2 mode mixity of the four point bend specimen 10 points a show that th

Question

2. Mode mixity of the four-point bend specimen (10 points)
a) Show that the energy release rate for the four-point bend specimen isA
where M is the applied moment per unit thickness, h and H are the thickness of the two
layers. Assume that both layers have the same Young's modulus E.
Hint: The following two papers developed the technique.
P.G. Charalambides, J. Lund, A.G. Evans, and R.M. McMeeking. A test specimen for
determining the fracture resistance of bimaterial interfaces. Journal of Applied Mechanics.
56, 77-82 (1989).
R.H. Dauskardt, M. Lane, Q. Ma, N. Krishna. Adhesion and debonding of multi-layer thin
film structures. Engineering Fracture mechanics 61, 141-162 (1998).
b) Charalambides et al (1989) used the finite element method to determine the mode angle.
When the two layers have identical elastic constants and identical thickness, one can
determine the mode angle analytically. Show that in this special case