Applications of SPH with the acceleration correction algorithm in structural impact computations

How to use artificial viscosity 'properly' (i.e. without excessively effecting the physics of the response) in smooth particle hydrodynamics (SPH) computations has been a long standing issue. Though SPH has great potential in problems related to dynamic structural mechanics, the loss of kinetic energy due to the 'inaccurate' choice of artificial viscosity parameters may result in physically unreal phenomena. Recently, the effect of artificial viscosity in SPH computations has been revisited and an acceleration correction algorithm to recover the majority of the 'lost' kinetic energy has been proposed by Shaw and Reid (2009). The essence of the acceleration correction algorithm is to calculate the change in the acceleration due to the artificial viscosity term and then correct the computed acceleration by subtracting a convex approximation of the 'changed' acceleration. The energy equation is accordingly modified. In the process, some of the unwanted energy dissipation is removed while retaining the basic effect of the artificial viscosity in order to have a stable computation. The approach used is relatively straightforward and, in due course, this approach will be optimized. In this article, some additional numerical aspects of the acceleration correction algorithm are discussed and the method is further explored in the context of some classical elastic-plastic impact problems. It is shown that, together with the acceleration correction algorithm, SPH can be used as a useful tool in dynamic, inelastic structural mechanics.

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