A Direct Derivation of the Griffith-Irwin Relationship using a Crack tip   Unloading Stress Wave Model
  It is the purpose of this short paper to show that the well known Griffiths theory of brittle fracture can be re-interpreted as a simple case of a modified Hamiltonian, and corresponds to a stationary action solution using the Euler-Lagrange equations. In this derivation it is still necessary to employ the equivalence with Irwins stress intensity factor approach to obtain the Griffith-Irwin equation. It is then shown that if physics of fracture is modelled using a simplified crack tip stress wave unloading model, then the Griffith-Irwin relationship can be derived in a single process, which is a major simplification of the procedure. Also the simplified crack tip stress wave unloading model employed gives a much clearer view of the basic physics of fracture.   Keywords: Fracture, Griffiths, Hamiltonians, stress waves. 
C.E. Neal-Sturgess