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. Requiring no mesh, SPH has the potential to model material fracture, large shear flows, and penetration. Smooth particle hydrodynamics is a gridless Lagrangian technique. Remeshing win allow the problem to continue for a short while, but the large distortions can prevent a complete analysis. Large distortions cause tangling of more ยป the mesh, which will eventually lead to numerical difficulties such as negative element area or ``bow tie`` elements. Typically these materials can be modeled for only a short time with a Lagrangian finite element code. One major difficulty associated with the Lagrangian fmite element method is modeling materials with no shear strength for example, gases, fluids and explosive bi-products. ![]() Example SPH-PRONTO calculations will also be presented. ![]() 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. A gridless numerical technique called smooth particle hydrodynamics (SPH) has been coupled to the transient dynamics finite element code, PRONTO.
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