Help for explaining a strange problem related with beam shear stiffness

There is a very strange problem puzzled quite a few in the rotor blades (including helicopter blades and wind turbine blades) community. We hope some mechanician on this board can help us explain the situation.

A beam with a square section is made of two layers with different isotropic material of equal thickness (z along the beam axis and x, y are in the cross-sectional plane). Suppose the layer interface is along y direction. One layer has material 1 (say E1=100, nu=0.2) while the other has material 2. Make it so that E2=E1/alpha (the same for nu). Evaluate the bending stiffness of the beam for bending around x direction in a rigorous fashion (such as the commercial code VABS). Plot the stiffness against alpha, one will expect the bending stiffness monotonically to decrease with increasing \alpha. However,  one can observe that the stiffness will reach a minimum for \alpha at the finite value. See attached pdf for a detailed description of the problem.

Thanks a lot for any insight you can shed for us!