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.

Obtaining shear relaxation modulus and creep compliance of linear viscoelastic materials from instrumented indentation using axisymmetric indenters of power-law profiles

2009 ◽  
Vol 24 (10) ◽  
pp. 3013-3017 ◽  
Author(s):  
Yang-Tse Cheng ◽  
Fuqian Yang
Keyword(s):  
Inverse Problem ◽  
Laplace Transform ◽  
Power Law ◽  
Creep Compliance ◽  
Relaxation Modulus ◽  
Instrumented Indentation ◽  
Loading Paths ◽  
Linear Viscoelastic ◽  
Shear Relaxation ◽  
Analytical Expressions

Using Laplace transform, we solve the inverse problem of obtaining the shear relaxation modulus and creep compliance of linear viscoelastic solids from indentation by axisymmetric indenters of power-law profiles. We identify several simple, though nontrivial, loading paths for carrying out indentation measurements such that the inverse problem has analytical solutions. We show that the shear relaxation modulus and creep compliance may be readily obtained using the newly derived analytical expressions together with proposed indentation loading paths.

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.

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.

scholarly journals Application of micro-computer tomography and inverse finite element analysis for characterizing the visco-hyperelastic response of bulk liver tissue using indentation

2021 ◽  
Vol 3 (5) ◽  
Author(s):  
Rajeswara R. Resapu ◽  
Roger D. Bradshaw
Keyword(s):  
Finite Element ◽  
Liver Tissue ◽  
Loading Rate ◽  
Time Dependent ◽  
Nonlinear Material ◽  
Computational Time ◽  
List Type ◽  
Prony Series ◽  
Time Dependent Behaviour ◽  
Dependent Behaviour

Abstract In-vitro mechanical indentation experimentation is performed on bulk liver tissue of lamb to characterize its nonlinear material behaviour. The material response is characterized by a visco-hyperelastic material model by the use of 2-dimensional inverse finite element (FE) analysis. The time-dependent behaviour is characterized by the viscoelastic model represented by a 4-parameter Prony series, whereas the large deformations are modelled using the hyperelastic Neo-Hookean model. The shear response described by the initial and final shear moduli and the corresponding Prony series parameters are optimized using ANSYS with the Root Mean Square (RMS) error being the objective function. Optimized material properties are validated using experimental results obtained under different loading histories. To study the efficacy of a 2D model, a three dimensional (3D) model of the specimen is developed using Micro-CT of the specimen. The initial elastic modulus of the lamb liver obtained was found to 13.5 kPa for 5% indentation depth at a loading rate of 1 mm/sec for 1-cycle. These properties are able to predict the response at 8.33% depth and a loading rate of 5 mm/sec at multiple cycles with reasonable accuracy. Article highlights The visco-hyperelastic model accurately models the large displacement as well as the time-dependent behaviour of the bulk liver tissue. Mapped meshing of the 3D FE model saves computational time and captures localized displacement in an accurate manner. The 2D axisymmetric model while predicting the force response of the bulk tissue, cannot predict the localized deformations.

Application of a Viscoelastic Model for Polyester Mooring

2010 ◽  
Author(s):  
J. W. Kim ◽  
J. H. Kyoung ◽  
A. Sablok
Keyword(s):  
Material Properties ◽  
Viscoelastic Model ◽  
Practical Method ◽  
Time Dependent ◽  
Mooring Line ◽  
New Model ◽  
Global Performance ◽  
Excitation Period ◽  
Linear Viscoelastic ◽  
Floating Platforms

A new practical method to simulate time-dependent material properties of polyester mooring line is proposed. The time-dependent material properties of polyester rope are modeled with a standard linear solid (SLS) model, which is one of the simplest forms of a linear viscoelastic model. The viscoelastic model simulates most of the mechanical properties of polyester rope such as creep, strain-stress hysteresis and excitation period-dependent stiffness. The strain rate-stress relation of the SLS model has been re-formulated to a stretch-tension relation, which is more suitable for implementation into global performance and mooring analyses tools for floating platforms. The new model has been implemented to a time-domain global performance analysis software and applied to simulate motion of a spar platform with chain-polyester-chain mooring system. The new model provides accurate platform offset without any approximation on the mean environmental load and can simulate the transient effect due to the loss of a mooring line during storm conditions, which has not been possible to simulate using existing dual-stiffness models.

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.

A new pressurizable dilatometer for measuring the time-dependent bulk modulus and pressure-volume-temperature properties of polymeric materials

2009 ◽  
Vol 80 (5) ◽  
pp. 053903 ◽  
Author(s):  
Yan Meng ◽  
Paul Bernazzani ◽  
Paul A. O’Connell ◽  
Gregory B. McKenna ◽  
Sindee L. Simon
Keyword(s):  
Bulk Modulus ◽  
Polymeric Materials ◽  
Time Dependent

Thermoelastic Constitutive Equations for Chemically Hardening Materials

1974 ◽  
Vol 41 (3) ◽  
pp. 652-657 ◽  
Author(s):  
Bernard W. Shaffer ◽  
Myron Levitsky
Keyword(s):  
Bulk Modulus ◽  
Strain Rate ◽  
Chemical Reaction ◽  
Constitutive Equations ◽  
Strain Energy ◽  
Elastic Solid ◽  
Time Dependent ◽  
Component Model ◽  
Two Component ◽  
Potential Applications

Thermoelastic constitutive equations are derived for a material undergoing solidification or hardening as the result of a chemical reaction. The derivation is based upon a two component model whose composition is determined by the degree of hardening, and makes use of strain-energy considerations. Constitutive equations take the form of stress rate-strain rate relations, in which the coefficients are time-dependent functions of the composition. Specific results are developed for the case of a material of constant bulk modulus which undergoes a transition from an initial liquidlike state into an isotropic elastic solid. Potential applications are discussed.

scholarly journals Effect of Preservation Period on the Viscoelastic Material Properties of Soft Tissues With Implications for Liver Transplantation

2010 ◽  
Vol 132 (10) ◽  
Author(s):  
Sina Ocal ◽  
M. Umut Ozcan ◽  
Ipek Basdogan ◽  
Cagatay Basdogan
Keyword(s):  
Liver Transplantation ◽  
Viscoelastic Material ◽  
Material Properties ◽  
Soft Tissues ◽  
Excitation Frequency ◽  
Viscoelastic Model ◽  
Relaxation Modulus ◽  
Bovine Liver ◽  
Dynamic Responses ◽  
Time Dependent

The liver harvested from a donor must be preserved and transported to a suitable recipient immediately for a successful liver transplantation. In this process, the preservation period is the most critical, since it is the longest and most tissue damage occurs during this period due to the reduced blood supply to the harvested liver and the change in its temperature. We investigate the effect of preservation period on the dynamic material properties of bovine liver using a viscoelastic model derived from both impact and ramp and hold experiments. First, we measure the storage and loss moduli of bovine liver as a function of excitation frequency using an impact hammer. Second, its time-dependent relaxation modulus is measured separately through ramp and hold experiments performed by a compression device. Third, a Maxwell solid model that successfully imitates the frequency- and time-dependent dynamic responses of bovine liver is developed to estimate the optimum viscoelastic material coefficients by minimizing the error between the experimental data and the corresponding values generated by the model. Finally, the variation in the viscoelastic material coefficients of bovine liver are investigated as a function of preservation period for the liver samples tested 1 h, 2 h, 4 h, 8 h, 12 h, 24 h, 36 h, and 48 h after harvesting. The results of our experiments performed with three animals show that the liver tissue becomes stiffer and more viscous as it spends more time in the preservation cycle.

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