Determining with High Accuracy the Relaxation Modulus and Creep Compliance of Asphaltic Materials in the Form of Sums of Exponential Functions from Mathematical Master Curves of Dynamic Modulus

Abstract

According to the physical causality principle, the two components of complex modulus are not independent yet interrelated to each other via Kramers-Kronig relationships. Using two mathematical functions to predict simultaneously the dynamic modulus (DM) and phase angle (PA) generally leads to the violation of the causality principle. Therefore, the calculation of one component based on the other one is a vital task for using mathematical models to predict the linear viscoelastic (LVE) behavior of asphaltic materials. In addition, the relaxation modulus (RM) or the creep compliance (CC) in the form of sums of exponential functions (SEFs) is necessary for the efficient resolution of the stress–strain relationship in the time domain. This paper presented a novel method for calculating with high accuracy the RM and CC in the form of SEFs based on the input DM master curve. First, the midpoint integration scheme was used to calculate the PA based on the exact relationship between the PA and DM. After that, the storage modulus and compliance were computed and decomposed with high accuracy into SEFs using a special technique. Then, the closed-form formula of the RM and CC were derived thanks to the special form function of the storage modulus and compliance. Finally, the special technique was used once again to decompose with high accuracy the RM and CC into SEFs for possible uses in finite-element method (FEM) analysis in the time domain. The results showed that the relative errors of all LVE properties computed were lower than 0.1 percent at all calculating points.