Significance of the Relationships:

We have already declared that there are only two independent elastic constants. But this is true only in the case of isotropic solids. The word isotropy means similar property in all directions. We have described Elastic Modulus as ratio among stress and strain and elaborates (without stating) in which the ratio holds good for all directions, i.e. σ_x/ ε _x = σ _y/ ε _y = σ_z/ ε _z.

Materials for that this is true are known as isotropic materials and throughout this course you will be learning only about isotropic solids.