A micromechanically-based, three-dimensional interface finite element for the modelling of the periodontal ligament.

Some ideas are presented for the implementation of an interface finite element capable to model in 3-dimensions several mechanical features of the periodontal ligament. Such an element is based on a simple 2-cable micromechanical model, able to reproduce the periodontal ligament stiffness and strength under any loading condition, including the pure torsion of a tooth. A single cable represents a sufficiently populated sample of collagen fibres, each with an initially crimped geometry; a single collagen fibre can provide a mechanical response, in tension, only when it is completely uncoiled. The macroscopic interface behaviour is obtained by statistical integrations over the uncoiled length of each collagen fibre, up to the fibre failure. Such a model can reproduce the periodontal ligament anisotropy due to the variable fibre orientation along the tooth root, its different behaviour in tension/compression/shear, its different behaviour for extrusive/intrusive loading, and so forth. Some numerical examples illustrate the potentialities of this interface element, quite simple in essence but rather complete from an engineering viewpoint.