Example 2
A sample of material subjected to a compressive stress ?z is confined so that it cannot deform in the y-dir., but deformation is permitted in the x-dir. Assume that the material is isotropic and exhibits linear-elastic behavior. Determine the following in terms of ?z and the elastic constant of the material:
(a) The stress that develops in the y-dir.
(b) The strain in the z-dir.
(c) The strain in the x-dir.
(d) The stiffness E’ = ?z /? z in the z-dir. Is this apparent modulus equal to the elastic modulus E from the uniaxial test on the material? Why or why not?