Generalized coordinate smoothed particle hydrodynamics with an overset method in total Lagrangian formulation

Abstract

This study proposes a generalized coordinate smoothed particle hydrodynamics (GCSPH) method coupled with an overset method using the total Lagrangian formulation for solving large deformation and crack propagation problems. In GCSPH, the physical space is decomposed into multiple domains, each of which is mapped to a generalized space to avoid coordinate singularities as well as to flexibly change the spatial resolution. The SPH particles are then non-uniformly distributed in the physical space (e.g., typically in a boundary-conforming manner) and defined uniformly in each generalized space, similar to the standard SPH. The SPH particles in the generalized and physical spaces are numerically related by coordinate transformation matrices. The use of non-uniform particle distributions decreases the total number of particles, thus significantly reducing the simulation cost. Three numerical cases: three-dimensional brittle crack propagation, Taylor impact, and plugging failure, are presented to validate the proposed method. The numerical results are sufficiently accurate compared with the standard total Lagrangian SPH. Furthermore, these results also show the benefits of GCSPH, which not only effectively reduces the computational cost but also eliminates the effects of particle arrangement. These advantages allow GCSPH to perform high-resolution three-dimensional problems, which are otherwise costly to perform with the standard SPH.