A Visco-Hyperelastic-Damage Constitutive Model for the Analysis of the Biomechanical Response of the Periodontal Ligament

Abstract

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.

Analytically determined mechanical properties of, and models for the periodontal ligament: Critical review of literature

“…Several modelling approaches (Natali et al, 2008;Qian et al, 2009;Zhurov et al, 2007) are highly robust and account for much of the observed and known PDL mechanical behaviour. For modelling the PDL's effect on orthodontic tooth movement, however, these models may be overly complex and too computationally intensive.…”

“…Natali et al (2007Natali et al ( , 2008 addressed the biomechanical behaviour of the PDL with the development of a visco-hyperelastic-damage structured model. The justification for such a model was that soft tissues, including the PDL, show a strongly nonlinear and time-dependent mechanical response and can undergo large strains under physiological loads.…”

Hydro-mechanical coupling in the periodontal ligament: A porohyperelastic finite element model

“…A global view of the PDL's response to mechanical loads was provided in a number of reports (Ledley and Huang, 1968;Miyakawa et al, 1985;Andersen et al, 1991;Wilson et al, 1994;Provatidis, 2000;Tanaka et al, 2007;Natali et al, 2008). These analyses approached PDL mechanics both in tension and in compression.…”

Stress distribution on maxillary central incisorunder similar traumatic situations with different loading forces: a 3-D finite element analysis.

“…26 Concerning the modeling process used to simulate the PDL, studies evaluating stress on the PDL emphasize the importance of using viscoelastic models due to its proximity to the real situation, allowing for the analysis of PDL under time-dependent forces. 5,15,27,28 However, some authors demonstrate that such models are best used in cases in which the traumatic force is applied for longer periods of time, situations found in studies on orthodontic tooth movement. 29 According to the same author, studies using viscoelastic models are more complex and, in some cases, do not promote a significant difference of results.…”