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Nonlocality and dynamic fracture: Are multiscale models the answer in dynamic fracture?

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Dynamic fracture is a complex phenomenon driven by what happens in a finite volume around the crack tip. Under sufficiently fast loading conditions a straight crack branches into two (and sometimes more) cracks that move along with speeds measured to be no more than 10% less than the speed measured just before branching. In spite of sustained efforts from the computational modeling and simulation community for the past few decades, the challenging problem of dynamic crack branching in brittle plates has not had a satisfactory solution. Existing solutions may show branching of the crack path, but the obtained crack propagation speeds are completely different from the measured values. Difficulties with mesh dependency and lack of convergence are also noticed. It has been recently argued that, in order to simulate dynamic fracture, multiscale models (coupling atomistic and continuum zones) may be needed. However, the “process zone” in dynamic crack branching, for example, may be in the order of millimeters and the time scales in the order of microseconds. These scales render a multiscale approach, even if possible, rather impractical, using the existing computational resources. Nonlocal models are better able to eliminate mesh dependency and convergence problems in problems involving damage. The new peridynamic method, a reformulation of classical continuum mechanics proposed by Silling in 2000, is used here to obtain the first correct prediction by computational simulation of the velocity profile and crack paths in dynamic crack branching of thin brittle plates. In peridynamics cracks are generated, propagate, and interact in an autonomous way. We like to say that in peridynamics cracks are not part of the problem, they are part of the solution. I will also show how adaptive refinement can be developed for this nonlocal method and give an example of mixed-mode fracture (the four-point bending problem). In the introduction, I will also give an overview of other research areas in my group: shape optimization and the shape of stegosaurus’ cooling plates, flexing granular materials and particle-size dependence, enhancing mixing and segregation in granular matter, penetration in granular materials, etc.

This talk is part of the Surfaces, Microstructure and Fracture Group series.

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