Investigation of the non linear viscous-elastic behaviour of the periodontal ligament

The mechanics of the periodontal ligament (PDL) is responsible of phenomena concerning the tooth mobility, both in short and long time. Together with the experimental evaluation of the mechanical characteristics of the tissue, the development of constitutive models capable of describing its response under general conditions is important. In fact, this is a mandatory step to develop numerical analyses which help in investigating complex phenomena that are at the basis of the role of PDL, representing a valid tool for interpreting clinical applications. The authors have proposed different constitutive models to describe the non-linear response of PDL considering non-linear elastic behaviour, visco-elastic response and possible damage phenomena due to relevant strains. The visco-elastic model adopted was limited to the assumption of linear viscosity, considering a suitable set of constant relaxation times and relative stiffness parameters. In this work the possible nature of nonlinear visco-elasticity of the PDL is considered, in particular focusing the attention to experimental data taken from relaxation tests on samples of animal model PDL . A non-linear visco-elastic constitutive model is developed on the basis of the theory of the fibre-reinforced continua, in order to define also the anisotropic response of the PDL due to the presence of highly orientated collagen fibres in the tissue. The model is fitted to the experimental data, showing its capability to interpret the dependency of the stress relaxation on the level of strain applied, which is the reason of the non-linearity of the viscous response of the tissue.