Model analysis of nonlinear viscoelastic behaviour by use of a single integral constitutive equation: Stresses and birefringence of a polystyrene melt in intermittent shear flows

1979 ◽  
Vol 18 (5) ◽  
pp. 615-622 ◽  
Author(s):  
H. M. Laun ◽  
M. H. Wagner ◽  
H. Janeschitz-Kriegl
Keyword(s):  
Constitutive Equation ◽  
Shear Flows ◽  
Model Analysis ◽  
Viscoelastic Behaviour ◽  
Polystyrene Melt ◽  
Nonlinear Viscoelastic ◽  
Single Integral ◽  
Integral Constitutive Equation

A Single‐Integral Constitutive Equation

1969 ◽  
Vol 13 (1) ◽  
pp. 103-109 ◽  
Author(s):  
Alden H. Emery ◽  
Michael L. White
Keyword(s):  
Constitutive Equation ◽  
Single Integral ◽  
Integral Constitutive Equation

A relation between shear flow material functions for a single-integral constitutive equation

1984 ◽  
Vol 23 (3) ◽  
pp. 250-254 ◽  
Author(s):  
J. Stastna ◽  
D. De Kee
Keyword(s):  
Constitutive Equation ◽  
Shear Flow ◽  
Material Functions ◽  
Single Integral ◽  
Integral Constitutive Equation

scholarly journals Nonlinear viscoelastic constitutive model for bovine liver tissue

2020 ◽  
Vol 19 (5) ◽  
pp. 1641-1662 ◽  
Author(s):  
Adela Capilnasiu ◽  
Lynne Bilston ◽  
Ralph Sinkus ◽  
David Nordsletten
Keyword(s):  
Constitutive Equation ◽  
Liver Tissue ◽  
Motor Vehicle ◽  
Bovine Liver ◽  
Disease Diagnosis ◽  
Tissue Response ◽  
Viscoelastic Behaviour ◽  
Biomechanical Models ◽  
Nonlinear Viscoelastic ◽  
Viscoelastic Constitutive Model

Abstract Soft tissue mechanical characterisation is important in many areas of medical research. Examples span from surgery training, device design and testing, sudden injury and disease diagnosis. The liver is of particular interest, as it is the most commonly injured organ in frontal and side motor vehicle crashes, and also assessed for inflammation and fibrosis in chronic liver diseases. Hence, an extensive rheological characterisation of liver tissue would contribute to advancements in these areas, which are dependent upon underlying biomechanical models. The aim of this paper is to define a liver constitutive equation that is able to characterise the nonlinear viscoelastic behaviour of liver tissue under a range of deformations and frequencies. The tissue response to large amplitude oscillatory shear (1–50%) under varying preloads (1–20%) and frequencies (0.5–2 Hz) is modelled using viscoelastic-adapted forms of the Mooney–Rivlin, Ogden and exponential models. These models are fit to the data using classical or modified objective norms. The results show that all three models are suitable for capturing the initial nonlinear regime, with the latter two being capable of capturing, simultaneously, the whole deformation range tested. The work presented here provides a comprehensive analysis across several material models and norms, leading to an identifiable constitutive equation that describes the nonlinear viscoelastic behaviour of the liver.

Bulge initiation in tubes of time-dependent materials

2015 ◽  
Vol 22 (4) ◽  
pp. 636-648 ◽  
Author(s):  
Alan S Wineman
Keyword(s):  
Constitutive Equation ◽  
Linear Viscoelasticity ◽  
Time Dependent ◽  
Branching Time ◽  
Deformation History ◽  
Thermally Induced ◽  
Relaxation Effects ◽  
Non Linear ◽  
Single Integral ◽  
Integral Constitutive Equation

This work considers the inflation and extension of an elastomeric tubular membrane when its material exhibits a time-dependent response. Three different models for time-dependent response are considered: finite linear viscoelasticity, Pipkin–Rogers non-linear viscoelasticity, and thermally induced chemorheological degradation. The first two are based on different assumptions about stress relaxation effects while the third accounts for time-dependent microstructural changes due to simultaneous scission and re-cross-linking of macromolecular network junctions. Each of these models describes a material response that softens with time. It is shown that the constitutive equations for all three models are included in a general non-linear single-integral constitutive equation. In previous work, for elastic membranes, the material is fixed and a localized bulge may form as the load increases. In this work, the load is specified, and a localized bulge may form as the membrane material undergoes a time-dependent response. It is assumed that the extension and inflation histories are initially uniform, but there may be a time when a localized bulge-like deformation starts to form. This is treated as branching from the uniform extension and inflation history. For times beyond this ‘branching time’, the governing equations are satisfied by both the continuation of the initial uniform deformation history and the branched deformation history for the bulge. A unified condition for determining this branching time, applicable to all three models, is derived in terms of the general non-linear single-integral constitutive equation. Post-branching response is not considered here.

Modeling nonlinear rheology of unentangled polymer melts based on a single integral constitutive equation

2020 ◽  
Vol 64 (1) ◽  
pp. 129-140 ◽  
Author(s):  
Esmaeil Narimissa ◽  
Manfred H. Wagner
Keyword(s):  
Constitutive Equation ◽  
Polymer Melts ◽  
Nonlinear Rheology ◽  
Single Integral ◽  
Integral Constitutive Equation
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