Explicit Reproducing Kernel Particle Methods for large deformation problems

The explicit Reproducing Kernel Particle Method (RKPM) is presented and applied to the simulations of large deformation problems. RKPM is a meshless method which does not need a mesh structure in its formulation. Because of this mesh-free property, RKPM is able to simulate large deformation problems without remeshing which is often required for the mesh-based methods such as the Þnite element method. The RKPM shape function and its derivatives are constructed by imposing the consistency conditions. An e¦cient treatment of essential boundary conditions is also proposed for explicit time integration. The Lagrangian method based on the reference conÞguration is employed for the RKPM simulation of large deformation problems. Several examples of non-linear elastic materials are solved to demonstrate the performance of the method. The numerical experiment for the problem of underwater bubble explosion is also performed using the explicit Lagrangian RKPM formulation