Formulation of Hyperelastic Constitutive Model for Human Periodontal Ligament Based on Fiber Volume Fraction

Collagen fibers of the Periodontal ligament (PDL) play a crucial role in determining its mechanical properties. Based on this premise, we investigated the effect of the volume fraction of human PDL collagen fibers on the hyperelastic mechanical behavior under transient loading. Samples were obtained from different root regions (neck, middle, and apex) of the PDL, prepared from fresh human anterior teeth. The collagen fibers volume fraction in various regions of the PDL was quantified by staining techniques combined with image processing software. The collagen fiber volume fractions were found to be 60.3% in the neck region, 63.1% in the middle region, and 52.0% in the apex region. A new hyperelastic constitutive model was constructed based on the volume fraction. A uniaxial tensile test was conducted on these samples, and the accuracy of the constitutive model was validated by fitting the test data. Also, relevant model parameters were derived. The results demonstrated that human PDL exhibited hyperelastic mechanical properties on the condition of transient loading. With an increase in the volume fraction of collagen fibers, the tensile resistance of the PDL was enhanced, demonstrating more significant hyperelastic mechanical properties. The hyperelastic constitutive model showed a good fit with the experimental results (R² > 0.997), describing the hyperelastic mechanical properties of the human PDL effectively.