Four-Parameter Viscoelastic Model for the Plates of Uniformly Varying Cross-Section

2018 ◽  
Vol 382 ◽  
pp. 196-200
Author(s):  
Gülçin Tekin ◽  
Fethi Kadıoğlu
Keyword(s):  
Cross Section ◽  
Mixed Finite Element ◽  
Viscoelastic Model ◽  
Material Behavior ◽  
Solid Model ◽  
Static Response ◽  
Kirchhoff Plates ◽  
Inverse Transform ◽  
Linear Viscoelastic Material ◽  
Linear Viscoelastic

This study aims to investigate the quasi-static response of linear viscoelastic Kirchhoff plates of uniformly varying cross-section subjected to time-dependent loads. Four-parameter solid model is used for defining the linear viscoelastic material behavior. Through an efficient systematic procedure based on the Gâteaux Differential (GD), a functional has been constructed for the analysis. For the analysis, mixed finite element (MFE) method in transformed Laplace-Carson space is used. For transformation of the solutions obtained in the Laplace-Carson domain to the real time domain, Dubner & Abate (D&A) numerical inverse transform technique is employed.

An Approach to Characterize Nonlinear Viscoelastic Material Behavior Using Dynamic Mechanical Tests and Analyses

1999 ◽  
Vol 66 (4) ◽  
pp. 872-878 ◽  
Author(s):  
H. J. Golden ◽  
T. W. Strganac ◽  
R. A. Schapery
Keyword(s):  
Viscoelastic Model ◽  
Dynamic Test ◽  
Mechanical Analysis ◽  
Mechanical Tests ◽  
Material Behavior ◽  
Dynamic Mechanical ◽  
Nonlinear Characterization ◽  
Nonlinear Viscoelastic ◽  
Linear Viscoelastic ◽  
Nonlinear Viscoelastic Model

Linear viscoelastic properties may be rapidly identified using dynamic mechanical analysis methods, yet these traditional methods do not properly identify nonlinear viscoelastic response. Herein, dynamic mechanical methodologies are extended to provide an approach for nonlinear characterization. The proposed method is based on Schapery's nonlinear viscoelastic model extended to dynamic mechanical theory. The oscillatory loading during a dynamic test is addressed within the nonlinear viscoelastic model. An experimental protocol is established. Analyses and experiments are performed for the characterization of thin-film polyethylene to validate the approach.

On the Development of Creep Laws for Rubber in the Parallel Rheological Framework

2019 ◽  
Vol 47 (1) ◽  
pp. 2-30 ◽  
Author(s):  
Gautam Sagar ◽  
Dong Zheng ◽  
Anuwat Suwannachit ◽  
Maik Brinkmeier ◽  
Kristin Fietz ◽  
...  
Keyword(s):  
Complex Modulus ◽  
Dynamic Stiffness ◽  
Viscoelastic Model ◽  
American Chemical Society ◽  
Small Strain ◽  
Chemical Society ◽  
Material Behavior ◽  
Constitutive Law ◽  
Rate Dependency ◽  
Linear Viscoelastic

ABSTRACT It is widely known that filler-reinforced rubber material in tires shows a very complicated material behavior when subjected to cyclic loadings. One of the most interesting effects for rolling tires is the nonlinear rate-dependent behavior, which is implicitly linked to the amplitude dependency of dynamic stiffness (Payne effect) at a given frequency and temperature. This effect, however, cannot be described by a conventional linear viscoelastic constitutive law, e.g., the Prony series model. Several nonlinear viscoelastic material models have been proposed in the last decades. Among others, Lapczyk et al. (Lapczyk, I., Hurtado, J. A., and Govindarajan, S. M., “A Parallel Rheological Framework for Modeling Elastomers and Polymers,” 182nd Technical Meeting of the Rubber Division of the American Chemical Society, Cincinnati, Ohio, October 2012) recently proposed a quite general framework for the class of nonlinear viscoelasticity, called parallel rheological framework (PRF), which is followed by Abaqus. The model has an open option for different types of viscoelastic creep laws. In spite of the very attractive nonlinear rate-dependency, the identification of material parameters becomes a very challenging task, especially when a wide frequency and amplitude range is of interest. This contribution points out that the creep law is numerically sound if it can be degenerated to the linear viscoelastic model at a very small strain amplitude, which also significantly simplifies model calibration. More precisely, the ratio between viscoelastic stress and strain rate has to converge to a certain value, i.e., the viscosity in a linear viscoelastic case. The creep laws implemented in Abaqus are discussed in detail here, with a focus on their fitting capability. The conclusion of the investigation consequently gives us a guideline to develop a new creep law in PRF. Here, one creep law from Abaqus that meets the requirements of our guideline has been selected. A fairly good fit of the model is shown by the comparison of the simulated complex modulus in a wide frequency and amplitude range with experimental results.

Solution of Viscoelastic Stress Analysis Problems Using Measured Creep or Relaxation Functions

1963 ◽  
Vol 30 (1) ◽  
pp. 127-133 ◽  
Author(s):  
E. H. Lee ◽  
T. G. Rogers
Keyword(s):  
Stress Analysis ◽  
Integral Equations ◽  
Creep Compliance ◽  
Relaxation Modulus ◽  
Material Behavior ◽  
Relaxation Functions ◽  
Analysis Theory ◽  
Linear Viscoelastic Material ◽  
Linear Viscoelastic ◽  
Improved Technique

Stress analysis problems for linear viscoelastic material behavior are solved on the basis of integral operator stress-strain relations. These characterize the material by relaxation modulus functions or creep compliances which are directly measurable over finite time ranges, and completely describe material behavior for stress determinations for the same duration. The stress analysis theory can lead to integral equations which are shown to be soluble with high accuracy by simple finite-difference numerical integration procedures. Examples are presented and compared with solutions obtained by other methods. A possible improved technique for relaxation modulus and creep compliance measurements is suggested, based on the method presented for numerical solution of the integral equations.

Creep Ovalization and Buckling of a Linear Viscoelastic Externally Pressurized Pipe

2004 ◽  
Vol 126 (2) ◽  
pp. 208-215 ◽  
Author(s):  
Carl H. Popelar ◽  
Donald Evans
Keyword(s):  
Cross Section ◽  
Viscoelastic Material ◽  
Inversion Method ◽  
Analysis Model ◽  
Initial Shape ◽  
Simple Estimate ◽  
Material Parameters ◽  
Linear Viscoelastic Material ◽  
Linear Viscoelastic ◽  
Good Agreement

An analysis model is developed for the creep ovalization and buckling of an imperfect plastic pipe subjected to a uniform external pressure. The pipe’s cross section is assumed to have a known initial out of roundness or ovality and to be composed of a linear viscoelastic material. The governing equations are transformed using Laplace and Carson transforms. The transformed deviation of the cross section from its initial shape is inverted exactly by evaluating the Bromwich integral and approximately by the simpler direct inversion method. The two inversion methods, which yield nearly identical results, are compared with the quasi-elastic method wherein the elastic modulus in the solution to the equivalent elastic problem is replaced by the relaxation modulus. The model predictions are quite sensitive to the viscoelastic material parameters for small values of the relaxation exponent and this sensitivity has direct implications with respect to the reliability of the predicted life expectancy for the pipe. Predictions and measurements made in creep ovalization tests of a high density polyethylene (HDPE) pipe at 50°C and different pressures are compared. Very good agreement is obtained between predicted and measured response in short-term tests and in an extended test. Bi-directional shifting is used to translate inferred material parameters at 50°C to 35°C for making comparisons of predictions with measurements at the latter temperature. While the predicted ovalization overestimates the measurement, very good agreement is obtained when one material parameter is decreased by 10% and the other is increased by 7%; thereby demonstrating the sensitivity of the predictions to small changes in the material parameters for small values of the relaxation exponent. The efficacy of a simple estimate for the limiting creep buckling or collapse pressure as a function of the design life is presented and compared with measurements.

Determination of Singular Residual Stresses in Epoxy Layer Deposited on Concrete Substrate

2005 ◽  
Vol 297-300 ◽  
pp. 1277-1284
Author(s):  
Sang Soon Lee
Keyword(s):  
Coating Layer ◽  
Viscoelastic Model ◽  
Stress Singularity ◽  
Epoxy Coating ◽  
Moisture Effects ◽  
Linear Viscoelastic Material ◽  
Linear Viscoelastic ◽  
Hygrothermal Stress ◽  
Local Yielding

This paper deals with the hygrothermal stress singularity induced at the interface corner between the epoxy coating layer and the concrete substrate as the coating layer absorbs hot moisture from the ambient environment. The epoxy layer is assumed to be a linear viscoelastic material and to be theromorheologically simple. It is further assumed that moisture effects are analogous to thermal effects. The viscoelastic boundary element method is employed to investigate the behavior of interface stresses. The order of the singularity is obtained numerically for a given viscoelastic model. The numerical results exhibit the relaxation of interface stresses and large stress gradients are observed in the vicinity of the free surface. Since the exceedingly large stresses cannot be borne by the epoxy coating layer, local yielding or the delamination can occur at the interface corner.

Parameter Estimation Using the Quasi-Linear Viscoelastic Model Proposed by Fung

1984 ◽  
Vol 106 (3) ◽  
pp. 198-203 ◽  
Author(s):  
L. J. M. G. Dortmans ◽  
A. A. H. J. Sauren ◽  
E. P. M. Rousseau
Keyword(s):  
Viscoelastic Model ◽  
Biological Tissues ◽  
Step Change ◽  
Dependent Behavior ◽  
Special Cases ◽  
Linear Viscoelastic Material ◽  
Linear Viscoelastic ◽  
Relaxation Experiments ◽  
Parameter Values ◽  
Linear Viscoelastic Model

Using the quasi-linear viscoelastic model proposed by Fung for the description of the viscoelastic properties of soft biological tissues, the parameters governing their time-dependent behavior are commonly estimated from relaxation experiments. Exact quantification is possible from the response to a step change in the strain. Since it is physically impossible to realize a true step change in the strain, in practice the response to a steplike strain change is used. In the present study the discrepancies between the exact and the estimated parameter values are investigated using a hypothetical quasi-linear viscoelastic material. The parameter τ1, governing the fast viscous phenomena, is found to be subject to the largest errors. Methods for obtaining better estimates of τ1 are outlined in a number of special cases.

scholarly journals On the Time-Dependent Behavior of FGM Plates

2008 ◽  
Vol 399 ◽  
pp. 63-70 ◽  
Author(s):  
Holm Altenbach ◽  
Victor A. Eremeyev
Keyword(s):  
Material Properties ◽  
Plate Theory ◽  
Functionally Graded ◽  
Material Behavior ◽  
Time Dependent ◽  
Classical Plate Theory ◽  
Graded Materials ◽  
Dependent Behavior ◽  
Linear Viscoelastic Material ◽  
Linear Viscoelastic

A non-classical plate theory based on the direct approach is introduced and applied to plates composed of functionally graded materials (FGM). The governing two-dimensional equations are formulated for a deformable surface, the viscoelastic stiffness parameters are identified assuming linear-viscoelastic material behavior. In addition, the material properties are changing in the thickness direction. Solving some problems of the global structural analysis it can be shown that in some cases the results based on the presented theory significantly differ from the results based on the Kirchhofftype theory.

Modeling of Tread Block Contact Mechanics Using Linear Viscoelastic Theory3

2008 ◽  
Vol 36 (3) ◽  
pp. 211-226 ◽  
Author(s):  
F. Liu ◽  
M. P. F. Sutcliffe ◽  
W. R. Graham
Keyword(s):  
High Speed ◽  
Slip Rate ◽  
Material Model ◽  
Contact Forces ◽  
Block Modeling ◽  
Rate Dependent ◽  
Linear Viscoelastic Material ◽  
Linear Viscoelastic ◽  
The Impact ◽  
Good Agreement

Abstract In an effort to understand the dynamic hub forces on road vehicles, an advanced free-rolling tire-model is being developed in which the tread blocks and tire belt are modeled separately. This paper presents the interim results for the tread block modeling. The finite element code ABAQUS/Explicit is used to predict the contact forces on the tread blocks based on a linear viscoelastic material model. Special attention is paid to investigating the forces on the tread blocks during the impact and release motions. A pressure and slip-rate-dependent frictional law is applied in the analysis. A simplified numerical model is also proposed where the tread blocks are discretized into linear viscoelastic spring elements. The results from both models are validated via experiments in a high-speed rolling test rig and found to be in good agreement.

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