Results from the efforts in meshfree method development for fragment-impact modeling during April 2009 to March 2011 are described in this report. These efforts focused on an enhanced semi-Lagrangian reproducing kernel particle method formulation for modeling large material deformation and damage mechanisms, multiscale homogenization based on the energy bridging theory pertinent to fragment penetration modeling of concrete materials, and enhanced kernel contact algorithms to model multi-body contact applicable to penetration problems. Several benchmark problems associated with contact-impact simulations as well as multiscale modeling of material damage have been performed to examine the effectiveness of the developed computational methods. These newly developed computational formulations and the associated numerical algorithms have been implemented into the parallel Nonlinear Meshfree Analysis Program (NMAP) code. The numerical formulations and NMAP code implementation accomplished under this effort have been evaluated through 18 verification and validation (V&V) tests based on penetration experiments conducted at ERDC. The latest version of the NMAP code has been delivered to ERDC. This report, together with the 2009 technical report (Chen et al. 2009), offers the theoretical foundation of NMAP for general users.