Atherosclerotic plaque in the femoral is the leading cause of peripheral artery disease (PAD), the worse consequence of which may lead to ulceration and gangrene of the feet. Numerical studies on fluid-structure interactions (FSI) of atherosclerotic femoral arteries enable quantitative analysis of biomechanical features in arteries. This study aims to investigate the hemodynamic performance and its interaction with femoral arterial wall based on the patient-specific model with multiple plaques (calcified and lipid plaques). Three types of models, calcification-only, lipid-only and calcification-lipid models, are established. Hyperelastic material coefficients of the human femoral arteries obtained from experimental studies are employed for all simulations. Oscillation of WSS is observed in the healthy downstream region in the lipid-only model. The pressure around the plaques in the two-plaque model is lower than that in the corresponding one-plaque models due to the reduction of blood flow domain, which consequently diminishes the loading forces on both plaques. Therefore, we found that stress acting on the plaques in the two-plaque model is lower than that in the corresponding one-plaque models. This finding implies that the lipid plaque, accompanied by the calcified plaque around, might reduce its risk of rupture due to the reduced the stress acting on it.

We consider flow along a finite-length collapsible channel driven by a fixed upstream flux, where a section of one wall of a planar rigid channel is replaced by a plane-strain elastic beam subject to uniform external pressure. A modified constitutive law is used to ensure that the elastic beam is energetically conservative. We apply the finite element method to solve the fully nonlinear steady and unsteady systems. In line with previous studies, we show that the system always has at least one static solution and that there is a narrow region of the parameter space where the system simultaneously exhibits two stable static configurations: an (inflated) upper branch and a (collapsed) lower branch, connected by a pair of limit point bifurcations to an unstable intermediate branch. Both upper and lower static configurations can each become unstable to self-excited oscillations, initiating either side of the region with multiple static states. As the Reynolds number increases along the upper branch the oscillatory limit cycle persists into the region with multiple steady states, where interaction with the intermediate static branch suggests a nearby homoclinic orbit. These oscillations approach zero amplitude at the upper branch limit point, resulting in a stable tongue between the upper and lower branch oscillations. Furthermore, this new formulation allows us to calculate a detailed energy budget over a period of oscillation, where we show that both upper and lower branch instabilities require an increase in the work done by the upstream pressure to overcome the increased dissipation.

In this paper we study flow driven through a finite-length planar rigid channel by a fixed upstream flux, where a segment of one wall is replaced by a pre-stressed elastic beam subject to uniform external pressure. The steady and unsteady systems are solved using a finite element method. Previous studies have shown that the system can exhibit three steady states for some parameters (termed the upper, intermediate and lower steady branches, respectively). Of these, the upper and lower are stable to non-oscillatory perturbations, while the intermediate branch is always unstable. These upper and lower steady branches can (independently) become unstable to self-excited oscillations. We show that for some parameter combinations the system is unstable to both upper and lower branch oscillations simultaneously. However, we show that these two instabilities eventually merge together for large enough Reynolds numbers, exhibiting a nonlinear limit cycle which retains characteristics of both the upper and lower branches of oscillations. Furthermore, we show that increasing the beam pre-tension suppresses the region of multiple steady states but preserves the onset of oscillations. Conversely, increasing the beam thickness (a proxy for increasing bending stiffness) suppresses both multiple steady states and the onset of oscillations.

We consider the stability of laminar high-Reynolds-number flow through a planar channel formed by a rigid wall and a heavy compliant wall under longitudinal tension with motion resisted by structural damping. Numerical simulations indicate that the baseline state (with Poiseuille flow and a flat wall) exhibits two unstable normal modes: the Tollmien–Schlichting (TS) mode and a surface-based mode which manifests as one of two flow-induced surface instabilities (FISI), known as travelling wave flutter (TWF) and static divergence (SD), respectively. In the absence of wall damping the system is unstable to TWF, where the neutrally stable wavelength becomes shorter as the wall mass increases. With wall damping, TWF is restricted to long wavelengths through interaction with the most unstable centre mode, while for wall damping greater than a critical value the system exhibits an SD mode with a two branch neutral stability curve; the critical conditions along the upper and lower branches are constructed in the limit of large wall damping. We compute the Reynolds–Orr and activation energy descriptions of these neutrally stable FISI by continuing the linear stability analysis to the following order in perturbation amplitude. We find that both FISI are primarily driven by the working of normal stress on the flexible wall, lower-branch SD has negative activation energy, while upper-branch SD approaches zero activation energy in the limit of large wall damping. Finally, we elucidate interaction between TS and TWF modes for large wall mass, resulting in stable islands within unstable regions of parameter space.