Accurate modeling of dynamic failure in solid materials is essential for predicting the response of structures under extreme conditions. These applications often involve large strain elastic- plastic deformation, fracture, and fragmentation, and most often arise in the simulation of high strain-rate thermomechanical loading. Example applications range from laser ablation to hypervelocity impact. The development of robust computational methods for Lagrangian frame simulation of material failure is of strong interest in these applications, and mesh free methods offer substantial advantages. However, existing Lagrangian methods present considerable challenges, for example: (a) tensile instabilities and boundary condition problems in Smoothed Particle Hydrodynamics (SPH) [1], and (b) difficulties in the determination and scaling of contact-impact model parameters in the Discrete Element Method (DEM) [2]. Recognizing these challenges, there exists a need for new mesh free particle methods that improve upon the stability and accuracy properties of current methods, and offer computational simplicity. In recent research [3] the authors have developed a new particle method employing a nonholonomic Hamiltonian modeling methodology. The new method offers advantages over existing Lagrangian numerical techniques: accurate strength modeling, completely general contact-impact modeling, and efficient fragment transport simulation are provided, while mass and energy discard, tensile instabilities, and numerical fracture are avoided. Application of the method shows good agreement with exact solutions in one dimensional test problems and good agreement with experimental results in three-dimensional shock physics simulations incorporating fracture, fragmentation, and large strain elastic–plastic deformation. The method offers opportunities to significantly improve simulation capabilities for a number of extreme conditions problems, including simulations of high velocity impact, thermal ablation, and laser-matter interaction.