Linear Viscoelasticity

Carreau, Pierre J.; Kee, Daniel C.R. De; Chhabra, R.P.

doi:10.3139/9781569907238.005

Cited by 1 publication

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“…The Laplace transform made the elastic problem and viscoelastic problem consistent. Thus, the viscoelastic problem could be solved by the elastic method [ 26 , 27 , 28 ], which is named the principle of elastic–viscoelastic correspondence. The Laplace transform is applied to Equation (5), and the expression is in the following form:

where

, and s is the variable of Laplace transform.…”

Section: Linear Viscoelastic Theory and Parameter Conversion Methodsmentioning

confidence: 99%

An Elementary Formula for the Initial Relaxation Modulus from the Creep Compliance for Asphalt Mixtures

Chen,

et al. 2023

Materials

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The conversion between the relaxation modulus and creep compliance is a traditional research topic in viscoelastic materials. Generally, different methods have been used to solve the numerical solution based on convolution theory. However, the initial relaxation modulus (relaxation modulus at t = 0) has been difficult to obtain. This paper aimed to propose a fast calculation method to derive the initial relaxation modulus from the creep compliance. First, three groups of uniaxial static creep tests of asphalt mixtures were conducted to determine the creep compliance of the experimental data. Then, the calculation of the initial relaxation modulus from the creep compliance by three inversion methods (midpoint method, approximate method, and Laplace numerical inversion method) was evaluated. The results indicate that approximate method and Laplace numerical inversion method cannot calculate the initial relaxation modulus value, and the calculation results of the midpoint method can only approach the exact value infinitely, for which calculating the relaxation modulus at 0.0005 s requires 2000 s. The results can only approach the exact value infinitely and take a lot of computing time. Finally, a fast calculation method for the initial relaxation modulus is proposed and verified by Laplace initial value theorem, and this method can directly derive a simple expression for calculating the initial relaxation modulus without requiring computational time. The proposed calculation methods of the initial relaxation modulus for various viscoelastic models were then put forward. The research results provide an effective tool for obtaining the initial relaxation modulus accurately.

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where

, and s is the variable of Laplace transform.…”

Section: Linear Viscoelastic Theory and Parameter Conversion Methodsmentioning

confidence: 99%