A robust SPH formulation for solids

Authors

  • Bertrand Maurel Laboratoire de Mécanique des contacts et des Solides INSA de Lyon/UMR CNRS 20 avenue Albert Einstein F-69621 Villeurbanne cedex
  • Alain Combescure Laboratoire de Mécanique des contacts et des Solides INSA de Lyon/UMR CNRS 20 avenue Albert Einstein F-69621 Villeurbanne cedex
  • Serguei Potapov Electricité de France, Direction des Etudes et Recherches 1 avenue du général de Gaulle BP 408, F-92141 Clamart cedex

Keywords:

SPH, stability, total Lagrangian formulation

Abstract

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.

Downloads

Download data is not yet available.

References

Belytschko T., Neal M.O., “Contact-Impact by the Pinball method with penalty and

Lagrangian Methods”, International journal for numerical methods in engineering,

Vol. 31, 1991, p. 547-572.

Belytschko T., Guo Y., Liu W.K., Xiao S.P., “A unified stability analysis of meshless particle

methods”, International journal for numerical methods in engineering, Vol. 40, 2000,

p. 1359-1400.

Belytschko T., Rabczuk T., Xiao S.P., “Stable particle methods based on Lagrangian

kernels”, Computer methods in applied mechanics and engineering, Vol. 193, 2004,

p. 1035-1063.

Dyka, Randles P.W., Ingel R.P., “Stress points for tension instability”, International journal

for numerical methods in engineering, Vol. 40, 1997, p. 2325-2341.

Gingold R.A., Monaghan J.J., “Smoothed particle hydrodynamics: theory and application to

non-spherical stars”, Mon. Not. R. astr. Soc., Vol. 181, 1977, p. 375.

Gray J.P., Monaghan J.J., “SPH elastic dynamics”, Computer methods in applied mechanics

and engineering, Vol. 190, 2001, p. 6641-6662.

Johnson G.R., Stryck R.A., Beissel S.R., “SPH for high velocity impact”, Computer methods

in applied mechanics and engineering, Vol. 139, 1996, p. 347-373.

Rabczuk T., Belytchko T., “Cracking particles: a simplified meshfree method for arbitrary

evolving cracks”, International journal for numerical methods in engineering, Vol. 61,

, p. 2316-2343.

Randles P.W., Libersky L.D., “Smoothed Particle Hydrodynamics: Some recent

improvements and applications”, Computer methods in applied mechanics and

engineering, Vol. 139, 1996, p. 375-408.

Randles P.W., Libersky L.D., “Normalized SPH with stress points”, International journal for

numerical methods in enginering, Vol. 48, 2000, p. 1445-1462.

Swegle J.W., Hicks D.L.,Wen Y., Stabilizing SPH with conservative smoothing, Sandia

Report, SAND94-1932, 1994.

Downloads

Published

2006-08-16

How to Cite

Maurel, B., Combescure, A. ., & Potapov, S. . (2006). A robust SPH formulation for solids. European Journal of Computational Mechanics, 15(5), 495–512. Retrieved from https://journals.riverpublishers.com/index.php/EJCM/article/view/2075

Issue

Section

Original Article