Stabilized updated Lagrangian corrected SPH for explicit dynamic problems

Abstract

Smooth particle hydrodynamics with a total Lagrangian formulation are, in general, more robust than finite elements for large distortion problems. Nevertheless, updating the reference configuration may still be necessary in some problems involving extremely large distortions. However, as discussed here, a standard updated formulation suffers the presence of zero‐energy modes that are activated and may completely spoil the solution. It is important to note that, unlike an Eulerian formulation, the updated Lagrangian does not present tension instability but only zero‐energy modes. Here a stabilization technique is incorporated to the updated formulation to obtain an improved method without any mechanisms and which is capable to solve problems with extremely large distortions.

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