Aortic aneurysm hemodynamics based on a double fractional maxwell arterial model

In this paper, a double fractional Maxwell constitutive model is introduced to simulate the viscoelastic behavior of arterial walls. The fractional order solid equation is combined with the conventional Navier–Stokes equation to form a complex and highly nonlinear fluid structure interaction (FSI) system, which is numerically calculated through the finite element method. To evaluate the effectiveness of the model in complex geometries, the above method is also employed in the FSI hemodynamics of 3D-specific abdominal aortic aneurysm. The results indicate that the viscoelastic behaviors of arterial walls are significantly different depending on varying fractional order parameters. Higher stress fractional order parameters α or lower strain fractional order parameters β result in greater displacement fluctuations and stronger elastic performance. Conversely, smaller α or higher β result in smaller displacement changes and reduced elastic performance. Compared with the integer order fluid structure interaction (IFSI) model, the fractional order fluid structure interaction (FFSI) model generates smaller displacement and strain values, with peak displacement and strain values differing by factors of 2.4 and 2.2, respectively. The normalized change in vascular area is the smallest in the aneurysm center compared with the non-diseased vessel region (above the abdomen and below the renal artery).