Response analysis of six-parameter fractional constitutive model

In this paper, a six-parameter fractional constitutive model was investigated by using the Laplace transform and its complex inverse formula. Our model includes all of the four types of viscoelasticity by the different values of two coefficients. We expressed the creep compliance and relaxation modulus as infinite real integrals which can be numerically calculated readily by the built-in numerical quadrature command of MATHEMATICA 11. Also, the infinite integration in the form of integral(+infinity)(0) P(r)e(-rt)dr is convenient for numerical computation and theory analysis. Finally, the stress responses to harmonic strain were considered and the stress-strain hysteresis loops were displayed.