Stabilized updated lagrangian corrected SPH for explicit dynamic problems

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 spoil completely 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 an stabilization technique is incorporated to the updated formulation to obtain an improved method without mechanisms and capable to solve problems with extremely large distortions. Copyright c© 2006 John Wiley & Sons, Ltd. key words: corrected smooth particle hydrodynamics; SPH; meshfree methods; updated Lagrangian formulation; large distortions. 1