Smoothed Particle Hydrodynamics and its Application to Solid Mechanics Problems

The Smoothed Particle Hydrodynamics (SPH) method was first developed tostudy astrophysics problems by Lucy and Gingold and Monaghan in 1977. As a numerical method, SPH falls into the category of meshless methods.These methods differ from the Finite Element Method (FEM) in the way the spatial domain is discretised. In the SPH method the domain is discretised using as set of points, called particles, as shown in Figure 1. In contrast to FEM nodes these points do not define volume elements with a fixed connectivity, but they interact through an interpolation kernel which is usually circular in 2D or spherical in 3D. A key difference between SPH and other meshless methods such as the Reproducing Kernel Particle Method (RKPM) or Element Free Galerkin (EFG) Method is that the SPH particles not only carry the field variables (displacements, velocities) but are also used as integration points. The RKPM and EFG Method generally use a background grid to evaluate integrals.