Shock Waves

, Volume 15, Issue 1, pp 21–29 | Cite as

Adaptive smoothed particle hydrodynamics for high strain hydrodynamics with material strength

  • M. B. Liu
  • G. R. Liu
  • K. Y. Lam
Original Article


This paper presents the implementation of an adaptive smoothed particle hydrodynamics (ASPH) method for high strain Lagrangian hydrodynamics with material strength. In ASPH, the isotropic kernel in the standard SPH is replaced with an anisotropic kernel whose axes evolve automatically to follow the mean particle spacing as it varies in time, space, and direction around each particle. Except for the features inherited from the standard SPH, ASPH can capture dimension-dependent features such as anisotropic deformations with a more generalized elliptical or ellipsoidal influence domain. Two numerical examples, the impact of a plate against a rigid surface and the penetration of a cylinder through a plate, are investigated using both SPH and ASPH. The comparative studies show that ASPH has better accuracy than the standard SPH when being used for high strain hydrodynamic problems with inherent anisotropic deformations.


Smoothed particle hydrodynamics Adaptive smoothed particle hydrodynamics Isotropic kernel Anisotropic kernel High strain hydrodynamics 


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Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.College of EngineeringNanyang Technological UniversityNanyangSingapore
  2. 2.Department of Mechanical EngineeringNational University of SingaporeNanyangSingapore

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