Combining peridynamics and generalized interpolation material point method via volume modification for simulating transient responses

By using nonlocal discrete force functions, peridynamics (PD) can effectively deal with the problems involving discontinuities and singularities. As a continuum-based particle method, the material point method (MPM) and its advanced version, generalized interpolation material point method (GIMP), use local and nonlocal spatial discretization, respectively, to effectively simulate large deformations and multi-phase (solid-fluid-gas) interactions via mapping and remapping between material points and associated background nodes. However, nonlocal constitutive modeling has rarely been employed in the MPM or GIMP for simulating failure evolution. To combine the strengths of both PD and MPM/GIMP for better simulating the failure evolution under transient loading, an attempt is made to eliminate the limitation in the original PD due to the volume integration so that both MPM/GIMP and PD could be smoothly combined via volume modification. One-dimensional examples are employed to demonstrate and verify the proposed volume modification peridynamics and its combination with MPM/GIMP.