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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)

##### MSC:
 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
ABAQUS/Explicit
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