On the migration of smooth particle hydrodynamic formulation in Cartesian coordinates to the axisymmetric formulation

Abstract

The smooth particle hydrodynamic (SPH) method has been extended for application to large deformation problems such as high velocity impacts by including the effect of material strength. This paper presents a simple modification of the kernel function that allows the SPH formulation in Cartesian coordinates to be migrated into an axisymmetric formulation. The proposed procedure is first applied to analyse transient deformations of a cylindrical rod impacting a rigid wall (Taylor impact test). A good agreement with published experimental data for the deformed shape is obtained. A sensitivity study of the key parameters required in the SPH formulation is conducted to provide better insight into the SPH modelling approach. Impacts between two bodies at high speed have also been simulated using an axisymmetric SPH code.

Keywords

SPH method axisymmetric formulation Taylor impact test

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References

Lucy

L. B.

A numerical approach to the testing of the fission hypothesis, Astron. J. 1977, 82, 1013–1024.

Gingold

R. A.

Monaghan

J. J.

Smoothed particle hydrodynamics: theory and application to non-spherical stars. Monthly Notices R. Astron. Soc., 1977, 181, 375–389.

Cloutman

L. D.

An evaluation of smooth particle hydrodynamics. Lect. Notes Phys., 1991, 395, 277–238.

Libersky

L. D.

Petschek

A. G.

Smooth particle hydrodynamics with strength of material. Lect. Notes Phys., 1991, 395, 248–257.

Johnson

G. R.

Petersen

E. H.

Stryk

R. A.

Incorporation of an SPH option into the EPIC code for a wide range of high velocity impact computations. Int. J. Impact Engng, 1993, 14(1), 385–394.

Batra

R. C.

Zhang

G. M.

Modified smoothed particle hydrodynamics (MSPH) basis functions for meshless methods, and their application to axisymmetric Taylor impact test. J. Comput. Phys., 2008, 227, 1962–1981.

Petschek

A. G.

Libersky

L. D.

Cylindrical smooth particle hydrodynamics. J. Comput. Mech., 1993, 109, 76–83.

Johnson

G. R.

Stryk

R. A.

Beissel

S. R.

SPH for high velocity impact computations. Comput. Methods Appl. Mech. Engng, 1996, 139, 347–373.

Hayhurst

C. J.

Clegg

Cylindrically symmetric SPH simulations of hypervelocity impacts on thin plates. Int. J. Impact Engng, 1997, 20, 337–348.

10.

Brookshaw

Smooth particle hydrodynamics in cylindrical coordinates. ANZIAM J., 2003, 44, C114–C139.

11.

Benz

Smoothed particle hydrodynamics: a review. In Numerical modeling of non-linear stellar pulsation: problems and prospects (Ed. Buchler

J. R.

), 1990, p. 269 (Kluwer, Boston, Massachusetts).

12.

Libersky

L. D.

Petschek

A. G.

Carney

T. C.

Hipp

J. R.

Allahdadi

F. A.

High strain Lagrangian hydrodynamics: a three-dimensional SPH code for dynamic material response. J. Comput. Phys., 1993, 109, 67–75.

13.

Camacho

G. T.

Ortiz

Adaptive ballistic modelling of ballistic penetration of metallic targets. Comput. Methods Appl. Mech. Engng, 1997, 142, 269–301.

14.

Sewell

D. A.

Ong

A. C. J.

Hallquist

J. O.

Penetration calculation using an erosion algorithm in DYNA. In Proceedings of the 12th International Symposium on Ballistics, San Antonio, Texas, 30 October–1 November, 1990, pp. 208–217 (Southwest Research Institute, San Antonio).

15.

Udaykumar

H. S.

Tran

Belk

D. M.

Vanden

K. J.

An Eulerian method for computation of multimaterial impact with ENO shock-capturing and sharp interfaces. J. Comput. Phys., 2003, 186, 136–177.