Viscoelastic models revisited: characteristics and interconversion formulas for generalized Kelvin–Voigt and Maxwell models

Singularities in the stress field of the stagnation-point flow of a viscoelastic fluid have been studied for various viscoelastic constitutive models. Analyzing the analytical solutions of these models is the most effective way to study this problem. In this paper, exact analytical solutions of two-dimensional steady wall-free stagnation-point flows for the generic Oldroyd 8-constant model are obtained for the stress field using different material parameter relations. For all solutions, compatibility with the conservation of momentum is considered in our analysis. The resulting solutions usually contain arbitrary functions, whose choice has a crucial effect on the stress distribution. The corresponding singularities are discussed in detail according to the choices of the arbitrary functions. The results can be used to analyze the stress distribution and singularity behavior of a wide spectrum of viscoelastic models derived from the Oldroyd 8-constant model. Many previous results obtained for simple viscoelastic models are reproduced as special cases. Some previous conclusions are amended and new conclusions are drawn. In particular, we find that all models have singularities near the stagnation point and most of them can be avoided by appropriately choosing the model parameters and free functions. In addition, the analytical solution for the stress tensor of a near-wall stagnation-point flow for the Oldroyd-B model is also obtained. Its compatibility with the momentum conservation is discussed and the parameters are identified, which allow for a non-singular solution.

Download Full-text

Identification of Nonlinear Viscoelastic Models of Flexible Polyurethane Foam From Uniaxial Compression Data

Journal of Engineering Materials and Technology ◽

10.1115/1.4032169 ◽

2016 ◽

Vol 138 (2) ◽

Cited By ~ 5

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.

Download Full-text

Viscoelastic Models for Ligaments and Tendons

Applied Mechanics Reviews ◽

10.1115/1.3124424 ◽

1994 ◽

Vol 47 (6S) ◽

pp. S282-S286 ◽

Cited By ~ 1

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.

Download Full-text