  This study proposes a generalized coordinates based smoothed particle
hydrodynamics (GSPH) method with overset methods using a Total Lagrangian (TL)
formulation for large deformation and crack propagation problems. In the
proposed GSPH, the physical space is decomposed into multiple domains, each of
which is mapped to a local coordinate space (generalized space) to avoid
coordinate singularities as well as to flexibly change the spatial resolution.
The smoothed particle hydrodynamics (SPH) particles are then non-uniformly,
e.g., typically in the boundary-conforming way, distributed in the physical
space while they are defined uniformly in each generalized space similarly to
the normal SPH method, which are numerically related by a coordinate
transformation matrix. By solving a governing equation in each generalized
space, the shape and size of the SPH kernel can be spatially changed in the
physical space so that a spatial resolution is adaptively varied a priori
depending on the deformation characteristics, and thus, a low-cost calculation
with the less number of particles is achieved in complex shape structures.
