Application of hourglass control to Eulerian smoothed particle hydrodynamics


Being a truly meshless method, smoothed particle hydrodynamics (SPH) raises expectations to naturally handle solid mechanics problems of large deformations. However, in a simple formulation it severely suffers from two instabilities, namely tensile instability and zero-energy modes, which hinders SPH from being an popular numerical tool in that area. Although Lagrangian SPH completely removes tensile instability, it is not yet able to prevent zero-energy modes. Furthermore, kernel updates are required to properly handle very large deformations which again triggers tensile instability. Additionally, Lagrangian SPH cannot naturally deal with contact problems. Pursuing an alternative route, this paper aims at stabilizing Eulerian SPH in order to accurately deal with large deformations while preserving the fundamental properties of SPH to easily handle contact problems as well as fluid–structure interaction in a straightforward monolithic manner. For this purpose, an hourglass control scheme already employed to prevent zero-energy modes in Lagrangian SPH framework is used. The advantage of the present scheme is that the stabilization method can be easily implemented in any Eulerian SPH code by making only few changes to the code. The proposed scheme is employed to simulate several cases of elasticity, plasticity, fracture and fluid–structure interaction in order to assess its accuracy and effectiveness. The obtained results are compared with analytical solutions and finite element results where very good agreement is found.

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The authors would like to thank Lars Pastewka and Matthias Teschner for helpful discussions. The financial support by the Deutsche Forschungsgemeinschaft (DFG) under Grant No. BI 1859/1-1 within the M-ERA.NET framework is greatly acknowledged. All SPH simulations are carried out using the SimPARTIX code developed by Fraunhofer IWM.

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Correspondence to Shoya Mohseni-Mofidi.

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Mohseni-Mofidi, S., Bierwisch, C. Application of hourglass control to Eulerian smoothed particle hydrodynamics. Comp. Part. Mech. 8, 51–67 (2021).

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  • Meshless methods
  • Smoothed particle hydrodynamics
  • Stabilization
  • Hourglass control