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Strain: The result of applying force which slightly deform/misalign the atomic structure of a material.

Stress: It is the result of strain in any material.

Therefore, it can be said that by applying some external force, if the atomic arrangements of a material can be altered slightly, then interatomic force will change, and as a result, the material will be called stressed/strained material.

Now, let us consider a point P having radius vector r and position vector (x, y, z) under stable condition. When an external force is applied, the point P shifted slightly at P’ and the new radius vector becomes r’ and new position vector becomes (x’, y’, z’). The displacement is given by [3];

(1.1)

and this displacement gives the measure of deformation of the material under strain quantitatively. The distance between the two points can be found by using the following relation:

(1.2)

is the distance in the relaxed solid.

Using the strain tensor matrix, equation (1.2) can be further written as,

(1.3)

(1.4)

Since the strain tensor is symmetrical in nature, the strain tensor can be diagonalized by appropriate coordinate transformation. After diagonalizing the strain tensor in a system, the modified distance ΔL′ can be expressed as,

(1.5)

So, for a small displacement along an axis α = ξ, ν, ζ, the change in length (L_α) becomes,

(1.6)

The strain tensor in this case simplified to,

(1.7)

The strain tensor, in general, can be written in terms of individual strain co-efficient (ε_αβ), and is given by [4],

(1.8)

The stress components for any lattice surface can be obtained from equation (1.8).