Evaluation of the Use of the Yeoh and Mooney-Rivlin Functions as Strain Energy Density Functions

What is it about?

Due to the importance ofthe intervertebral disc in the mechanical behavior ofthe human spine, special attention has been paid to it during the development offinite elementmodels ofthe human spine. Themechanical behavior ofthe intervertebral disc is nonlinear, heterogeneous, and anisotropic and, due to the low permeability, is usually represented as a hyperelastic model. The intervertebral disc is composed ofthe nucleus pulposus, the endplates, and the annulus fibrosus. The annulus fibrosus is modeled as a hyperelastic matrix reinforced with several fiber families, and researchers have used different strain energy density functions to represent it. This paper presents a comparative study between the strain energy density functions most frequently used to represent the mechanical behavior of the annulus fibrosus: the Yeoh and Mooney-Rivlin functions. A finite element model of the annulus fibrosus of the L4-L5 segment under the action ofthree independent and orthogonal moments of8 N-mwas used, employing Abaqus software. A structured mesh with eight divisions along the height and the radial direction ofannulus fibrosus and tetrahedron elements for the endplates were used, and an exponential energy function was employed to represent the mechanical behavior of the fibers. A total of 16 families were used; the fiber orientation varied with the radial coordinate from 25∘ on the outer boundary to 46∘ on the inner boundary, measuring it with respect to the transverse plane. Themechanical constants were taken from the reported literature. The range ofmotion was obtained by finite element analysis using different values of the mechanical constants and these results were compared with the reported experimental data. It was found that the Yeoh function showed a better fit to the experimental range of motion than the Mooney-Rivlin function, especially in the nonlinear region.

Featured Image

Why is it important?

It was found that the Yeoh function showed a better fit to the experimental range of motion than the Mooney-Rivlin function, especially in the nonlinear region.

Perspectives