A fundamental framework for the undertaking of computational science provides clear distinctions between theory, model, and simulation. Consistent embedding provides a set of principles which when appropriately applied can create multi-scale models that capture the physical behavior of more computationally challenging methods within methods that are more easily computed. The consistent embedding methodology is illustrated within the context of brittle fracture for two serial and one concurrent multi-scale modeling examples. The examples demonstrate how predictive modeling hierarchies can be established.
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