Coupling of smooth particle hydrodynamics with the finite element method

Abstract

Abstract A gridless technique called smooth particle hydrodynamics (SPH) has been coupled with the transient dynamics finite element code pronto . In this paper, a new weighted residual derivation for the SPH method will be presented, and the methods used to embed SPH within pronto will be outlined. Example SPH pronto calculations will also be presented. One major difficulty associated with the Lagrangian finite element method is modeling materials with no shear strength; for example, gases, fluids and explosive biproducts. Typically, these materials can be modeled for only a short time with a Lagrangian finite element code. Large distortions cause tangling of the mesh, which will eventually lead to numerical difficulties, such as negative element area or “bow tie” elements. Remeshing will allow the problem to continue for a short while, but the large distortions can prevent a complete analysis. SPH is a gridless Lagrangian technique. Requiring no mesh, SPH has the potential to model material fracture, large shear flows and penetration. SPH computes the strain rate and the stress divergence based on the nearest neighbors of a particle, which are determined using an efficient particle-sorting technique. Embedding the SPH method within pronto allows part of the problem to be modeled with quadrilateral finite elements, while other parts are modeled with the gridless SPH method. SPH elements are coupled to the quadrilateral elements through a contact-like algorithm.