Analysis of deformable bi-cuspid valve dynamics in pulsatile flow using a coupled peridynamics–lattice Boltzmann-immersed boundary framework

Multi-leaflet valves enable passive, one-way fluid transport and are increasingly applied in biological systems, soft robotics, and other industrial applications to prevent backflow. Despite extensive studies on biological valves, understanding the coupled fluid–structure dynamics of biological and synthetic bi-cuspid valves under material degradation and flow conditions remains limited. This work investigates operational modes of bi-cuspid valves using a strongly coupled framework combining the cascaded lattice Boltzmann method for fluid flow and bond-based peridynamics for solid mechanics modeling. The scheme is validated against other numerical data and applied to two-dimensional valve models subjected to pulsatile inlet conditions. Systematic variations in Young's modulus (E) and Reynolds number (Re) reveal their influence on leaflet deformation, aperture size, and flow features such as jet formation, recirculation zones, and inversion during reverse flow. Flexible leaflets (low E) exhibit larger apertures and higher variability, with increased risk of wall contact and asymmetry, while stiffer valves (high E) promote regular motion but reduce opening, enlarging stagnation regions. Higher Re amplifies the aperture and jet velocity, altering downstream flow separation. Simulations highlight the necessity of multi-cycle analysis to capture transient dynamics and inversion phenomena. These findings offer insights into the design of robust soft valves for applications that require controlled unidirectional flow under complex operating conditions.