached to an oscillating base is investigated. Steady-state and transient sinusoidal oscillations are applied to the base to which the suspension is attached. The response of the mass is recorded for various combinations of linear and nonlinear springs and dampers. Solutions are obtained with a differential analyzer.

Steady-State Wave Propagation in Multilayered Viscoelastic Media Excited by a Moving Dynamic Distributed Load

2009 ◽  
Vol 76 (4) ◽  
Author(s):  
Lu Sun ◽  
Wenjun Gu ◽  
Feiquan Luo
Keyword(s):  
Steady State ◽  
Moving Load ◽  
Impulse Response Function ◽  
Constitutive Models ◽  
Numerical Algorithms ◽  
Point Load ◽  
Fast Evaluation ◽  
Viscoelastic Media ◽  
Distributed Load ◽  
Novel Approach

An analytical solution of steady-state dynamic response of a multilayered viscoelastic medium to a moving distributed load is obtained using a novel approach that combines transfer matrix method with Sun’s convolution representation integrated over impulse response function of the layered medium. The layered media under consideration include elastic and viscoelastic media with four different viscoelastic constitutive models, while the moving load is allowed to have a circular spatial distribution, which is more realistic for mimicking tire footprint than a commonly used point load. Efficient numerical algorithms based on fast evaluation of various integral transformations and their inversions are developed and validated through numerical example.

scholarly journals Prony series calculation for viscoelastic behavior modeling of structural adhesives from DMA data.

2020 ◽  
Vol 21 (2) ◽  
pp. 1-10
Author(s):  
Manuel Alejandro Tapia Romero ◽  
Mariamne Dehonor Gomez ◽  
Luis Edmundo Lugo Uribe
Keyword(s):  
Product Design ◽  
Complex Modulus ◽  
Loss Modulus ◽  
Viscoelastic Behavior ◽  
Relaxation Modulus ◽  
Mechanical Analysis ◽  
Behavior Modeling ◽  
Prony Series ◽  
Product Design Process ◽  
Material Sample

In product design is important to choose the correct material for a specific application. Viscoelastic behavior let us know how much energy the material can dissipate on its internal structure or either return it to the surroundings, and the property that describe this is the Complex Modulus G*, it is a complex quantity that can be separated in a real and an imaginary part called G' storage modulus and iG'' loss modulus respectively. These properties can be measured experimentally from a small material sample easily by performing Dynamical Mechanical Analysis (DMA). In Product Design process there are both, computational and physical validations and there is the need of improving computational studies by understanding the physics of each component. Viscoelastic characteristics of materials can be represented by Prony series, also known as relaxation modulus in function of time. Relaxation modulus can be defined in most of Computer Aided Engineering (CAE) Software. In this article the procedure for calculating Prony Series from DMA data will be explained.

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