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A finite element model of the temporomandibular joint (TMJ) and the human mandible was fabricated to study the effect of abnormal loading, such as awake and asleep bruxism, on the articular disc. A quasilinear viscoelastic model was used to simulate the behaviour of the disc. The viscoelastic nature of this tissue is shown to be an important factor when sustained (awake bruxism) or cyclic loading (sleep bruxism) is simulated. From the comparison of the two types of bruxism, it was seen that sustained clenching is the most detrimental activity for the TMJ disc, producing an overload that could lead to severe damage of this tissue.

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In this paper, the equations of motion of flexible multibody systems are derived using a nonlinear formulation which retains the second-order terms in the strain-displacement relationship. The strain energy function used in this investigation leads to the definition of three stiffness matrices and a vector of nonlinear elastic forces. The first matrix is the constant conventional stiffness matrix; the second one is the first-order geometric stiffness matrix; and the third is a second-order stiffness matrix. It is demonstrated in this investigation that accurate representation of the axial displacement due to the foreshortening effect requires the use of large number or special axial shape functions if the nonlinear stiffness matrices are used. An alternative solution to this problem, however, is to write the equations of motion in terms of the axial coordinate along the deformed (instead of undeformed) axis. The use of this representation yields a constant stiffness matrix even if higher order terms are retained in the strain energy expression. The numerical results presented in this paper demonstrate that the proposed new approach is nearly as computationally efficient as the linear formulation. Furthermore, the proposed formulation takes into consideration the effect of all the geometric elastic nonlinearities on the bending displacement without the need to include high frequency axial modes of vibration.