Numerical analysis of the wall stress in abdominal aortic aneurysm influence of the material model incompressibility
Résumé
Recently, hyperelastic mechanical models were proposed to well capture the aneurismal arterial wall anisotropic and nonlinear features experimentally observed. These models were formulated assuming the material incompressibility. However in numerical analysis, a nearly incompressible approach, i.e., a mixed formulation pressure-displacement, is usually adopted to perform finite element stress analysis of abdominal aortic aneurysm (AAA). Therefore, volume variations of the material are controlled through the volumetric energy which depends on the initial bulk modulus κ. In this paper, an analytical analysis of the influence of κ on the mechanical response of two invariant-based anisotropic models is first performed in the case of an equibiaxial tensile test. This analysis shows that for the strongly nonlinear anisotropic model, even in a restricted range of deformations, large values of κ are necessary to ensure the incompressibility condition, in order to estimate the wall stress with a reasonable precision. Finite element simulations on idealized AAA geometries are then performed. Results from these simulations show that the maximum stress in the AAA wall is underestimated in previous works, committed errors vary from 26% to 58% depending on the geometrical model complexity. In addition to affect the magnitude of the maximum stress in the aneurysm, we found that too small value of κ may also affect the location of this stress.
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