Mathematical Sciences: Transient Studies of Dislocation-based Micromechanical Effects in Fracture

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The work proposed considers the fracture of linearly elastic materials under dynamic loading in the presence of limited plastic effects. A micromechanical view is adopted, and the effects represented by arrays of crystals defects, or dislocations. These are studied in a series of idealized, transient problems. This transient nature itself distinguishes the work from many existing crack-dislocation studies. Such analyses must confront mathematical difficulties which do not arise in quasi-static studies. Nevertheless, length scale and wave propagation considerations place a premium on exact, preferably analytic, solutions. A major task of the proposed work is in boundary/initial value problem solution development.