A viscoelastic constitutive model for the periodontal ligament (PDL) capable of accounting for large strains, anisotropy, and inelastic time-dependent effects was developed. Anisotropy characteristics are determined by the composite nature of the tissue and, in particular, by the distribution of collagen fibres. Time-dependent viscous phenomena are due to microstructural modifications during loading, such as fluid fluxes moving through the solid matrix and the internal rearrangement of fibers and constitutive adaptation. The viscoelastic model presented here was implemented in a general purpose finite element code. In vitro experimental tests were carried out on the PDL specimens of adult pigs to obtain stress-relaxation and cyclic stress-strain curves. The comparison of experimental and numerical results revealed good correspondence and confirmed the capability of the formulation assumed to properly interpret the viscoelastic behavior of the PDL.

The periodontal ligament (PDL), as other soft biological tissues, shows a strongly non-linear and time-dependent mechanical response and can undergo large strains under physiological loads. Therefore, the characterization of the mechanical behavior of soft tissues entails the definition of constitutive models capable of accounting for geometric and material non-linearity. The microstructural arrangement determines specific anisotropic properties. A hyperelastic anisotropic formulation is adopted as the basis for the development of constitutive models for the PDL and properly arranged for investigating the viscous and damage phenomena as well to interpret significant aspects pertaining to ordinary and degenerative conditions. Visco-hyperelastic models are used to analyze the time-dependent mechanical response, while elasto-damage models account for the stiffness and strength decrease that can develop under significant loading or degenerative conditions. Experimental testing points out that damage response is affected by the strain rate associated with loading, showing a decrease in the damage limits as the strain rate increases. These phenomena can be investigated by means of a model capable of accounting for damage phenomena in relation to viscous effects. The visco-hyperelastic-damage model developed is defined on the basis of a Helmholtz free energy function depending on the strain-damage history. In particular, a specific damage criterion is formulated in order to evaluate the influence of the strain rate on damage. The model can be implemented in a general purpose finite element code. The accuracy of the formulation is evaluated by using results of experimental tests performed on animal model, accounting for different strain rates and for strain states capable of inducing damage phenomena. The comparison shows a good agreement between numerical results and experimental data.

Knowledge of the material properties of the periodontal ligament is fundamental to an understanding of orthodontic tooth movement and thus to selection of an optimal force system for orthodontic treatment.

The experimental results allow characterization of the tissue and thus contribute to an understanding of the biomechanics of tooth displacement under externally applied loads.

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