SMOOTHED PARTICLE HYDRODYNAMICS STABILITY ANALYSIS

SPH (smoothed particle hydrodynamics) is a gridless Lagrangian techniq ue which is appealing as a possible alternative to numerical technique s currently used to analyze large deformation events. Recent tests of the standard SPH method using the cubic B-spline kernel indicated the possibility of an instability in the tensile regime, even though no su ch difficulties were observed in compression. A von Neumann stability analysis of the SPH algorithm has been carried out which identifies th e criterion for stability or instability in terms of the stress state and the second derivative of the kernel function. The analysis explain s the observation that the method is unstable in tension while apparen tly stable in compression but shows that it is possible to construct k ernel functions which are stable in tension and unstable in compressio n. The instability is shown to result from an effective stress with a negative modulus (imaginary sound speed) being produced by the interac tion between the constitutive relation and the kernel function and is not caused by the numerical time integration algorithm. That is, chang es in the effective stress act to amplify, rather than reduce, perturb ations in the strain. The analysis and the stability criterion provide insight into possible methods for removing the instability. (C) 1995 Academic Press, Inc.