Development of a new interconversion tool for hot mix asphalt (HMA) linear viscoelastic functions

2010 ◽  
Vol 37 (8) ◽  
pp. 1071-1081 ◽  
Author(s):  
Sheng Hu ◽  
Fujie Zhou
Keyword(s):  
Hot Mix Asphalt ◽  
Least Squares Method ◽  
Complex Modulus ◽  
Relaxation Modulus ◽  
Original Data ◽  
Prony Series ◽  
Practical Applications ◽  
Original Curve ◽  
Linear Viscoelastic ◽  
Key Steps

The relaxation modulus E(t), creep compliance D(t), and complex modulus E*(ω) are functions often used to characterize the linear viscoelastic (LVE) behavior of hot mix asphalt (HMA). Interconversions among these LVE functions are often required. To perform an interconversion, one of the key steps is to express both the source and target LVE functions in Prony series representations. To obtain the corresponding Prony series coefficients, the collocation method and linear least squares method were often used in the past. However, the problem encountered with these two methods is in manually assigning part of the Prony series coefficients; resulting in unrealistic or negative Prony coefficients and big discrepancies between the fitting data and the original data. To address this problem, this paper developed a new algorithm by incorporating the Levenberg–Marquardt method. This new algorithm has four unique features, it (1) allows all the Prony series coefficients to be freely adjustable, (2) guarantees all positive Prony series coefficients, (3) determines all Prony series coefficients automatically and simultaneously, and (4) ensures very accurate interconversion through the fact that the fitting curve almost completely coincides with the original curve. Furthermore, to facilitate the implementation of practical applications of this new algorithm, it was incorporated into a stand-alone, windows-based software named “LVEmaster”. The simplicity and accuracy of this new interconversion software was demonstrated through a series of interconversions among HMA LVE functions.

Interconversions between linear viscoelastic functions with a time-dependent bulk modulus

2017 ◽  
Vol 23 (6) ◽  
pp. 879-895 ◽  
Author(s):  
Dao-Long Chen ◽  
Tz-Cheng Chiu ◽  
Tei-Chen Chen ◽  
Ping-Feng Yang ◽  
Sheng-Rui Jian
Keyword(s):  
Bulk Modulus ◽  
Relaxation Modulus ◽  
Time Dependent ◽  
Reasonable Assumption ◽  
Prony Series ◽  
Relaxation Rates ◽  
Unknown Parameters ◽  
Linear Viscoelastic ◽  
Shear Relaxation ◽  
Increasing Function

The interconversion relations for viscoelastic functions are derived with the consideration of the time-dependent bulk modulus, K( t), for both traditional and fractional Prony series representations of viscoelasticity. The application of these relations is to replace the fitting parameters of Young’s relaxation modulus, E( t), by the unknown parameters of K( t) and the known parameters of the shear relaxation modulus, G( t), and to fit the E( t) to the experimental data for obtaining the parameters of K( t). The fitting results show that only two experiments for measuring the viscoelastic functions of an isotropic material are not enough to determine the other viscoelastic functions. However, if we consider the relaxation rates of K( t) and G( t), we may conclude that the constant bulk modulus is a more reasonable assumption, and the corresponding Poisson’s ratio, ν( t), is a monotonic-increasing function.

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.

scholarly journals Comparison of Relaxation Modulus Converted from Frequency- and Time-Dependent Viscoelastic Functions through Numerical Methods

2018 ◽  
Vol 8 (12) ◽  
pp. 2447 ◽  
Author(s):  
Weiguang Zhang ◽  
Bingyan Cui ◽  
Xingyu Gu ◽  
Qiao Dong
Keyword(s):  
Least Squares ◽  
Collocation Method ◽  
Creep Compliance ◽  
Least Squares Method ◽  
Relaxation Modulus ◽  
Prony Series ◽  
Significant Difference ◽  
Time Region ◽  
The Difference ◽  
Reduced Time

Due to the difficulty of obtaining relaxation modulus directly from experiments, many interconversion methods from other viscoelastic functions to relaxation modulus were developed in previous years. The objectives of this paper were to analyze the difference of relaxation modulus converted from dynamic modulus and creep compliance and explore its potential causes. The selected methods were the numerical interconversions based on Prony series representation. For the dynamic to relaxation conversion, the time spectrum was determined by the collocation method. Meanwhile, for the creep to relaxation conversion, both the collocation method and least squares method were adopted to perform the Laplace transform. The results show that these two methods do not present a significant difference in estimating relaxation modulus. Their difference mostly exists in the transient reduced time region. Calculating the average of two methods is suggested to avoid great deviation of single experiment. To predict viscoelastic responses from creep compliance, the collocation method yields comparable results to the least squares method. Thus, simply-calculated collocation method may be preferable in practice. Further, the master curve pattern is sensitive to the Prony series coefficients. The difference in transient reduced time region may be attributed to the indeterminate Prony series coefficients.

Dynamic, Regional Mechanical Properties of the Porcine Brain: Indentation in the Coronal Plane

2011 ◽  
Vol 133 (7) ◽  
Author(s):  
Benjamin S. Elkin ◽  
Ashok Ilankova ◽  
Barclay Morrison
Keyword(s):  
Large Strain ◽  
Series Representation ◽  
Relaxation Modulus ◽  
Short Time Scale ◽  
Prony Series ◽  
Porcine Brain ◽  
Linear Viscoelastic ◽  
Viscoelastic Theory ◽  
Linear Viscoelastic Theory ◽  
Anatomic Region

Stress relaxation tests using a custom designed microindentation device were performed on ten anatomic regions of fresh porcine brain (postmortem time <3 h). Using linear viscoelastic theory, a Prony series representation was used to describe the shear relaxation modulus for each anatomic region tested. Prony series parameters fit to load data from indentations performed to ∼10% strain differed significantly by anatomic region. The gray and white matter of the cerebellum along with corpus callosum and brainstem were the softest regions measured. The cortex and hippocampal CA1/CA3 were found to be the stiffest. To examine the large strain behavior of the tissue, multistep indentations were performed in the corona radiata to strains of 10%, 20%, and 30%. Reduced relaxation functions were not significantly different for each step, suggesting that quasi-linear viscoelastic theory may be appropriate for representing the nonlinear behavior of this anatomic region of porcine brain tissue. These data, for the first time, describe the dynamic and short time scale behavior of multiple anatomic regions of the porcine brain which will be useful for understanding porcine brain injury biomechanics at a finer spatial resolution than previously possible.

Interconversion of Frequency Domain Complex Modulus to Time Domain Modulus and Compliance of Asphalt Concrete: Numerical Modeling and Laboratory Validation

2016 ◽  
Author(s):  
A. S. M. Asifur Rahman ◽  
Rafiqul A. Tarefder
Keyword(s):  
Viscoelastic Material ◽  
Asphalt Concrete ◽  
Creep Compliance ◽  
Complex Modulus ◽  
Relaxation Modulus ◽  
Modulus Function ◽  
Approximate Methods ◽  
Material Functions ◽  
Linear Viscoelastic Material ◽  
Linear Viscoelastic

Viscoelastic material functions such as time domain functions, such as, relaxation modulus and creep compliance, or frequency domain function, such as, complex modulus can be used to characterize the linear viscoelastic behavior of asphalt concrete in modeling and analysis of pavement structure. Among these, the complex modulus has been adopted in the recent pavement Mechanistic-Empirical (M-E) design software AASHTOWare-ME. However, for advanced analysis of pavement, such as, use of finite element method requires that the complex modulus function to be converted into relaxation modulus or creep compliance functions. There are a number of exact or approximate methods available in the literature to convert complex modulus function to relaxation modulus or creep compliance functions. All these methods (i.e. exact or approximate methods) are applicable for any linear viscoelastic material up to a certain level of accuracy. However, the applicability and accuracy of these interconversion methods for asphalt concrete material were not studied very much in the past and thus question arises if these methods are even applicable in case of asphalt concrete, and if so, what is the precision level of the interconversion method being used. Therefore, to investigate these facts, this study undertaken an effort to validate a numerical interconversion technique by conducting representative laboratory tests. Cylindrical specimens of asphalt concrete were prepared in the laboratory for conducting complex modulus, relaxation modulus, and creep compliance tests at different test temperatures and loading rates. The time-temperature superposition principle was applied to develop broadband linear viscoelastic material functions. A numerical interconversion technique was used to convert complex modulus function to relaxation modulus and creep compliance functions, and hence, the converted relaxation modulus and creep compliance are compared to the laboratory tested relaxation modulus and creep compliance functions. The comparison showed good agreement with the laboratory test data. Toward the end, a statistical evaluation was conducted to determine if the interconverted material functions are similar to the laboratory tested material functions.

Relationships Among Rate-Dependent Stiffnesses of Asphalt Concrete Using Laboratory and Field Test Methods

1998 ◽  
Vol 1630 (1) ◽  
pp. 3-9 ◽  
Author(s):  
Jo Sias Daniel ◽  
Y. Richard Kim
Keyword(s):  
Asphalt Concrete ◽  
Creep Compliance ◽  
Complex Modulus ◽  
Relaxation Modulus ◽  
Test Methods ◽  
Rate Dependent ◽  
Creep Stiffness ◽  
Linear Viscoelastic ◽  
Linear Viscoelastic Theory ◽  
Falling Weight

As the application of nondestructive testing on pavements in service becomes more frequent, it is increasingly important to relate the resulting stiffnesses to those from laboratory test methods. The relationship among stiffnesses measured from five test methods currently used for asphalt concrete is addressed: creep compliance, complex modulus, impact resonance, falling weight deflectometer, and surface wave. Established relationships from linear viscoelastic theory are used to relate stiffnesses, including a comparison of creep stiffness, S( t), and relaxation modulus, E( t), calculated from creep compliance, D( t). Using laboratory and field measured stiffnesses, a linear relationship was discovered between stiffness and frequency on a log-log scale.

Relaxation modulus—complex modulus interconversion for linear viscoelastic materials

2012 ◽  
Vol 17 (3) ◽  
pp. 465-479 ◽  
Author(s):  
Jon García-Barruetabeña ◽  
Fernando Cortés ◽  
José Manuel Abete ◽  
Pelayo Fernández ◽  
María Jesús Lamela ◽  
...  
Keyword(s):  
Complex Modulus ◽  
Relaxation Modulus ◽  
Viscoelastic Materials ◽  
Linear Viscoelastic

STRESS RELAXATION OF MAGNETORHEOLOGICAL FLUIDS

2002 ◽  
Vol 16 (17n18) ◽  
pp. 2655-2661
Author(s):  
W. H. LI ◽  
G. CHEN ◽  
S. H. YEO ◽  
H. DU
Keyword(s):  
Stress Relaxation ◽  
Viscoelastic Model ◽  
Relaxation Modulus ◽  
Damping Function ◽  
Mr Fluids ◽  
Large Step ◽  
Linear Viscoelastic ◽  
Predicted Values ◽  
Two Parameters ◽  
Step Strain

In this paper, the experimental and modeling study and analysis of the stress relaxation characteristics of magnetorheological (MR) fluids under step shear are presented. The experiments are carried out using a rheometer with parallel-plate geometry. The applied strain varies from 0.01% to 100%, covering both the pre-yield and post-yield regimes. The effects of step strain, field strength, and temperature on the stress modulus are addressed. For small step strain ranges, the stress relaxation modulus G(t,γ) is independent of step strain, where MR fluids behave as linear viscoelastic solids. For large step strain ranges, the stress relaxation modulus decreases gradually with increasing step strain. Morever, the stress relaxation modulus G(t,γ) was found to obey time-strain factorability. That is, G(t,γ) can be represented as the product of a linear stress relaxation G(t) and a strain-dependent damping function h(γ). The linear stress relaxation modulus is represented as a three-parameter solid viscoelastic model, and the damping function h(γ) has a sigmoidal form with two parameters. The comparison between the experimental results and the model-predicted values indicates that this model can accurately describe the relaxation behavior of MR fluids under step strains.

Sign in / Sign up

Export Citation Format

Share Document