11:An initially square thin plate is subjected to the following motion: x=AX+kY;y=X+AY; z = Z, where...

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11:An initially square thin plate is subjected to the following motion: x=A₁X+k₁Y;y=X+A₂Y; z = Z, where A₁, K₁, A₂ 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 λ, u are the material constants, determine the corresponding Cauchy stress tensor σ; 1 0= - FSFT. det F 11:An initially square thin plate is subjected to the following motion: x=A₁X+k₁Y;y=X+A₂Y; z = Z, where A₁, K₁, A₂ 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 λ, u are the material constants, determine the corresponding Cauchy stress tensor σ; 1 0= - FSFT. det F