Determining the parameters of the fractional exponential heredity kernels of linear viscoelastic materials

The parameters of the fractional exponential creep and relaxation kernels of linear viscoelastic materials are determined. Methods that approximate the kernel by using the Mittag-Leffler function, the Laplace-Carson transform, and direct approximation of the creep function by the original equation are analyzed. The parameters of fractional exponential kernels are determined for aramid fibers, parapolyamide fibers, glass-reinforced plastic, and polymer concrete. It is shown that the kernel parameters calculated through the direct approximation of the creep function provide the best agreement between theory and experiment. The methods are experimentally validated for constant-stress and variable-stress loading in the modes of additional loading and complete unloading.