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I will present a general framework for the analysis of material defects embedded into a homogeneous crystalline environment.A key result in this framework is a generic regularity estimate that gives qualitatively sharp bounds on the "defect core".I will then show examples how this framework can be employed(ⅰ)in the analysis of dislocation models,(ⅱ)multi scale simulation,and(ⅲ)to construct atomistic models of material failure.