It has been shown in class that the energy-release rate of a linear-elastic cracked solid is given by P² dC G 2b da where P is the applied load, b is the specimen width, a is the crack length, and C is the compliance (defined as C = u/P, where u is the displacement of the loads) Consider a double-cantilever beam shown below. This represents a commonly used geometry to measure the toughness of interfaces. The two arms have the same modulus, E. The top arm is of thickness hi, the bottom arm is of thickness h2. By assuming that you can model the two halves of the geometry as two cantilever beams of length a built into a rigid foundation at the crack tip, and using the equations you know for the displacement at the tip of a cantilever beam, show that the energy-release rate is approximately given by G- 6P2 a² 1 1 Eb² h h₂ (This result is not quite correct, because the beams are not built in at the crack tip, and there is some shear deformation of the beams so the compliance and the energy-release rate are slightly higher. However, this is a very good approximation if a > 10 h)