A robust SPH formulation for solids - Maurel, Bertrand; Combescure, Alain; Potapov, Serguei (European Journal of Computational Mechanics, 2006)
The smoothed particle hydrodynamics method such as other meshless methods is a very efficient numerical method for some types of modelling such as fracturing of solids. This technique, initially developed for fluid or gas, was extended to solids but it suffers from severe instability problems. The origins of these instabilities have been identified by the SPH community and solutions were developed to remove them. An overview of the different proposed techniques is presented. Among them it appears that for solids the use of the total Lagrangian formulation is the most simple and valuable solution. In the same time stress points can be added to this new formulation in order to improve accuracy and convergence rate despite an increase in computational cost.