The propagation of star-shaped brittle cracks

The paper studies the dynamical propagation of star-shaped cracks symmetrically arranged in an elastic thin plate, subjected to the action of instantly applied, comprehensively (uniformly) stretching stresses, which implies a self-similar problem with homogeneous stresses and velocities of particles. Occurrence of such motion patterns is established through experiments. By using the Smirnov--Sobolev functional-invariant solutions method and a careful choice of mappings, the problem is reduced to some boundary value problem of the theory of complex variable functions, and exact analytic solution of the original problem, including a closed-form solution for important stress intensity coefficient near the end of the crack, is derived. We also establish a fundamental theoretical limit imposed on the number of cracks--there has to be at least three cracks. [DOI: 10.1115/1.4000900]