A general method for solving dynamically accelerating multiple co-linear cracks

We present a general method for analyzing dynamically accelerating multiple co-linear cracks that can be applied to the contexts of plane strain or antiplane shear in an elastic material. The difficulty in solving such problems lies in the fact that the space-time regions containing known data evolve as the crack propagates in an a priori unknown manner. Using an analog to a Dirichlet-to-Neumann map, we can find complete knowledge of the stress and displacement along the fracture plane, facilitating the application of fracture criteria that require these values away from the crack tip. The method is demonstrated for a semi-infinite or finite mode III crack as well as for a pair of cracks in elastic material, using a stress intensity factor fracture criterion for simplicity.