An elastic material is distorted so that the point x1 x2 x3

An elastic material is distorted so that the point (x_1, x_2, x₃) is moved to (x₁ , x₂ + 2x₁, x₃ + x₃) where is a small real number.

Find the strain tensor e_ij

Solution

Solution: given starting point is (x₁,x₂,x₃) and moves to (x₁,x₂+2ex₁,x₃+ex₃)

first we calculate change in distance between thies point =((2ex₁)²+(ex₃)²)^1/2

the initial distence origine to starting point=(x₁²+x₂²+x₃²)^1/2

the strain tensor is=(change in distance)/length

                            =((2ex₁)²+(ex₃)²)^1/2/(x₁²+x₂²+x₃²)^1/2

                          e_ij =e((2x₁)²+(x₃)²)^1/2/(x₁²+x₂²+x₃²)^1/2