Evaluation of the Use of the Yeoh and Mooney-Rivlin Functions as Strain Energy Density Functions for the Ground Substance Material of the Annulus Fibrosus

Abstract

Due to the importance of the intervertebral disc in the mechanical behavior of the human spine, special attention has been paid to it during the development of finite element models of the human spine. The mechanical behavior of the 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 of the 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 of three independent and orthogonal moments of 8 N-m was used, employing Abaqus software. A structured mesh with eight divisions along the height and the radial direction of annulus 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. The mechanical constants were taken from the reported literature. The range of motion 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.

Modeling the Impact of Meniscal Tears on von Mises Stress of Knee Cartilage Tissue

“…With an undamaged meniscus ( Figure 7 a,e), the stresses are distributed almost uniformly; no stress concentrators are found. This observation is in good agreement with the results reported previously [ 15 , 28 ]. The maximum values of stress (see Figure 8 ) are also small (1.31 MPa for the first patient and 1.24 MPa for the second patient).…”

“…The Mooney–Rivlin strain energy density function is expressed as a two-constant formulation [ 28 ]: where C 1 and C 2 are the first and second material constants, respectively, related to the distortional response, and K is the material constant related to the volumetric response. I 1 , I 2 , and I 3 are the reduced invariants of the Cauchy–Green deformation tensor and can be expressed in terms of principal stretch ratios.…”

Research on polygon suppression of resilient wheels under multiple operating conditions

“…Table 4 exhibits the material parameters of rubber elements of rigid and resilient wheels. [19][20][21][22][23] According to the use of the American AAR standard five-level orbit spectrum as the excitation condition, [24][25][26] as demonstrated in Figure 4.…”