## 2aSC9. A nonlinear finite-element model of the vocal fold.

### Session: Tuesday Morning, May 14

### Time: 10:45

**Author: Arthur P. Lobo**

**Author: Michael O'Malley**

**Location: Berkeley Speech Technologies, 2246 Sixth St., Berkeley, CA 94710**

**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.

from ASA 131st Meeting, Indianapolis, May 1996