Fragmentation is a fundamental material process that naturally spans spatial scales from microscopic to macroscopic. We developed a mathematical framework using an innovative combination of hierarchical material modeling (HMM) and adaptive mesh refinement (AMR) to connect the continuum to microstructural regimes. This framework has been implemented in a new multi-physics, multi-scale, 3D simulation code, NIF ALE-AMR. New multi-material volume fraction and interface reconstruction algorithms were developed for this new code, which is leading the world effort in hydrodynamic simulations that combine AMR with ALE (Arbitrary Lagrangian-Eulerian) techniques. The interface reconstruction algorithm is also used to produce fragments following material failure. In general, the material strength and failure models have history vector components that must be advected along with other properties of the mesh during remap stage of the ALE hydrodynamics. The fragmentation models are validated against an electromagnetically driven expanding ring experiment and dedicated laser-based fragmentation experiments conducted at the Jupiter Laser Facility. As part of the exit plan, the NIF ALE-AMR code was applied to a number of fragmentation problems of interest to the National Ignition Facility (NIF). One example shows the added benefit of multi-material ALE-AMR that relaxes the requirement that material boundaries must be along mesh boundaries. I. Introduction/Background Great strides have been made in numerical modeling of problems in solid mechanics in the last 20 years. For example, Lagrangian simulations of automobile crashes with millions of zones on modest computer clusters are routinely used by industry to design safer automobiles. Despite these advances, computational solid mechanics (CSM) lags in comparison to computational fluid dynamics (CFD) in many areas. While CFD simulations that are uniformly second-order accurate in both time and space are routine, and the development of higher-order-accurate algorithms is an area of intense research, multi-material Eulerian CSM simulations are still only first-order accurate at material interfaces. In addition, there are entire areas of physical phenomena in solid mechanics that are poorly understood theoretically, and reliable simulation technology is virtually nonexistent. Fragmentation, for example, occurs at a wide range of temporal and spatial scales, from atomistic to cosmological, but the underlying phenomenology is poorly understood, and the simulation technology is primitive. Fragmentation is a phenomenon that is intrinsically multi-scale; small variations in the microstructure lead to a distribution of