On Implementation of a Finite Element Visco-Hyperelastic Material Model for Spinal Ligaments in Explicit Time Integration Method With an Infinite Impulse Response Filtering Technique

Abstract

This study introduced the development and validation of a transversely isotropic, visco-hyperelastic constitutive model for human spinal ligaments, implemented using the Finite Element Method (FEM). The model, incorporating a Neo-Hookean strain energy function for the isotropic matrix and a polynomial function for the anisotropic fibers, enriched with viscous aspects, was employed within the Ansys LS-Dyna environment. Infinite Impulse Response filtering techniques were integrated into the numerical analysis as a novel approach, aimed at refining the stability and computational efficiency of the simulations under various strain rates ($0.5s^{-1}$, $20s^{-1}$, $150s^{-1}$, and $300s^{-1}$). This feature significantly mitigated numerical instabilities that could appear when an explicit time integration scheme was used with high strain rate scenarios, critical in modeling vehicular collisions. Material parameters of ligament tissues were acquired through nonlinear least squares fitting to low and high strain experimental data. A comparative analysis of the FEM results against analytical solutions demonstrated the model's validity, with an excellent agreement across various statistical metrics. It was observed that the constitutive model could properly describe the visco-hyperelastic biomechanical behavior of the spine ligaments under high strain rates. The model could be applied to other soft tissues exhibiting visco-hyperelastic responses. Hence, the implementation of this constitutive law was successfully adopted for analyses considering various ligamentous structures.