A generalization of the Boltzmann superposition principle to polymer networks undergoing scission

1976 ◽  
Vol 64 (1) ◽  
pp. 430-430 ◽  
Author(s):  
J. Moacanin ◽  
J. J. Aklonis ◽  
R. F. Landel
Keyword(s):  
Superposition Principle ◽  
Polymer Networks ◽  
Boltzmann Superposition Principle

Stability Properties of a Viscoelastic Column Under a Periodic Force

1992 ◽  
Vol 59 (1) ◽  
pp. 16-19 ◽  
Author(s):  
G. Cederbaum ◽  
M. Mond
Keyword(s):  
Superposition Principle ◽  
Viscoelastic Behavior ◽  
Equation Of Motion ◽  
Stable System ◽  
Elastic Model ◽  
Periodic Force ◽  
Stability Properties ◽  
Viscoelastic Column ◽  
The Stability ◽  
Boltzmann Superposition Principle

The dynamic stability of a viscoelastic column subjected to a periodic longitudinal load is investigated. The viscoelastic behavior is given in terms of the Boltzmann superposition principle which yields an integro-differential equation of motion. The stability boundaries of this equation are determined analytically by using the multiplescales method. It is shown that due to the viscoelasticity the stability regions are expanded, relative to the elastic ones, and the time for which a stable system becomes unstable is given. In addition, the stability properties of the viscoelastic column are time dependent and an initially stable system can turn unstable after a finite time, unlike columns that are described by the elastic model.

Lifetime Prediction of Tires with Regard to Oxidative Aging5

2008 ◽  
Vol 36 (1) ◽  
pp. 63-79 ◽  
Author(s):  
L. Nasdala ◽  
Y. Wei ◽  
H. Rothert ◽  
M. Kaliske
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Temperature Distribution ◽  
Superposition Principle ◽  
Accelerated Aging ◽  
Material Model ◽  
Aging Behavior ◽  
Element Analysis ◽  
Material Parameters ◽  
Reaction Processes

Abstract It is a challenging task in the design of automobile tires to predict lifetime and performance on the basis of numerical simulations. Several factors have to be taken into account to correctly estimate the aging behavior. This paper focuses on oxygen reaction processes which, apart from mechanical and thermal aspects, effect the tire durability. The material parameters needed to describe the temperature-dependent oxygen diffusion and reaction processes are derived by means of the time–temperature–superposition principle from modulus profiling tests. These experiments are designed to examine the diffusion-limited oxidation (DLO) effect which occurs when accelerated aging tests are performed. For the cord-reinforced rubber composites, homogenization techniques are adopted to obtain effective material parameters (diffusivities and reaction constants). The selection and arrangement of rubber components influence the temperature distribution and the oxygen penetration depth which impact tire durability. The goal of this paper is to establish a finite element analysis based criterion to predict lifetime with respect to oxidative aging. The finite element analysis is carried out in three stages. First the heat generation rate distribution is calculated using a viscoelastic material model. Then the temperature distribution can be determined. In the third step we evaluate the oxygen distribution or rather the oxygen consumption rate, which is a measure for the tire lifetime. Thus, the aging behavior of different kinds of tires can be compared. Numerical examples show how diffusivities, reaction coefficients, and temperature influence the durability of different tire parts. It is found that due to the DLO effect, some interior parts may age slower even if the temperature is increased.

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