Several corrections and modifications have been proposed to increase the accuracy of SPH predictions. Since its emergence proposed by Lucy and Gingold and Monaghan to originally solve astrophysics problems in open space, smoothed particles hydrodynamics (SPH) has been developing by many researchers and employed in various fields such as fluid dynamics, solid mechanics and fluid–structure interaction. The obtained results are compared with analytical solutions and finite element results where very good agreement is found.

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 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. For this purpose, an hourglass control scheme already employed to prevent zero-energy modes in Lagrangian SPH framework is used. 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. Additionally, Lagrangian SPH cannot naturally deal with contact problems. Furthermore, kernel updates are required to properly handle very large deformations which again triggers tensile instability. Although Lagrangian SPH completely removes tensile instability, it is not yet able to prevent zero-energy modes. 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. Being a truly meshless method, smoothed particle hydrodynamics (SPH) raises expectations to naturally handle solid mechanics problems of large deformations.

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