Abstract: The present thesis focuses on applications of numerical methods to create tools for material characterization, design and selection. The tools generated in this work incorporate a variety of programming concepts, from digital image analysis, geometry, optimization, and parallel programming to data-mining, databases and web design. The first portion of the thesis focuses on methods for characterizing clustering in bimodal 5083 Aluminum alloys created by cryomilling and powder metallurgy. The bimodal samples analyzed in the present work contain a mixture of a coarse grain phase, with a grain size on the order of several microns, and an ultra-fine grain phase, with a grain size on the order of 200 nm. The mixing of the two phases is not homogeneous and clustering is observed. To investigate clustering in these bimodal materials, various microstructures were created experimentally by conventional cryomilling, Hot Isostatic Pressing (HIP), Extrusion, Dual-Mode Dynamic Forging (DMDF) and a new \'Gradient\' cryomilling process. Two techniques for quantitative clustering analysis are presented, formulated and implemented. The first technique, the Area Disorder function, provides a metric of the quality of coarse grain dispersion in an ultra-fine grain matrix and the second technique, the Two-Point Correlation function, provides a metric of long and short range spatial arrangements of the two phases, as well as an indication of the mean feature size in any direction. The two techniques are implemented on digital images created by Scanning Electron Microscopy (SEM) and Electron Backscatter Detection (EBSD) of the microstructures. To investigate structure-property relationships through modeling and simulation, strategies for generating synthetic microstructures are discussed and a computer program that generates randomized microstructures with desired configurations of clustering described by the Area Disorder Function is formulated and presented. In the computer program, two-dimensional microstructures are generated by Random Sequential Adsorption (RSA) of voxelized ellipses representing the coarse grain phase. A simulated annealing algorithm is used to geometrically optimize the placement of the ellipses in the model to achieve varying user-defined configurations of spatial arrangement of the coarse grains. During the simulated annealing process, the ellipses are allowed to overlap up to a specified threshold, allowing triple junctions to form in the model. Once the simulated annealing process is complete, the remaining space is populated by smaller ellipses representing the ultra-fine grain phase. Uniform random orientations are assigned to the grains. The program generates text files that can be imported in to Crystal Plasticity Finite Element Analysis Software for stress analysis. Finally, numerical methods and programming are applied to current issues in green engineering and hazard assessment. To understand hazards associated with materials and select safer alternatives, engineers and designers need access to up-to-date hazard information. However, hazard information comes from many disparate sources and aggregating, interpreting and taking action on the wealth of data is not trivial. In light of these challenges, a Framework for Automated Hazard Assessment based on the GreenScreen list translator is presented. The framework consists of a computer program that automatically extracts data from the GHS-Japan hazard database, loads the data into a machine-readable JSON format, transforms the JSON document in to a GreenScreen JSON document using the GreenScreen List Translator v1.2 and performs GreenScreen Benchmark scoring on the material. The GreenScreen JSON documents are then uploaded to a document storage system to allow human operators to search for, modify or add additional hazard information via a web interface.