State-Based Peridynamic Approach for Modelling Particle Motion in Oscillatory Channel Flow with Flexible Leaflets

  • Davidson, Sarah (University of Edinburgh)
  • Zhang, Ya (Northwestern Polytechnical University)
  • Zhang, Yonghao (Chinese Academy of Sciences)
  • Haeri, Sina (University of Edinburgh/ HR Wallingford)

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The interaction between fluid and structures is studied in many disciplines and the action of the fluid on the solid can inflict damage. Subsequently, this can alter the expected behaviour of the fluid and the system. This study presents a novel investigation utilising the damage and fracture propagation capabilities of Peridynamics (PD). Peridynamics permits natural development of cracks within a material by using a non-local form of the continuum mechanics formulation. The aim of this work is to assess how damage affects the operation of bicuspid valves. Peridynamics has been coupled with other methods to capture the erosive impact of particles [1]. This investigation models deformable beams using PD, coupled with the surrounding fluid (Cascaded Lattice Boltzmann Method) via a strong coupling (using the Immersed Boundary Method). The method used for this study has been shown to capture the interaction of solids and liquids for both beams bending and oscillating due to an applied flow velocity [2]. An extension to the PD-IB-CLBM model is presented to include state-based Peridynamics, allowing simulation of a wider range of solid materials due to the variable Poisson’s ratio (as opposed to the bond-based formulation). The additional inclusion of non-deformable particles involves use of the Discrete Element Method. Fluid-structure interaction and solid-solid collision are considered for the case of particulates in a pulsing flow with deformable PD beams. The model is then extended to allow for damage to the Peridynamic solids. Results include analysis of the fluid and solid behaviour for flexible leaflet valves, the behaviour of particles in the flow, and the fracture characteristics of beams. This provides insight into the failure behaviour of valves of this type and provides the initial step for more complex analysis of breakage, illness cascade in biological systems, valve replacement development, and understanding the changing fluid and solid dynamics. [1] Y. Zhang, et al., “A multi-physics peridynamics-DEM-IB-CLBM framework for the prediction of erosive impact of solid particles in viscous fluids,” Comput. Methods Appl. Mech. Eng., vol. 352, 675 - 690 (2019). [2] Y. Zhang, et al., “Strongly coupled peridynamic and lattice Boltzmann models using immersed boundary method for flow-induced structural deformation and fracture,” J. Comput. Phys., vol. 435, 11027 (2021).