Self-healing pulse solution in a continuum model of fracture propagation

An analytical solution that represents a self-healing pulse of slip is presented for a dynamical model of fracture in a two-dimensional continuum medium. Even without the cohesive region, the solution does not show a singular behavior in the stress at the resticking point unlike at the breaking point, where the stress is diverging as [Formula Presented] This means that the physical condition at the resticking point should depend on the microscopic processes of resticking while the condition at the breaking point is known to be described by the phenomenological fracture energy.