Viscoelastic material model for the temporomandibular joint disc derived from dynamic shear tests or strain-relaxation tests

Viscoelastic material models for the temporomandibular joint disc, based upon strain relaxation, were considered to underestimate energy absorption for loads with time constants beyond the relaxation time. Therefore, the applicability of a material model that takes the viscous behavior at a wide range of frequencies into account was assessed. To that purpose a non-linear multi-mode Maxwell model was tested in cyclic large-strain compression tests. Its material constants were approximated from dynamic small-strain shear deformation tests.The storage and loss moduli as obtained from a disc sample could be approximated with a four-mode Maxwell model. In simulated large-strain compression tests it behaved similarly as observed from the experimental tests. The underestimation of energy dissipation, as obtained from a single-mode Maxwell model was considerably reduced, especially for deformations with a higher strain rate. Furthermore, in contrast to the latter it was able to predict the increase of the stress amplitude with the compression frequency much better.In conclusion, the applied four-mode Maxwell model, based upon dynamic shear tests, was considered more suitable to predict higher frequency viscoelastic response, for instance during shock absorption, than a model based upon strain-relaxation.