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A unified SPH framework for shell-related interactions

Dong Wu, Shuaihao Zhang, Weiyi Kong, Xiangyu Hu

Abstract

A unified Smoothed Particle Hydrodynamics (SPH) framework is proposed to simulate interaction dynamics involving thin shells modeled by a reduced-dimensional, single-layer particle discretization, as opposed to full-dimensional SPH solids. The framework encompasses one-sided fluid-shell interactions, with the fluid present on only one side of the shell, as well as solid-shell, shell-shell, and shell-self interactions The study introduces a novel concept of imaginary shell contact particles, generated by projecting real shell particles along the local normal direction within the cut-off radius of the fluid particle, thereby mapping this reduced-dimensional shell model into a full-dimensional representation. With the volume of the imaginary particles defined based on the local shell curvature, the projection preserves kernel completeness for fluid-shell interactions while leaving the fluid-structure interaction (FSI) dynamics unchanged, such that the fluid-shell coupling algorithm is the same as in standard fluid-solid coupling. In addition, a particle-to-particle contact model for solid-solid interactions is developed by analogy to fluid dynamics: a contact density is computed using a fluid-style density initialization, and the resulting contact forces follow a momentum-equation-inspired formulation. Combined with the projection strategy, this contact formulation is directly extended to efficiently handle shell-related contact problems. The proposed method is validated using a series of benchmark tests, demonstrating stable and accurate performance across diverse interaction scenarios.

A unified SPH framework for shell-related interactions

Abstract

A unified Smoothed Particle Hydrodynamics (SPH) framework is proposed to simulate interaction dynamics involving thin shells modeled by a reduced-dimensional, single-layer particle discretization, as opposed to full-dimensional SPH solids. The framework encompasses one-sided fluid-shell interactions, with the fluid present on only one side of the shell, as well as solid-shell, shell-shell, and shell-self interactions The study introduces a novel concept of imaginary shell contact particles, generated by projecting real shell particles along the local normal direction within the cut-off radius of the fluid particle, thereby mapping this reduced-dimensional shell model into a full-dimensional representation. With the volume of the imaginary particles defined based on the local shell curvature, the projection preserves kernel completeness for fluid-shell interactions while leaving the fluid-structure interaction (FSI) dynamics unchanged, such that the fluid-shell coupling algorithm is the same as in standard fluid-solid coupling. In addition, a particle-to-particle contact model for solid-solid interactions is developed by analogy to fluid dynamics: a contact density is computed using a fluid-style density initialization, and the resulting contact forces follow a momentum-equation-inspired formulation. Combined with the projection strategy, this contact formulation is directly extended to efficiently handle shell-related contact problems. The proposed method is validated using a series of benchmark tests, demonstrating stable and accurate performance across diverse interaction scenarios.
Paper Structure (22 sections, 64 equations, 21 figures, 1 table, 1 algorithm)

This paper contains 22 sections, 64 equations, 21 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Governing equations
  3. Fluid dynamics equations
  4. Solid dynamics equations
  5. Shell dynamics equations
  6. Interaction modeling
  7. Preliminary work
  8. SPH discretization
  9. Time stepping
  10. Fluid-shell interaction
  11. Generation of imaginary shell particles
  12. Equivalent value of kernel function
  13. Solid-shell interaction
  14. Numerical examples
  15. Hydrostatic FSI
  16. ...and 7 more sections

Figures (21)

  • Figure 1: Setup of imaginary shell particles.
  • Figure 2: Hydrostatic FSI: Model setup.
  • Figure 3: Hydrostatic FSI: The pressure distribution of the water column and the plate particles colored by von Mises stress.
  • Figure 4: Hydrostatic FSI: Time history of the vertical mid-span displacement of the elastic plate.
  • Figure 5: Dam-break flow through an elastic gate: Initial configuration and geometric parameters.
  • ...and 16 more figures