Problem 3 Spinel (MgAl2O4) "optical ceramic" is a transparent polycrystalline ceramic with a combination of high hardness, low density, and optical properties that make it very attractive for fracture resistant windows. It has the mechanical properties listed below. A rectangular plate with dimensions 1mm10mm100mm is mounted for use as a protective window over a sensor. During the process, a compressive load of 2.5kN is exerted along the long (100mm) axis. Assume this to be the x direction. The other two axes are not constrained initially. (a) Calculate the stress and strain along the x axis, (b) Calculate the strain along the width and thickness of the plate (y and z directions) (c) Assume that the plate is now rigidly constrained along its width (the 10mm or y direction). As a result, the plate cannot change length along that axis. Calculate the stress induced in the y direction due to the above constraint, if the same compressive 2.5kN load is applied in the x direction and the strain in the x direction. Explain why the strain in the x direction is different from the result in part (a)