Multiple-scale reproducing kernel particle methods for large deformation problems

Reproducing Kernel Particle Method (RKPM) with a built-in feature of multiresolution analysis is reviewed and applied to large deformation problems. Since the application of multiresolution RKPM to the large deformation problems is still in its early stage of development, we introduce, in this paper, the concept of a multiple-scale measure which is a extension of the linear formulations to nonlinear problems. We also propose an appropriate measure to properly detect the high-scale response of a largely deformed material. Via this technique of multilevel decomposition of a reproducing kernel function, the high-scale component of the measure is used in deriving an adaptive algorithm by simply inserting extra particles. Numerical experiments for non-linear elastic materials are performed to demonstrate the completeness of multiple-scale Reproducing Kernel Particle Method.