Definition and Application of Linear Viscoelastic Unit Slope Response Functions for Efficiently Dealing with Piecewise Linear Excitations on Asphaltic Materials

Abstract

Relaxation modulus (RM) and creep compliance (CC) are two characteristic functions of a linear viscoelastic (LVE) material in the time domain, respectively defined as the responses of the stress and strain caused by the unit step functions of the strain and stress. When handling excitation histories other than the step function such as the linear excitation that is widely used in destructive and nondestructive tests, formulations based on RM or CC functions are rather cumbersome with a large number of time-shifted functions being created upon time discretization. This causes substantial difficulties in terms of handling and computing efforts for the resolution of inverse problems wherein the LVE characteristics must be back-calculated from the measured responses of the material. In this paper, new LVE functions that are more suited to piecewise linear excitations were defined as the stress and strain responses caused by the linear function using a unit rate of excitation called the unit slope response (SR) functions. It was demonstrated that the newly defined functions are just the time-domain integrals of the RM and CC functions and possess all fundamental properties of an LVE function, such as monotonic variation, time-frequency, and time-temperature interconvertibility. Numerical and experimental examples were also performed to verify the validity of the proposed formulation, and the obtained results showed that using the unit SR functions significantly improved the computing efficiency, and a better level of accuracy was gained.