Comparative Analysis of Viscoelastic Models for Head-Tissue Layers under Step Loading

Abstract This study compares four linear viscoelastic networks for scalp, skull, cerebrospinal fluid, and brain contributions. An eight-element parallel network describes stress relaxation, while an eight-element series network describes creep. Reduced Maxwell and Kelvin models are evaluated alongside these configurations. Closed-form equations connect the spring–dashpot arrangements to their response curves. Under a 5% step strain, the parallel network relaxes from 400.835 to 400.334 MPa, a decrease of about 0.125%. The skull spring accounts for most of the stress. At a held stress of 24.010 kPa, the series network approaches a strain rate of 4802.05 s−1 because its free dashpots sustain flow. The reduced Kelvin network gives bounded creep with a 7 ms time constant. Its strain reaches 14.6224 at 0.1 s, exceeding the small-strain range at the selected load. The three-element Maxwell approximation closely follows the total relaxation stress, with a maximum difference of 0.015082 MPa. Comparison of the normalized relaxing components reveals the difference in decay rates. The findings connect network structure, material inputs, and loading to the resulting relaxation and creep behavior, providing a basis for further development of reduced head-tissue models.