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Stress points for tension instability in SPH. (English) Zbl 0890.73077
The stress-point approach, which was developed to address tension instability and improve accuracy of smoothed particle hydrodynamics (SPH) methods, is further extended and applied to one-dimensional problems. A stability analysis reveals a reduction in the critical time step by a factor of \(1/ \sqrt 2\) when the stress points are located at the extremes of the SPH particle. An elementary damage law is also introduced into the one-dimensional formulation. Application to a one-dimensional impact problem indicates far less oscillation in the pressure at the interface for coarse meshes than with the standard SPH formulation. Damage predictions and backface velocity histories for a bar appear to be quite reasonable.
Reviewer: Reviewer (Berlin)

74S30 Other numerical methods in solid mechanics (MSC2010)
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs
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