3.7 [SECTION 3.4] Consider the deformation defined by x1 = X3 - X1 - 2X1, x1 = V2(X1 -2X2), x; = X3 + X1 +2X). 1. Calculate the deformation gradient, F 2. Determine the polar decomposition of F = RU 3. Consider a line element dX lying along the X , axis with length dS . Under this deformation the lime element is stretched and rotated into the line element dx . a. Calculate the length, ds = dx . b. Calculate the vector, dy = UdX, and show dy = ds. This shows that all the stretching is represented by U . c. Explain why dy is parallel to dX . Is this true in general? d. Calculate the vector dz = R dX and show that dz = dS, i.e. R is a pure rotation with no change in length