Significance of the Relationships:

Already we have mentioned that there are just two independent elastic constants. But this is true just in the case of isotropic solids. The term isotropy means similar property in all directions. We have described Elastic Modulus as ratio among stress & strain and implied (without stating) that the ratio holds good for all of directions, that means σ_x / ε _x = σ _y  / ε _y = σ_z/ ε _z  .

Materials for which it is true are called as isotropic materials and during this course you shall be learning only regarding isotropic solids.