Transversely isotropic hyperelastic laws for 2D FEM modeling of human thoracic spine ligaments

Abstract

Abstract A comparative analysis of three transversely isotropic hyperelastic constitutive laws is presented to characterize the mechanical behavior of spinal ligaments within finite element simulations. In each material model, the total strain energy is partitioned into ground‑matrix and fiber contributions. The ground‑matrix response was represented by three strain‑energy functions, Neo‑Hookean, Mooney‑Rivlin, and Yeoh, whereas the fiber response was captured by a fourth‑order polynomial. Constitutive parameters were calibrated against experimental uniaxial tension data from human thoracic spinal ligaments. The models were implemented via user‑defined material subroutines in Abaqus and LS‑Dyna and evaluated with finite shell elements. Performance of the afore-mentioned constitutive laws was assessed based on their ability to fit experimental data and their computational efficiency. The results indicate that, although the Yeoh model provides the best fit to the experimental data in terms of root mean square error, it tends to underestimate the fiber contribution to the overall material response, resulting in an over-stiffening effect in simulations of short-sample tensile tests. In contrast, the Neo-Hookean and Mooney-Rivlin models do not exhibit this issue.