THE ENERGY OF A STEADY-STATE CRACK IN A STRIP

WE CALCULATE the total energy of a semi-infinite crack moving in a two-dimensional brittle-elastic strip. First we prove a virial theorem relating kinetic and potential energy. Second, we use the Wiener-Hopf technique to find the stress fields surrounding the crack. The energy is computed exactly. Almost all of the computation can be accomplished without carrying out the Wiener-Hopf decomposition explicitly. We describe a numerical technique by which to perform the Wiener-Hopf decomposition when needed. Finally, an adiabatic argument allows one to deduce an equation of motion for the crack. We show that energy flux to the tip must depend upon acceleration in our geometry, and compute the dependence explicitly.