Smoothed Particle Hydrodynamics (SPH)

Paper 1: Jian-Yu Chen, and Fue-Sang Lien. "Simulations for soil explosion and its effects on structures using SPH method." International Journal of Impact Engineering 112 (2018): 41-51.

Paper 2: Jian-Yu Chen, Chong Peng, and Fue-Sang Lien. "Simulations for three-dimensional landmine detonation using the SPH method." International Journal of Impact Engineering 126 (2019): 40-49.

Paper 3: Jian-Yu Chen, Chong Peng, Fue-Sang Lien, and Xiao-Hua Zhao. "Simulations for the explosion in a water-filled tube including cavitation using the SPH method" Computational Particle Mechanics (2019): 1-13.

Basic ideas of  the SPH method

Kernel approximation

Kernel approximation
Kernel approximation

Particle approximation

Particle approximation
Particle approximation
Particle approximation

Navier-Stokes (NS) equation

  • Continuity density equation
Continuity density equation
  • Particle approximation of momentum
Particle approximation of momentum
  • Particle approximation of energy
Particle approximation of energy
  • Equation of state
Equation of state

 Artificial viscosity

Artificial viscosity
Artificial viscosity
Artificial viscosity
Artificial viscosity

Soil model

Stress-strain relationship

Stress-strain relationship

 Yield criterion (Drucker-Prager)

Yield criterion (Drucker-Prager)

 Plastic multiplier

Plastic multiplier

 Numerical errors

Numerical errors

 Tension cracking (D-E) and stress scaling back procedure

Tension cracking (D-E) and stress scaling back procedure
Tension cracking (D-E) and stress scaling back procedure

 Axisymmetric collapse of dry sand

Axisymmetric collapse of dry sand

 Impact force of sand on a rigid wall

Impact force of sand on a rigid wall
Impact force of sand on a rigid wall