For the case of plane
strain, where the strains in the z direction are
considered to be negligible,  , the stress-strain stiffness relationship
for an isotropic
material becomes,
The three zero'd strain entries in the strain vector indicate
that we can ignore their associated columns in the stiffness matrix
(i.e. columns 3, 4, and 5). If we also ignore the rows associated
with the stress components with z-subscripts, the stiffness matrix reduces to a simple 3x3
matrix,
The compliance matrix for plane
stress is found by inverting the plane stress stiffness matrix, and
is given by,
Note that the compliance matrix for plane stress is NOT found by removing columns and rows from the
general isotropic
compliance matrix. | 
is,
