Dynamic Fracture of an Idealized Fiber-Reinforced Cantilever

The dynamic fracture of a double cantilever beam of fiber-reinforced material is discussed. The material is modeled by assuming that the fibers are inextensible and continuously distributed. The examples considered reduce to the solution of the wave equation on a time-dependent interval; the method of characteristics is used. Two fracture criteria are used to calculate the crack speed. One of these criteria is the energy release rate commonly used in elastic fracture mechanics. In the present model some fibers can carry a finite force; the second criterion is based on the force in the fiber through the crack tip. Three simple examples are given to illustrate the model.