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Generation of Material Representative Volume Elements

          Modern full-field property and performance simulations require high-quality representations of material structures. Reliability analysis and model verification and validation rely on multiple simulations with variable material input. Measuring such datasets, especially in 3D, is expensive in time, material and cost. Furthermore, many simulation techniques require periodic boundary conditions which are not present in collected micrographs or 3D volumes. In this paper, we present a technique which builds periodic surface and volume elements from a library of patches, or regions, extracted from an ensemble of characterized 3D micrographs. The regions are defined such that they are as large as possible whilst staying within a user-defined error tolerance through the administration of an overlap region between consecutive best patch selections. Resynthesis of the overlap region is achieved through the use of an overcomplete dictionary which utilizes the K-SVD technique, an iterative method that alternates between sparse coding of microstructure data based on the current dictionary and a consistent update of dictionary atoms. Comparison to other existing techniques demonstrates that our process results in efficient, statistically variable micrograph images in a considerably shorter amount of time.