A nonlinear finite-element model of the vocal fold.

Abstract

A large-displacement large-strain 3-D finite-element model of the vocal fold was developed. The structure is discretized into 720 elements with 3003 displacement and 720 pressure degrees of freedom. The model incorporates material and geometric nonlinearities. For the constitutive law, the Mooney–Rivlin rubber material formulation for an anisotropic hyperelastic material is used. Average incompressibility constraints are introduced by adding a hydrostatic pressure work term (Lagrange multiplier) to the strain energy density function. This term is a function of the bulk modulus which has the numerical equivalence of the penalty parameter. The nodal displacements and pressure are solved for independently, using a mixed displacement/pressure formulation with 8 displacement nodes (trilinear/hexahedron) and a constant (uniform) pressure term per element. Static condensation of the discontinuous pressure variable at the element level keeps the half-bandwidth of the stiffness matrix the same as for the displacement-only formulation. All nodes on the anterior commissure, vocal processes and the lateral surface (attached to the thyroid cartilage) are fixed-essential boundary conditions. An incremental-iterative strategy solves the dynamic equilibrium equations of motion in the total Lagrangian formulation. The vocal fold deformation was studied under a periodically time-varying pressure profile (natural boundary conditions) applied on 117 medial surface nodes.