Smoothed particle hydrodynamics in a generalized coordinate system with a finite-deformation constitutive model

This study proposes smoothed particle hydrodynamics (SPH) in a generalized coordinate system. The present approach allocates particles inhomogeneously in the Cartesian coordinate system and arranges them via mapping in a generalized coordinate system in which the particles are aligned at a uniform spacing. This characteristic enables us to employ fine division only in the direction required, for example, in the through-thickness direction for a thin-plate problem and thus to reduce computation cost. This study provides the formulation of SPH in a generalized coordinate system with a finite-deformation constitutive model and then verifies it by analyzing quasi-static and dynamic problems of solids. High-velocity impact test was also performed with an aluminum target and a steel sphere, and the predicted crater shape agreed well with the experiment. Furthermore, the numerical study demonstrated that the present approach successfully reduced the computation cost with marginal degradation of accuracy.