Shear Wave Propagation and Estimation of Material Parameters in a Nonlinear, Fibrous Material

This paper describes the propagation of shear waves in a Holzapfel–Gasser–Ogden (HGO) material and investigates the potential of magnetic resonance elastography (MRE) for estimating parameters of the HGO material model from experimental data. In most MRE studies the behavior of the material is assumed to be governed by linear, isotropic elasticity or viscoelasticity. In contrast, biological tissue is often nonlinear and anisotropic with a fibrous structure. In such materials, application of a quasi-static deformation (predeformation) plays an important role in shear wave propagation. Closed form expressions for shear wave speeds in an HGO material with a single family of fibers were found in a reference (undeformed) configuration and after imposed predeformations. These analytical expressions show that shear wave speeds are affected by the parameters (μ0, k1, k2, κ) of the HGO model and by the direction and amplitude of the predeformations. Simulations of corresponding finite element (FE) models confirm the predicted influence of HGO model parameters on speeds of shear waves with specific polarization and propagation directions. Importantly, the dependence of wave speeds on the parameters of the HGO model and imposed deformations could ultimately allow the noninvasive estimation of material parameters in vivo from experimental shear wave image data.

Determination of the Material Parameters in the Holzapfel-Gasser-Ogden Constitutive Model for Simulation of Age-Dependent Material Nonlinear Behavior for Aortic Wall Tissue under Uniaxial Tension

In this study, computational simulations and experiments were performed to investigate the mechanical behavior of the aorta wall because of the increasing occurrences of aorta-related diseases. The study focused on the deformation and strength of porcine and healthy human abdominal aortic tissues under uniaxial tensile loading. The experiments for the mechanical behavior of the arterial tissue were conducted using a uniaxial tensile test apparatus to validate the simulation results. In addition, the strength and stretching of the tissues in the abdominal aorta of a healthy human as a function of age were investigated based on the uniaxial tensile tests. Moreover, computational simulations using the ABAQUS finite element analysis program were conducted on the experimental scenarios based on age, and the Holzapfel–Gasser–Ogden (HGO) model was applied during the simulation. The material parameters and formulae to be used in the HGO model were proposed to identify the failure stress and stretch correlation with age.

Implémentation éléments finis du modèle hyperélastique anisotrope HGO

Anisotropic hyperelastic constitutive laws are often used to determine strain and stress in biological soft tissues such as ligaments, tendons or arterial walls. In this paper, the implementation of the HGO model in the finite element code FER is presented. Three numerical examples are studied: homogeneous uniaxial tension test where analytical solutions are available; uniaxial tension test highlighting the anisotropic behavior (contracting and swelling of the section in two perpendicular directions); contact and impact between hand and soft biological tissues in the framework of application using a virtual mannequin generator.

VIRIAL COEFFICIENTS FOR THE HARD GAUSSIAN OVERLAP MODEL

Monte Carlo estimates of virial coefficients up to the sixth for the Hard Gaussian Overlap (HGO) model are presented for values of the aspect ratio parameter κ of the model ranging from 0.05 to 10. The sixth coefficients are new and the lower coefficients are improvements on previous numerical estimates. The second virials are found to be in excellent agreement with an analytical integration reported in the literature. Padé (3, 3) approximations to the pressure and residual Helmholtz energy were constructed. Attempts to represent coefficients in these approximations by analytical functions of κ were not successful due to singularities in these functions. In the approximate range of 4.5≤κ≤ 5.5, the (3, 3) Padé approximations were found to be no better than lower ones. Comparisons with available Monte Carlo simulated pressures for moderately aspherical fluids were found to be good.