Consider a square element under pure shear deformation as shown in the figure. The relation between deformed and undeformed coordinates becomes
x1 = X1 + kX2, x2 = kX1 + X2
(a) Calculate deformation gradient F, Lagrangian strain E, Eulerian strain e, and engineering strain ε.
(b) Calculate principal stretch tensors U and V and rotation tensor Q.
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