For the fourth-order isotropic tensor given in Exercise 1.9, show that if = , then the tensor will have the following symmetry

For the fourth-order isotropic tensor given in Exercise 1.9, show that if β = γ  , then the tensor will have the following symmetry C_ijkl = C_klij.

Data from exercise 1.9

The most general form of a fourth-order isotropic tensor can be expressed by:

where α, β, and γ   are arbitrary constants. Verify that this form remains the same under the
general transformation given by (1.5.1)5.

Equation 1.5.1

+ ; +