11:An initially square thin plate is subjected to the following motion: x=AX+kY;y=X+AY; z = Z, where A, K, A are constants. a) Determine the deformation gradient F, Green-St.Venant strain E, and linearized strain measure &, and compare the two strain measures. b) If the body is made of an isotropic compressible material with the following constitutive relation S = 2trace(E)I + E, where S is the second Piola Kirchhoff stress and , u are the material constants, determine the corresponding Cauchy stress tensor ; 1 0= - FSFT. det F