An Immersed Reproducing Kernel Particle Method for Modeling Inhomogeneous Media

Structures involving multiple materials are difficult for meshfree methods to model accurately due to the strain discontinuity introduced at the material interface. An immersed Reproducing Kernel Particle Method (RKPM) approach is proposed to model inhomogeneous materials using an immersed domain approach to allow independent approximations and discretizations for the background matrix and the foreground inclusion. In this approach, Nitsche’s method is introduced to enforce the interface compatibility conditions in a variationally consistent manner. The proposed method simplifies the spatial discretization procedures for multi-material problems involving complex geometries because the conforming requirements in discretization at the interface are avoided. Efficient and stable domain integration methods for the immersed RKPM discretization are investigated, and the performance of several approaches are compared. Specifically, conforming and non-conforming domain integration between the foreground and background domains are discussed. Optimal convergence is achieved without tedious procedures such as enrichment functions or boundary singular kernels commonly employed in other meshfree methods for solving multi-material problems. Several numerical examples are presented to examine the effectiveness of the proposed method. A non-linear formulation of the immersed RKPM method is also presented and its effectiveness in modeling brittle materials using an elastic-damage model is investigated