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The mathematical foundation of fracture mechanics has seen considerable advances in the last fifteen years. While this progress has been substantial, it has been largely limited to quasi-static evolutions based on global energy minimization, which is known to produce non-physical results. What is missing is a generally accepted mathematical theory of dynamic crack growth, which accounts for material inertia. Such a theory would not only be able to describe the most physically realistic setting, but it would also provide a trusted starting point to resolve pressing questions about quasistatic evolutions, e.g., a rigorous justification of the quasi-static setting as an asymptotic limit of inertial dynamics. This workshop brought together researchers in mathematical analysis, mechanics, applied mathematics, and numerical analysis and laid the groundwork for progress on these questions.
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Gianni Dal Maso, Christopher J. Larsen, Christoph Ortner, Mini-Workshop: Mathematical Models, Analysis, and Numerical Methods for Dynamic Fracture. Oberwolfach Rep. 8 (2011), no. 2, pp. 1207–1240